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+# UNEVEN: UNIVERSAL VALUE EXPLORATION FOR MULTI-AGENT REINFORCEMENT LEARNING
+
+Anonymous authors Paper under double-blind review
+
+# ABSTRACT
+
+This paper focuses on cooperative value-based multi-agent reinforcement learning (MARL) in the paradigm of centralized training with decentralized execution (CTDE). Current state-of-the-art value-based MARL methods leverage CTDE to learn a centralized joint-action value function as a monotonic mixing of each agent’s utility function, which enables easy decentralization. However, this monotonic restriction leads to inefficient exploration in tasks with nonmonotonic returns due to suboptimal approximations of the values of joint actions. To address this, we present a novel MARL approach called Universal Value Exploration (UneVEn), which uses universal successor features (USFs) to learn policies of tasks related to the target task, but with simpler reward functions in a sample efficient manner. UneVEn uses novel action-selection schemes between randomly sampled related tasks during exploration, which enables the monotonic joint-action value function of the target task to place more importance on useful joint actions. Empirical results on a challenging cooperative predator-prey task requiring significant coordination amongst agents show that UneVEn significantly outperforms stateof-the-art baselines.
+
+# 1 INTRODUCTION
+
+Learning control policies for cooperative multi-agent reinforcement learning (MARL) remains challenging as agents must search the joint-action space, which grows exponentially with the number of agents. Current state-of-the-art value-based methods such as VDN (Sunehag et al., 2017) and QMIX (Rashid et al., 2020b) learn a centralized joint-action value function as a monotonic factorization of decentralized agent utility functions and can therefore cope with large joint action spaces. Due to this monotonic factorization, the joint-action value function can be decentrally maximized as each agent can simply select the action that maximizes its corresponding utility function.
+
+This monotonic restriction, however, prevents VDN and QMIX from representing nonmonotonic joint-action value functions (Mahajan et al., 2019) where an agent’s best action depends on what actions the other agents choose. For example, consider a predator-prey task where at least three agents need to coordinate to capture a prey and any capture attempts by fewer agents are penalized with a penalty of magnitude $p$ . As a result, both VDN and QMIX tend to get stuck in a suboptimal equilibrium (also called the relative overgeneralization pathology, Panait et al., 2006; Wei et al., 2018) in which agents simply avoid the prey (Mahajan et al., 2019; Bohmer et al., 2020). This happens ¨ for two reasons. First, depending on $p$ , successful coordination by at least three agents is a needle in the haystack and any step towards it is penalized. Second, the monotonically factorized jointaction value function lacks the representational capacity to distinguish the values of coordinated and uncoordinated joint actions during exploration.
+
+Recent work addresses the problem of inefficient exploration by VDN and QMIX due to monotonic factorization. QTRAN (Son et al., 2019) and WQMIX (Rashid et al., 2020a) address this problem by weighing important joint actions differently, which can be found by simultaneously learning a centralized value function, but these approaches still rely on inefficient $\epsilon$ -greedy exploration which may fail on harder tasks (e.g., the predator-prey task above with higher value of $p$ ). MAVEN (Mahajan et al., 2019) learns an ensemble of monotonic joint-action value functions through committed exploration by maximizing the entropy of the trajectories conditioned on a latent variable. Their exploration focuses on diversity in the joint team behaviour using mutual information. By contrast, this paper proposes Universal Value Exploration (UneVEn), which follows the intuitive premise that tasks with a simpler reward function than the target task (e.g., a smaller miscoordination penalty in predator-prey) can be efficiently solved using a monotonic factorization of the joint-action value function. Therefore, UneVEn samples tasks related to the target task, that are often easier to solve, but often have similar important joint actions. Selecting actions based on these related tasks during exploration can bias the monotonic approximation of the value function towards important joint actions of the target task (Son et al., 2019; Rashid et al., 2020a), which can overcome relative overgeneralization. To leverage the policies of the sampled related tasks, which only differ in their reward functions, UneVEn uses Universal Successor Features (USFs, Borsa et al., 2018) which have demonstrated excellent zero-shot generalization in single-agent tasks with different reward functions (Barreto et al., 2017; 2020). USFs generalize policy dynamics over tasks using Universal Value Functions (UVFs, Schaul et al., 2015), along with Generalized Policy Improvement (GPI, Barreto et al., 2017), which combines solutions of previous tasks into new policies for unseen tasks.
+
+Our contributions are as follows. First, we propose Multi-Agent Universal Successor Features (MAUSFs) factorized into novel decentralized agent-specific SFs with value decomposition networks (Sunehag et al., 2017) from MARL. This factorization enables agents to compute decentralized greedy policies and to perform decentralized local GPI, which is particularly well suited for MARL, as it allows to maximize over a combinatorial set of agent policies. Second, we propose Universal Value Exploration (UneVEn), which uses novel action-selection schemes based on related tasks to solve tasks with nonmonotonic values with monotonic approximations thereof. We evaluate our novel approach in predator-prey tasks that require significant coordination amongst agents and highlight the relative overgeneralization pathology. We empirically show that UneVEn with MAUSFs significantly outperforms current state-of-the-art value-based methods on the target tasks and in zero-shot generalization (Borsa et al., 2018) across MARL tasks with different reward functions, which enables us to leverage UneVEn effectively.
+
+# 2 BACKGROUND
+
+Dec-POMDP: A fully cooperative decentralized multi-agent task can be formalized as a decentralized partially observable Markov decision process (Dec-POMDP, Oliehoek et al., 2016) consisting of a tuple $\dot { G } = \langle S , \mathcal { U } , P , R , \Omega , O , n , \gamma \rangle$ . $s \in \mathcal { S }$ describes the true state of the environment. At each time step, each agent $a \in \mathcal { A } \equiv \{ 1 , . . . , n \}$ chooses an action $u ^ { a } \in \mathcal { U }$ , forming a joint action $\pmb { u } \in \mathcal { U } \equiv \mathcal { U } ^ { n }$ . This causes a transition in the environment according to the state transition kernel $P ( s ^ { \prime } | s , \pmb { u } ) : S \times \pmb { \mathcal { U } } \times S  [ 0 , 1 ]$ . All agents are collaborative and share therefore the same reward function $R ( s , { \pmb u } ) : \mathcal { S } \times \mathcal { U }  \mathbb { R }$ and $\gamma \in [ 0 , 1 )$ is a discount factor.
+
+Due to partial observability, each agent $a$ cannot observe the true state $s$ , but receives an observation $o ^ { a } \in \Omega$ drawn from observation kernel $o ^ { a } \sim O ( s , a )$ . At time $t$ , each agent $a$ has access to its action-observation history $\tau _ { t } ^ { a } \in \mathcal { T } _ { t } \equiv ( \Omega \times \mathcal { U } ) ^ { t } \times \Omega$ , on which it conditions a stochastic policy $\pi ^ { a } ( u _ { t } ^ { a } | \tau _ { t } ^ { a } )$ . $\tau _ { t } \in \mathcal { T } _ { t } ^ { n }$ denotes the histories of all agents. The joint stochastic policy $\pi ( \boldsymbol { u } _ { t } | \boldsymbol { s } _ { t } , \mathbf { \bar { \tau } } _ { t } ) \equiv$ $\begin{array} { r } { \prod _ { a = 1 } ^ { n } \pi ^ { a } ( u _ { t } ^ { a } | \tau _ { t } ^ { a } ) } \end{array}$ induces a joint-action value function : $Q ^ { \pi } ( s _ { t } , \pmb { \tau } _ { t } , \pmb { u } _ { t } ) = \mathbb { E } \left[ G _ { t } | s _ { t } , \pmb { \tau } _ { t } , \pmb { u } _ { t } \right]$ , where $\begin{array} { r } { G _ { t } = \sum _ { i = 0 } ^ { \infty } \gamma ^ { i } r _ { t + i } } \end{array}$ is the discounted return.
+
+CTDE: We adopt the framework of centralized training and decentralized execution (CTDE Kraemer & Banerjee, 2016), which assumes access to all action-observation histories $\tau _ { t }$ and global state $s _ { t }$ during training, but each agent’s decentralized policy $\pi ^ { a }$ can only condition on its own actionobservation history $\tau ^ { a }$ . This approach can exploit information that is not available during execution and also freely share parameters and gradients, which improves the sample efficiency considerably (see e.g., Foerster et al., 2018; Rashid et al., 2020b; Bohmer et al., 2020). ¨
+
+Value Decomposition Networks: A naive way to learn in MARL is independent $Q$ -learning (IQL, Tan, 1993), which learns an independent action value function $Q ^ { a } \left( \tau _ { t } ^ { a } , u _ { t } ^ { a } ; \theta ^ { a } \right)$ for each agent $a$ that conditions only on its local action-observation history $\tau _ { t } ^ { a }$ . To make better use of other agents’ information in CTDE, value decomposition networks (VDN, Sunehag et al., 2017) represent the joint-action value function $Q _ { t o t }$ as a sum of per-agent utility functions $Q ^ { a } \colon Q _ { t o t } ( \tau , \boldsymbol { u } ; \theta ) \equiv$ $\textstyle \sum _ { a = 1 } ^ { n } { \dot { Q ^ { a } } } ( \tau ^ { a } , u ^ { a } ; \theta )$ . Each $Q ^ { a }$ still conditions only on individual action-observation histories and can be represented by an agent network that shares parameters across all agents. The joint-action value function $Q _ { t o t }$ can be trained using Deep Q-Networks (DQN, Mnih et al., 2015). Compared to VDN, QMIX (Rashid et al., 2020b) allows joint-action value function $Q _ { t o t }$ to be represented as a nonlinear monotonic combination of individual utility functions. The greedy joint action in both VDN and QMIX can be computed decentrally by individually maximizing each agent’s utility. See OroojlooyJadid & Hajinezhad (2019) for a more in-depth overview of cooperative deep MARL.
+
+Task based Universal Value Functions: In this paper, we consider tasks that differ only in their reward functions $R _ { \pmb { w } } ( s , \pmb { u } ) \equiv \pmb { w } ^ { \top } \phi ( s , \pmb { u } )$ , which are linear combinations of a set of basis functions $\phi : \mathcal { S } \times \mathcal { U } \to \mathbb { R } ^ { d }$ . Intuitively, the basis functions $\phi$ encode potentially rewarded events, such as opening a door or picking up an object. We use the weight vector $\textbf { \em w }$ to denote the task with reward function $R _ { w }$ . Universal Value Functions (UVFs, Schaul et al., 2015) is an extension of DQN that learns a generalizable value function conditioned on tasks. UVFs are typically of the form $Q ^ { \pi } ( s _ { t } , \pmb { u } _ { t } , \pmb { w } )$ to indicate the action-value function of task $\textbf { \em w }$ under policy $\pi$ at time $t$ as:
+
+$$
+Q ^ { \pi } ( s _ { t } , u _ { t } , w ) = \mathbb { E } ^ { \pi } \big [ \sum _ { i = 0 } ^ { \infty } \gamma ^ { i } R _ { w } ( s _ { t + i } , u _ { t + i } ) \big | s _ { t } , u _ { t } \big ] = \mathbb { E } ^ { \pi } \big [ \sum _ { i = 0 } ^ { \infty } \gamma ^ { i } \phi ( s _ { t + i } , u _ { t + i } ) ^ { \top } w \big | s _ { t } , u _ { t } \big ] .
+$$
+
+Successor Features: The Successor Representation (Dayan, 1993) has been widely used in singleagent settings (Barreto et al., 2017; 2018; Borsa et al., 2018) to generalize across tasks with given reward specifications. By simply rewriting the definition of the action value function $Q ^ { \pi } ( s _ { t } , \pmb { u } _ { t } , \pmb { w } )$ of task $\textbf { \em w }$ from Equation 1 we have:
+
+$$
+Q ^ { \pi } ( s _ { t } , u _ { t } , w ) ~ = ~ \mathbb { E } ^ { \pi } \big [ \sum _ { i = 0 } ^ { \infty } \gamma ^ { i } \phi ( s _ { t + i } , u _ { t + i } ) \big | s _ { t } , u _ { t } \big ] ^ { \top } w ~ \equiv ~ \psi ^ { \pi } ( s _ { t } , u _ { t } ) ^ { \top } w ,
+$$
+
+where $\psi ^ { \pi } ( s , \pmb u )$ are the Successor Features (SFs) under policy $\pi$ . For the optimal policy $\pi _ { z } ^ { \star }$ of task $_ z$ , the SFs $\psi ^ { \pi _ { z } ^ { \star } }$ summarize the dynamics under this policy, which can then be weighted with any reward vector $\pmb { w } \in \mathbb { R } ^ { d }$ to instantly evaluate policy $\pi _ { z } ^ { \star }$ on it: $Q ^ { \pi _ { z } ^ { \star } } ( s , \pmb { u } , \pmb { w } ) = \psi ^ { \pi _ { z } ^ { \star } } ( s , \mathbf { \bar { u } } ) ^ { \top } \pmb { w }$ .
+
+Universal Successor Features and Generalized Policy Improvement: Borsa et al. (2018) introduce universal successor features (USFs) which learns SFs conditioned on tasks using the generalization power of UVFs. Specifically, they define UVFs of the form $Q ( s , \pmb { u } , z , \pmb { w } )$ which represents the value function of policy $\pi _ { z }$ evaluated on task $\pmb { w } \in \mathbb { R } ^ { d }$ . These UVFs can be factored using the SFs property (Equation 2) as: $Q ( s , \pmb { u } , z , \pmb { w } ) = \pmb { \psi } ( s , \pmb { u } , z ) ^ { \top } \pmb { w }$ , where $\psi ( s , u , z )$ are the USFs that generate the SFs induced by task-specific policy $\pi _ { z }$ . One major advantage of using SFs is the ability to efficiently do generalized policy improvement (GPI, Barreto et al., 2017), which allows a new policy to be computed for any unseen task based on instant policy evaluation of a set of policies on that unseen task with a simple dot-product. Formally, given a set $\mathcal { C } \subseteq \mathbb { R } ^ { d }$ of tasks and their corresponding SFs $\{ \psi ( s , \pmb { u } , z ) \} _ { z \in \mathcal { C } }$ induced by corresponding policies $\{ \pi _ { z } \} _ { z \in { \mathcal C } }$ , a new policy $\pi _ { w } ^ { \prime }$ for any unseen task $\pmb { w } \in \mathbb { R } ^ { d }$ can be derived using:
+
+$$
+\begin{array} { r l r } { \pi _ { \pmb { w } } ^ { \prime } ( s ) } & { \in } & { \underset { \ b { u } \in \mathcal { U } } { \operatorname { a r g m a x } } \underset { \ b { z } \in \mathcal { C } } { \operatorname* { m a x } } Q ( s , \pmb { u } , z , \pmb { w } ) = \underset { \ b { u } \in \mathcal { U } } { \operatorname { a r g m a x } } \underset { \pmb { z } \in \mathcal { C } } { \operatorname* { m a x } } \psi ( s , \pmb { u } , z ) ^ { \top } \pmb { w } . } \end{array}
+$$
+
+Setting ${ \mathcal C } = \{ { w } \}$ allows us to revert back to UVFs, as we evaluate SFs induced by policy $\pi _ { w }$ on task $\textbf { \em w }$ itself. However, we can use any set of tasks that are similar to $\pmb { w }$ based on some similarity distribution $\mathcal { D } ( \cdot | \boldsymbol { w } )$ . The computed policy $\pi _ { w } ^ { \prime }$ is guaranteed to perform no worse on task $\pmb { w }$ than each of the policies $\{ \pi _ { z } \} _ { z \in { \mathcal C } }$ (Barreto et al., 2017), but often performs much better. SFs thus enable efficient use of GPI, which allows reuse of learned knowledge for zero-shot generalization.
+
+# 3 MULTI-AGENT UNIVERSAL SUCCESSOR FEATURES
+
+In this section, we introduce Multi-Agent Universal Successor Features (MAUSFs), extending single-agent USFs (Borsa et al., 2018) to multi-agent settings and show how we can learn generalized decentralized greedy policies for agents. The USFs based centralized joint-action value function $Q _ { t o t } ( \tau , u , z , w )$ allows evaluation of joint policy $\pi _ { z } = \left. \pi _ { z } ^ { 1 } , \ldots , \pi _ { z } ^ { n } \right.$ comprised of local agent policies $\boldsymbol { \pi } _ { z } ^ { a }$ of same task $_ z$ on task $\pmb { w }$ . However, each agent $a$ may execute a different policy $\pi _ { z ^ { a } } ^ { a }$ of different task $z ^ { a } \in \mathcal { C }$ , resulting in a combinatorial set of joint-policies. Maximizing over all combinations $\bar { z } \equiv \langle z ^ { 1 } , \dots , z ^ { n } \rangle \in \bar { \mathcal { C } } ^ { n }$ should therefore enormously improve GPI. To enable this flexibility, we define joint-action value function $( Q _ { t o t } )$ of joint policy $\pi _ { \bar { z } } = \{ \pi _ { z ^ { a } } ^ { a } \} _ { z ^ { a } \in \mathcal { C } }$ evaluated on any task ${ \mathbf { \boldsymbol { w } } \in \mathbb { R } ^ { d } }$ as: $Q _ { t o t } ( \tau , u , \bar { z } , w ) = \psi _ { t o t } ( \bar { \tau } , u , \bar { z } ) ^ { \dag } w$ , where $\psi _ { t o t } ( \tau , { \pmb u } , \bar { z } )$ are the MAUSFs of $( \pmb { \tau } , \pmb { u } )$ summarizing the joint dynamics of the environment under joint policy $\pi _ { \bar { z } }$ . However, training centralized MAUSFs and using centralized GPI to achieve maximization over a combinatorial space of $\bar { z }$ becomes impractical when there are more than a handful of agents, since the joint action space $( u )$ and joint task space $( \mathcal { C } ^ { n } )$ of the agents grows exponentially with the number of agents. To leverage CTDE and enable decentralized execution by agents, we therefore propose novel agentspecific $S F s$ for each agent $a$ following local policy $\pi _ { z ^ { a } } ^ { a }$ , which condition only on its own local action-observation history and task $z ^ { a }$ .
+
+![](images/2af4766bb77e273d65f636fb1ea78aa96e8e6e6af2c47e108166e12dcb67c333.jpg)  
+Figure 1: Schematic illustration of the MAUSFs training and UneVEn exploration with GPI policy.
+
+Decentralized Execution: We define local utility functions for each agent $a$ as $Q ^ { a } ( \tau ^ { a } , u ^ { a } , z ^ { a } , \pmb { w } ) =$ $\psi ^ { a } ( \tau ^ { a } , u ^ { a } , z ^ { a } ; \theta ) ^ { \top } \pmb { w }$ , where $\psi ^ { a } ( \tau ^ { a } , u ^ { a } , z ^ { a } ; \theta )$ are the local agent-specific SFs induced by local policy $\pi _ { z ^ { a } } ^ { a } ( u ^ { a } | \tau ^ { a } )$ of agent $a$ sharing parameters $\theta$ . Intuitively, $Q ^ { \bar { a } } ( \tau ^ { a } , u ^ { a } , z ^ { a } , w )$ is the utility function for agent $a$ when local policy $\pi _ { z ^ { a } } ^ { a } ( u ^ { a } | \tau ^ { a } )$ of task $z ^ { a }$ is executed on task $\textbf { \em w }$ . We use VDN decomposition to represent MAUSFs $\psi _ { t o t }$ as a sum of local agent-specific SFs for each agent $a$ :
+
+$$
+{ \cal Q } _ { t o t } ( \tau , u , \bar { z } , w ) = \sum _ { a = 1 } ^ { n } { \cal Q } ^ { a } ( \tau ^ { a } , u ^ { a } , z ^ { a } , w ) = \sum _ { a = 1 } ^ { n } \psi ^ { a } ( \tau ^ { a } , u ^ { a } , z ^ { a } ; \theta ) ^ { \top } w = \psi _ { t o t } ( \tau , u , \bar { z } ; \theta ) ^ { \top } w .
+$$
+
+We can now learn local agent-specific SFs $\psi ^ { a }$ for each agent $a$ that can be instantly weighted with any task vector $\pmb { w } \in \mathbb { R } ^ { d }$ to generate local utility functions $Q ^ { a }$ , thereby allowing agents to use the GPI policy in a decentralized manner.
+
+Decentralized Local GPI: Our novel agent-specific SFs allows each agent $a$ to locally perform decentralized GPI by instant policy evaluation of a set $\mathcal { C }$ of local task policies $\{ \pi _ { z ^ { a } } ^ { a } \} _ { z ^ { a } \in \mathcal { C } }$ on any unseen task $\pmb { w }$ to compute a local GPI policy. Due to linearity of the VDN decomposition, this is equivalent to maximization over all combinations of $\bar { z } \equiv \langle z ^ { 1 } , \ldots , z ^ { n } \rangle \in \mathcal { C } \times \ldots \times \bar { \mathcal { C } } \equiv \mathcal { C } ^ { n }$ as:
+
+$$
+\begin{array} { r c l l } { \pi _ { w } ^ { \prime } ( \tau ) } & { \in } & { \displaystyle \operatorname * { a r g m a x } _ { u \in \mathcal { U } } \operatorname* { m a x } _ { \bar { z } \in \mathcal { C } ^ { n } } Q _ { t o t } ( \tau , u , \bar { z } , w ) } & { = } & { \displaystyle \left\{ \underset { u ^ { a } \in \mathcal { U } } { \operatorname * { a r g m a x } } \operatorname* { m a x } _ { z ^ { a } \in \mathcal { C } } \psi ^ { a } ( \tau ^ { a } , u ^ { a } , z ^ { a } ; \theta ) ^ { \top } w \right\} _ { a = 1 } ^ { n } . } \end{array}
+$$
+
+As all of the above relies on the linearity of the VDN decomposition, it cannot be directly applied to nonlinear mixing techniques like QMIX (Rashid et al., 2020b).
+
+Training: MAUSFs for task combination $\bar { z }$ are trained end-to-end by gradient descent on the loss:
+
+$$
+\begin{array} { r l r } { \mathcal { L } ( \boldsymbol { \theta } , \boldsymbol { \bar { z } } ) } & { = } & { \mathbb { E } _ { \sim \mathcal { B } } \left[ \left| \left| \phi ( s _ { t } , u _ { t } ) + \gamma \psi _ { t o t } ( \tau _ { t + 1 } , u _ { \bar { z } } ^ { \prime } , \bar { z } ; \boldsymbol { \theta } ^ { - } ) - \psi _ { t o t } ( \tau _ { t } , u _ { t } , \bar { z } ; \boldsymbol { \theta } ) \right| \right| _ { 2 } ^ { 2 } \right] , } \end{array}
+$$
+
+where the expectation is over a minibatch of samples $\{ ( s _ { t } , \pmb { u } _ { t } , \pmb { \tau } _ { t } ) \}$ from the replay buffer $\boldsymbol { B }$ (Lin, 1992), $\theta ^ { - }$ denotes the parameters of a target network (Mnih et al., 2015) and joint actions ${ \pmb u } _ { \bar { z } } ^ { \prime } = $ $\{ u _ { z ^ { a } } ^ { \prime a } \} _ { a = 1 } ^ { n }$ are selected individually by each agent network using the current parameters $\theta$ (called Double $Q$ -learning, van Hasselt et al., 2016): $\begin{array} { r } { u _ { z ^ { a } } ^ { \prime a } = \arg \operatorname* { m a x } _ { u \in \mathcal { U } } \psi ^ { a } ( \tau _ { t + 1 } ^ { a } , \stackrel { } { u } , z ^ { a } ; \theta ) ^ { \top } z ^ { a } } \end{array}$ . Each agent learns therefore local agent-specific SFs $\psi ^ { a } ( \tau ^ { a } , u ^ { a } , z ; \theta )$ by gradient descent on $\mathcal { L } ( \boldsymbol { \theta } , \bar { \boldsymbol { z } } )$ for all $z \in \mathcal { C } \equiv \nu \cup \{ w \}$ , where $\dot { \nu } \sim \mathcal { \bar { D } } ( \cdot | \pmb { w } )$ is drawn from a distance measure around target task $\pmb { w }$ . The green region of Figure 1 shows a CTDE based architecture to train MAUSFs for a given target task $\textbf { \em w }$ . A detailed algorithm is present in Appendix A.
+
+# 4 UNEVEN
+
+In this section, we present UneVEn (red region of Figure 1), which leverages MAUSFs and decentralized GPI to enable efficient exploration on the target task $\pmb { w }$ . The joint-action value function of the target task $\pmb { w }$ suffers from suboptimal approximations due to monotonic factorization. At the beginning of every exploration episode, we sample a set of related tasks $\nu = \{ z \sim \mathcal { D } ( \cdot | \pmb { w } ) \}$ , containing potentially simpler reward functions, from a distribution $\mathcal { D }$ around the target task. The basic idea is that some of these related tasks can be efficiently learned using a monotonic joint-action value function. These tasks will therefore be solved early and exploration will concentrate on stateactions that are useful to them. As the sampled tasks are similar to $\pmb { w }$ , this has the potential to put more weight on the important joint actions of the target task (Rashid et al., 2020a). This implicit weighting allows the learning of the joint-action value function of the target task to focus on accurately representing the value of the more important joint actions, and thereby overcome the relative overgeneralization pathology.
+
+Many choices for $\mathcal { D }$ are possible, but in the following we sample related tasks using a normal distribution centered around the target task $\pmb { w } \in \mathbb { R } ^ { d }$ with a fixed variance $\sigma$ as $\mathcal { D } = \bar { \mathcal { N } } ( \boldsymbol { w } , \sigma \mathbf { I } _ { d } )$ . The resulting task vectors weight the basis functions $\phi$ differently and represent different reward functions. In particular the varied reward functions can make these tasks much easier, but also harder, to solve with monotonic value functions. However, the approach has the advantage of not requiring any domain knowledge. The consequences of sampling harder tasks on learning are discussed with the corresponding action-selection schemes below.
+
+Action-Selection Schemes: UneVEn uses two novel schemes to enable action selection based on related tasks. To emphasize the importance of the target task, we define a probability $\alpha$ of selecting actions based on the target task. Therefore, with probability $1 - \alpha$ , the action is selected based on the related task. Similar to other exploration schemes, $\alpha$ is annealed from 0.3 to 1.0 in our experiments over a fixed number of steps at the beginning of training. Once this exploration stage is finished (i.e., $\alpha = 1$ ), actions are always taken based on the target task’s joint-action value function. Each actionselection scheme employs a local decentralized GPI policy, that maximizes over a set of policies $\pi _ { z }$ based on $z \in { \mathcal { C } } _ { 1 }$ (also referred to as the evaluation set) to estimate the $Q$ -values of another set of tasks k ∈ C2 (also referred to as the target set) using: Qa(τat ,u,z,k)
+
+$$
+\begin{array} { r l } & { \mathrm { \mathrm { \mathrm { \mathrm { \mathrm { \mathrm { \arctan ~ } } a s ~ t h e \mathrm { \Lambda } t a r g e t \ s e t } ) \ u s i n g } : } } \qquad Q ^ { a } ( \tau _ { t } ^ { a } , u , z , k ) } \\ & { u _ { t } = \Bigl \{ u _ { t } ^ { a } = \underset { u \in \mathcal { U } } { \mathrm { \operatorname* { \arg m a x } } } \underset { k \in \mathcal { C } _ { 2 } } { \operatorname* { m a x } } \underset { z \in \mathcal { C } _ { 1 } } { \operatorname* { m a x } } \widehat { \psi ^ { a } \big ( \tau _ { t } ^ { a } , u , z ; \theta \big ) ^ { \top } k } \Bigr \} _ { a \in \mathcal { A } } . } \end{array}
+$$
+
+Here $\mathcal { C } _ { 1 } = \nu \cup \{ w \}$ is the set of target and related tasks which induce the policies that are evaluated (dot-product) on the set of tasks $\mathcal { C } _ { 2 }$ , which varies with different action-selection schemes. The red box in Figure 1 illustrates UneVEn exploration. For example, $Q$ -learning always picks actions based on the target task, i.e., the target set $\mathcal { C } _ { 2 } = \{ w \}$ . However, this scheme does not favour important joint actions. We call this default action-selection scheme target GPI and execute it with probability $\alpha$ . We now propose two novel action-selection schemes based on related tasks with probability $1 - \alpha$ , and thereby implicitly weighting joint actions during learning.
+
+Uniform GPI: At the beginning of each episode, this action-selection scheme uniformly picks one related task, i.e., the target set $\mathcal { C } _ { 2 } = \{ k \sim \mathrm { U n i f o r m } ( \nu ) \}$ , and selects actions based on that task using the GPI policy throughout the episode. This uniform task selection explores the learned policies of all related tasks in $\mathcal { D }$ . This works well in practice as there are often enough simpler tasks to induce the required bias over important joint actions. However, if the sampled related task is harder than the target task, the action-selection based on these harder tasks might hurt learning on the target task and lead to higher variance during training.
+
+Greedy GPI: At every time-step $t$ , this action-selection scheme picks the task $\pmb { k } \in \nu \cup \{ \pmb { w } \}$ that gives the highest $Q$ -value amongst the related and target tasks, i.e., the target set becomes $\mathcal { \bar { C } } _ { 2 } \overset { \cdot } { = } \nu \cup \{ w \}$ . Due to the greedy nature of this action-selection scheme, exploration is biased towards solved tasks, as those have larger values. We are thus exploring the solutions of tasks that are both solvable and similar to the target task $\pmb { w }$ , which makes them great candidates for important joint actions of $\textbf { \em w }$ .
+
+NO-GPI: To demonstrate the influence of GPI on the above schemes, we also investigate ablations, where we define the evaluation set ${ \mathcal C } _ { 1 } = \{ k \}$ to only contain the currently estimated task $\boldsymbol { k }$ , i.e., using $\begin{array} { r } { \boldsymbol { \mathsf { \Pi } } \boldsymbol { u } _ { t } = \{ u _ { t } ^ { a } = \arg \operatorname* { m a x } _ { \boldsymbol { u } \in \mathcal { U } } \operatorname* { m a x } _ { \boldsymbol { k } \in \mathcal { C } _ { 2 } } \psi ^ { a } ( \tau _ { t } ^ { a } , \boldsymbol { u } , \boldsymbol { k } ; \theta ) ^ { \top } \boldsymbol { k } \} _ { a \in \mathcal { A } } } \end{array}$ for action selection.
+
+# 5 EXPERIMENTS
+
+In this section, we evaluate UneVEn on a variety of complex domains. For evaluation, all experiments are carried out with five random seeds and results are shown with $\pm$ standard error across
+
+seeds. We compare our method against a number of SOTA value-based MARL approaches: IQL (Tan, 1993), VDN (Sunehag et al., 2017), QMIX (Rashid et al., 2020b), MAVEN (Mahajan et al., 2019), WQMIX (Rashid et al., 2020a), QTRAN (Son et al., 2019), and QPLEX (Wang et al., 2020a).
+
+# Domain 1 : $m$ -step matrix game
+
+We first evaluate UneVEn on $m$ -step matrix game proposed by Mahajan et al. (2019). This task is difficult to solve using simple $\epsilon$ -greedy exploration policies as committed exploration is required to achieve the optimal return. Appendix E shows the $m$ -step matrix game from Mahajan et al. (2019), in which the first joint decision of two agents determines the maximal outcome after another $m { - } 1$ decisions. One initial joint action can reach a return of up to $m + 3$ , whereas another only allows for $m$ . This challenges monotonic value functions, as the optimal joint reward function of the first decision is nonmonotonic. Figure 2 shows results of all methods on this task for $m = 1 0$ after training for $3 5 k$ steps. UneVEn with greedy (UneVEn-Greedy-GPI) action selection scheme converges to an optimal return and both greedy and uniform (UneVEn-Uniform-GPI) schemes outperforms all other methods, which suffer from poor $\epsilon$ -greedy exploration and often learn to take the suboptimal action in the beginning. Due to the nonmonotonicity of the initial state, it becomes difficult to switch the policy later, leading to suboptimal returns and only rarely converging to optimal solutions.
+
+![](images/d14f0c0218ca6b0de6d0665be8e512aec4d46c2675ea9fe7ae1e6c8ab2ffe9a0.jpg)  
+Figure 2: Baseline results for $m = 1 0$ .
+
+# Domain 2 : Cooperative Predator-Prey
+
+We next evaluate UneVEn on challenging cooperative predator-prey tasks similar to one proposed by Son et al. (2019), but significantly more complex in terms of the coordination required amongst agents. We use a complex partially observable predator-prey (PP) task involving eight agents (predators) and three prey that is designed to test coordination between agents, as each prey needs to be captured by at least three surrounding agents with a simultaneous capture action. If only one or two surrounding agents attempt to capture the prey, a negative reward of magnitude $p$ is given. Successful capture yields a positive reward of $+ 1$ . This task is challenging for two reasons. First, depending on the magnitude of penalty $p$ , exploration is difficult as even if a single agent miscoordinates, the penalty is given, and therefore, any steps toward successful coordination are penalized. Second, the agents must be able to differentiate between the values of successful and unsuccessful collaborative actions, which monotonic value functions can only do if all agents already act optimally. More details about the task are available in Appendix B.
+
+Proposition 1. For the predator-prey game defined above, the optimal joint action reward function for any group of $2 \leq k \leq n$ predator agents surrounding a prey is nonmonotonic (as defined by Mahajan et al., 2019) iff $p > 0$ . (Proof is provided in Appendix B).
+
+Simpler PP Tasks: We first demonstrate that both VDN and QMIX with monotonic joint-action value functions can learn on target tasks with simpler reward functions. To generate a simpler task, we remove the penalty associated with miscoordination, i.e., $p = 0$ , thereby making the returns monotonic. Figure 3 shows that both QMIX and VDN can solve this task as there is no miscoordination penalty and the monotonic joint-action value function can learn to efficiently represent the optimal joint-action values. Other SOTA value-based approaches (MAVEN, WQMIX and QPLEX) and UneVEn with both uniform (UneVEn-Uniform-GPI) and greedy (UneVEn-Greedy-GPI) action-selection schemes can also solve this monotonic target task.
+
+![](images/6ffe61f3b66bfb419a79e53800afd6e8beb65fa72e3f545ed6c3194d82e823a9.jpg)  
+Figure 3: Baseline results for $p = 0$ .
+
+Harder PP Tasks: We now make the target task nonmonotonic by increasing the magnitude of the penalty associated with each miscoordination, i.e., $p \in \{ 0 . 0 0 4 , 0 . \dot { 0 } 0 8 , 0 . 0 1 2 , 0 . 0 1 6 \}$ . For a smaller penalty of $p = 0 . 0 0 4$ , Figure 4 (top left) shows that VDN is still able to solve the task, further suggesting that simpler reward related tasks (with lower penalties) can be solved with monotonic approximations. However, both QMIX and VDN fail to learn on three other higher penalty target tasks due to their monotonic constraints, which hinder the accurate learning of the joint-action value functions. Intuitively, when uncoordinated joint actions are much more likely than coordinated ones, the penalty term can dominate the average value estimated by each agent’s utility. This makes it difficult to learn an accurate monotonic approximation that will select the optimal joint actions.
+
+![](images/8441944d933d45b5da981c6694668cd8b868581094eeb8f4954eaaf731b92bfb.jpg)  
+Figure 4: Comparison between UneVEn and SOTA MARL baselines with $p \in \{ 0 . 0 0 4 , 0 . 0 0 8 , 0 . 0 1 2 , 0 . 0 1 6 \}$
+
+![](images/d78c1d09d81679154fb17f10d003566b49307b534cbf06fcb7efd0389bd57ed0.jpg)  
+Figure 5: Ablation results: Comparison between different action selection of UneVEn for $p \in \{ 0 . 0 1 2 , 0 . 0 1 6 \}$
+
+Interestingly, other SOTA value-based approaches that aim to address the monotonicity restriction of QMIX and VDN such as MAVEN, QTRAN, WQMIX and QPLEX also fail to learn on higher penalty tasks. WQMIX solves the task when $p = 0 . 0 0 4$ , but fails on other three higher penalty target tasks. Although WQMIX uses an explicit weighting mechanism to bias learning towards important joint actions, it must identify these actions by learning a nonmonotonic value function first. An $\epsilon$ -greedy exploration based on the target task will take a long time to learn such a value function, which is visible in the large standard error for $p \in \{ 0 . 0 0 8 , 0 . 0 1 2 , 0 . 0 1 6 \}$ in Figure 4. By contrast, both UneVEn-Uniform-GPI and UneVEn-Greedy-GPI can approximate nonmonotonic value functions more accurately and solve the task for all values of $p$ . As expected, the variance of UneVEn-Uniform-GPI is high on higher penalty target tasks (for e.g., $p = 0 . 0 1 6 $ ) as exploration suffers from action selection based on harder related tasks. UneVEn-Greedy-GPI does not suffer from this problem. Videos of learnt policies are available at $\mathtt { \tau \mathtt { l t t p s : / / r b . 9 Y / r d w p o 5 } }$ .
+
+Ablations: Figure 5 shows ablation results for higher penalty tasks, i.e., $p = \{ 0 . 0 1 2 , 0 . 0 1 6 \}$ . To contrast the effect of UneVEn on exploration, we compare our two novel action-selection schemes to UneVEn-Target-GPI, which only selects the greedy actions of the target task. The results clearly show that UneVEn-Target-GPI fails to solve the higher penalty nonmonotonic tasks as the employed monotonic joint value function of the target task fails to accurately represent the values of different joint actions. This demonstrates the critical role of UneVEn and its action-selection schemes.
+
+Next we evaluate the effect of GPI by comparing against UneVEn with MAUSFs without using the GPI policy, i.e., setting the evaluation set ${ \mathcal C } _ { 1 } = \{ k \}$ in Equation 7. First, UneVEn using a NOGPI policy with both uniform (Uniform-NOGPI) and greedy (Greedy-NOGPI) action selection outperform Target-NOGPI, further strengthening the claim that UneVEn with its novel action-selection scheme enables efficient exploration and bias towards optimal joint actions. Next, Figure 5 clearly shows that for each corresponding action-selection scheme (uniform, greedy, and target), using a GPI policy $( * \mathrm { - } \mathrm { { G P I } ) }$ is always favourable as it performs either similarly to the NOGPI policy (∗- NOGPI) or much better. GPI appears to improve zero-shot generalization of MAUSFs across tasks, which in turn enables good action selection for related tasks during UneVEn exploration.
+
+Zero-Shot Generalization: Lastly, we evaluate this zero-shot generalization for all methods to check if the learnt policies are useful for unseen high penalty test tasks. We train all methods for 8 million environmental steps on a task with $p ~ = ~ 0 . 0 0 4$ , and test 60 rollouts of the resulting policies of all methods that are able to solve the training task, i.e., UneVEn-Greedy-GPI, UneVEn-Uniform-GPI, VDN, MAVEN, and WQMIX, on tasks with $p \in \{ 0 . 2 , 0 . 5 \}$ . For policies trained with UneVEn-Greedy-GPI and UneVEn-Uniform-GPI, we use the NOGPI policy for the zero-shot testing, i.e., $\mathcal { C } _ { 1 } = \mathcal { C } _ { 2 } = \{ \pmb { w } \}$ . Figure 6 shows that UneVEn with both uniform and greedy schemes exhibits great zero-shot generalization and solves both test tasks even with very high penalties. As MAUSFs learn the reward’s basis functions, rather than the reward itself, zero-shot generalization to larger penalties follow naturally. Furthermore, using UneVEn exploration allows the agents to collect enough diverse behaviour to come up with a near optimal policy for the test tasks. On the other hand, the learnt policies for all other methods that solve the target task with $p = 0 . 0 0 4$ are ineffective in these higher penalty nonmonotonic tasks, as they do not learn to avoid unsuccessful capture attempts. More details about the implementations are included in Appendix C. Additional ablation experiments are discussed in Appendix D.
+
+![](images/e4904bdafc87b842b96bdbbc873f6d05489d25bb373504b7f233003b59ad1b75.jpg)  
+Figure 6: Zero-shot generalization comparison; training on $p = 0 . 0 0 4$ , testing on $p \in \{ 0 . { \overset { - } { 2 } } , 0 . 5 \}$ .
+
+# Domain 3 : Starcraft Multi-Agent Challenge (SMAC)
+
+We now evaluate UneVEn on challenging cooperative StarCraft II maps from the SMAC benchmark (Samvelyan et al., 2019). We consider SMAC maps where each ally agent unit is additionally penalized for being killed or suffering damage from the enemy, in addition to receiving positive reward for killing/inflicting damage on enemy units, which has recently shown to improve performance (Son et al., 2020). We present the results for one super hard map (MMM2, involving 10 units of 3 types), two hard asymmetric maps (5m vs 6m and 10m vs 11m) and three easy maps (2s3z, 1c3s5z and $8 \mathrm { m }$ ).
+
+Figure 7 presents the mean test win rate for all maps. Both VDN and QMIX achieve almost $100 \%$ win rate on these maps, which leads us to conclude that they do not suffer from relative overgeneralization and that simple $\epsilon$ -greedy policies suffices for these maps. Thus, the additional complexity of learning MAUSFs in our approach results in slightly slower convergence. However, UneVEn with both GPI schemes matches the performance as VDN and QMIX in most maps, with only small deviations in $5 \mathrm { m } _ { - } \mathrm { v } s _ { - } 6 \mathrm { m }$ , demonstrating that our method can scale well to large complex tasks.
+
+![](images/854b4ab7a8aabf41f7b95285fcea6cc0f2d08281bceef2f3e33a082565abf136.jpg)  
+Figure 7: Comparison between UneVEn, VDN and QMIX on SMAC maps.
+
+# 6 RELATED WORK
+
+Improving monotonic value function factorization in CTDE MAVEN (Mahajan et al., 2019) shows that the monotonic joint-action value function of QMIX and VDN suffers from suboptimal approximations on nonmonotonic tasks. It addresses this problem by learning a diverse ensemble of monotonic joint-action value functions conditioned on a latent variable by optimizing the mutual information between the joint trajectory and the latent variable. Deep Coordination Graphs (DCG) (Bohmer et al., 2020) uses a predefined coordination graph (Guestrin et al., 2002) to represent the ¨ joint-action value function. However, DCG is not a fully decentralized approach and specifying the coordination graph can require significant domain knowledge. Son et al. (2019) propose QTRAN that addresses the monotonic restriction of QMIX by learning a (decentralizable) VDN-factored joint-action value function along with an unrestricted centralized critic. The corresponding utility functions are distilled from the critic by solving a linear optimization problem involving all joint actions, but its exact implementation is computationally intractable and the corresponding approximate versions have instable performance. QPLEX (Wang et al., 2020a) uses a duplex dueling (Wang et al., 2016) network architecture to factorize the joint-action value function with linear decomposition structure. WQMIX (Rashid et al., 2020a) learns a QMIX-factored joint-action value function along with an unrestricted centralized critic and proposes explicit weighting mechanisms to bias the monotonic approximation of the optimal joint-action value function towards important joint actions, which is similar to our work. However, in our work, the weightings are implicitly done through action-selection based on simpler reward related tasks, which are easier to solve.
+
+Exploration There exists a plethora of techniques for exploration in model-free single-agent RL, based on intrinsic novelty reward (Bellemare et al., 2016; Tang et al., 2017), predictability (Pathak et al., 2017), pure curiosity (Burda et al., 2019) or Bayesian posteriors (Osband et al., 2016; Gal et al., 2017; Fortunato et al., 2018; O’Donoghue et al., 2018). In the context of multi-agent RL, Bohmer ¨ et al. (2019) discuss the influence of unreliable intrinsic reward and Wang et al. (2020b) quantify the influence that agents have on each other’s return. Zheng & Yue (2018) propose to coordinate exploration between agents by shared latent variables, whereas Jaques et al. (2018) investigate social motivations of competitive agents. However, these techniques aim to visit as much of the state-action space as possible, which exacerbates the relative overgeneralization pathology. Approaches that use state abstraction (e.g., Roderick et al., 2018) can speed up exploration, but only by restricting the considered space with prior knowledge. In contrast, UneVEn explores similar tasks. This guides exploration to states and actions that prove useful, which restricts the explored space and overcomes relative overgeneralization. To the best of our knowledge, the only other work that explores the task space is Leibo et al. (2019): they use the evolution of competing agents as an auto-curriculum of harder and harder tasks. Collaborative agents cannot compete against each other, though, and their approach does therefore not affect relative overgeneralization.
+
+Successor Features Most of the work on SFs have been focused on single-agent settings (Dayan, 1993; Kulkarni et al., 2016; Lehnert et al., 2017; Zhu et al., 2017; Barreto et al., 2017; 2018; Borsa et al., 2018; Lehnert & Littman, 2019; Lee et al., 2019; Hansen et al., 2019) for transfer learning and zero-shot generalization across tasks with different reward functions. Gupta et al. (2019) uses single-agent SFs in a transition-independent multi-agent setting to estimate the probability of events.
+
+# 7 CONCLUSION
+
+This paper presents novel multi-agent universal successor features (MAUSFs) decomposed as local agent-specific SFs, which enables decentralized version of the GPI to maximize over a combinatorial space of agent policies, making MAUSFs a perfect fit for MARL. We then propose UneVEn, which leverages the generalization power of MAUSFs to perform action-selection based on simpler related tasks to address the issue of sub-optimality of target task’s monotonic joint-action value function in current SOTA methods. Our experiments show that UneVEn significantly outperforms VDN, QMIX and other state-of-the-art value-based MARL methods on nonmonotonic tasks by a substantial margin.
+
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+
+# A TRAINING ALGORITHM
+
+Algorithm 1 presents the training of MAUSFs with UneVEn. Our method is able to learn on all tasks (target $\pmb { w }$ and sampled $_ z$ ) simultaneously in a sample efficient manner using the same feature $\phi _ { t } \equiv \phi ( s _ { t } , { \boldsymbol { u } } _ { t } )$ due to the linearly decomposed reward function (Equation 1).
+
+# Algorithm 1 Training MAUSFs with UneVEn
+
+Require: , $\alpha$ , $\beta$ target task $\textbf { \em w }$ , set of agents $\mathcal { A }$ , standard deviation $\sigma$
+
+1: procedure TRAIN:   
+2: Initialize the local-agent SF network $\psi ^ { a } ( \tau ^ { a } , u ^ { a } , z ; \theta )$ and replay buffer $\mathcal { M }$   
+3: for fixed number of epochs do   
+4: $\boldsymbol \nu \sim \mathcal { N } ( \boldsymbol { \boldsymbol w } , \sigma \mathbf { I } _ { d } )$ ; ${ \pmb { o } } _ { 0 } \gets \mathrm { R E S E T E N V } ( )$ $\ u \ u \ash \pmb \sigma _ { t } \equiv \{ o _ { t } ^ { a } \} _ { a \in \mathcal { A } }$   
+5: $t = 0 \mathrm { ; } \quad \mathcal { M } \gets \mathrm { N E W E P I S O D E } ( \mathcal { M } , \nu , \pmb { \sigma } _ { 0 } )$   
+6: while not terminated do   
+7: if Bernoull $( \epsilon ) { = } 1$ then $\mathbf { \delta } u _ { t } \gets \mathrm { U n i f o r m } ( \mathcal { U } )$   
+8: else ${ \mathbf { \delta u } } _ { t } \gets \mathrm { U N E V E N } ( \tau _ { t } , \nu )$   
+9: $\langle o _ { t + 1 } , \phi _ { t } \rangle \gets \mathrm { E N V S T E P } ( u _ { t } )$   
+10: $\begin{array} { r l } & { \mathcal { M }  \mathrm { A D D T R A N S I T I O N } ( \mathcal { M } , \boldsymbol { u } _ { t } , o _ { t + 1 } , \phi _ { t } ) } \\ & { t  t + 1 } \end{array}$   
+11:   
+12: $\begin{array} { r } { \begin{array} { r l } { \mathcal { L } \gets 0 ; } & { { } \mathcal { B } \gets \mathrm { S A M P L E M I N I B A T C H } ( \mathcal { M } ) } \end{array} } \end{array}$   
+13: foreach $\left\{ \tau _ { t } , \boldsymbol { u } _ { t } , \phi _ { t } , \tau _ { t + 1 } , \nu \right\} \in \mathcal { B }$ do   
+14: foreach $z \in \nu \cup \{ w \}$ do   
+15: $\begin{array} { r l } & { u _ { z } ^ { \prime } \gets \{ \underset { u \in \mathcal { U } } { \mathrm { a r g } \operatorname* { m a x } } \psi ^ { a } ( \tau _ { t + 1 } ^ { a } , u , z ; \theta ) ^ { \top } z \} _ { a \in A } } \\ & { \mathcal { L } \gets \mathcal { L } + \left\| \phi _ { t } + \gamma \psi _ { t o t } ( \tau _ { t + 1 } , u _ { z } ^ { \prime } , z ; \theta ^ { - } ) - \psi _ { t o t } ( \tau _ { t } , u _ { t } , z ; \theta ) \right\| _ { 2 } ^ { 2 } } \\ & { \theta \gets \mathrm { O P T I M I Z E } ( \theta , \nabla _ { \theta } \mathcal { L } ) } \\ & { \theta ^ { - } \gets ( 1 - \beta ) \theta ^ { - } + \beta \theta } \end{array}$   
+16:   
+17:   
+18:   
+19: procedure $\operatorname { U N E V E N } ( \tau _ { t } , \nu )$ :   
+20: if Bernoulli $( \alpha ) = 1$ or Scheme is Target then   
+21: $\mathcal { C } _ { 2 } \gets \{ w \}$   
+22: else   
+23: if Scheme is Uniform then   
+24: $\mathcal { C } _ { 2 }  \nu \sim \mathrm { U n i f o r m } ( \nu )$   
+25: else if Scheme is Greedy then   
+26: $\mathcal { C } _ { 2 }  \nu \cup \{ w \}$   
+27: if Use GPI Policy is True then   
+28: $\begin{array} { r l } & { \mathcal { C } _ { 1 } \gets \nu \cup \{ \pmb { w } \} } \\ & { \mathbf { \ } u _ { t } \gets \{ u _ { t } ^ { a } = \arg \operatorname* { m a x } \underset { \mathbf { \substack { u \in \mathcal { U } } } } { \operatorname* { m a x } } \underset { \mathbf { \substack { k \in \mathcal { C } _ { 2 } \ : z \in \mathcal { C } _ { 1 } } } } { \operatorname* { m a x } } \psi ^ { a } ( \tau _ { t } ^ { a } , u , z ; \theta ) ^ { \top } \mathbf { k } \} _ { a \in \mathcal { A } } } \end{array}$   
+29:   
+30: else   
+31: $\begin{array} { r l } & { \mathbf { \delta } \mathbf { \psi } _ { \mathbf { { u } } _ { t } } \gets \{ u _ { t } ^ { a } = \arg \operatorname* { m a x } _ { \mathbf { \theta } _ { u \in \mathcal { U } } } \operatorname* { m a x } _ { \mathbf { \theta } _ { k \in \mathcal { C } _ { 2 } } } \psi ^ { a } ( \tau _ { t } ^ { a } , u , k ; \theta ) ^ { \top } k \} _ { a \in \mathcal { A } } } \\ & { \mathbf { u r n } \ : u _ { t } } \end{array}$   
+ret
+
+# B EXPERIMENTAL DOMAIN DETAILS AND ANALYSIS
+
+We consider a complicated partially observable predator-prey (PP) task in an $1 0 \times 1 0$ grid involving eight agents (predators) and three preys that is designed to test coordination between agents, as each prey needs a simultaneous capture action by at least three surrounding agents to be captured. Each agent can take 6 actions i.e. move in one of the 4 directions (Up, Left, Down, Right), remain still (no-op), or try to catch (capture) any adjacent prey. The prey moves around in the grid with a probability of 0.7 and remains still at its position with probability 0.3. Impossible actions for both agents and prey are marked unavailable, for eg. moving into an occupied cell or trying to take a capture action with no adjacent prey.
+
+A1-Capture   
+
+<table><tr><td></td><td>A2-Capture</td><td>A2-Other</td></tr><tr><td>A3-Capture</td><td>+1</td><td>-p</td></tr><tr><td>A3-Other</td><td>-p</td><td>-p</td></tr></table>
+
+A1-Other   
+Table 1: Joint-Reward function of three agents surrounding a prey. The first table indicates jointrewards when Agent 1 takes capture action and second table indicates joint-rewards when Agent 1 takes any other action. Notice that there are numerous joint actions leading to penalty $p$ .   
+
+<table><tr><td></td><td>A2-Capture</td><td>A2-Other</td></tr><tr><td>A3-Capture</td><td>-p</td><td>-p</td></tr><tr><td>A3-Other</td><td>-p</td><td>0</td></tr></table>
+
+If either a single or a pair of agents take a capture action on an adjacent prey, a negative reward of magnitude $p$ is given. If three or more agents take the capture action on an adjacent prey, it leads to a successful capture of that prey and yield a positive reward of $+ 1$ . The maximum possible reward for capturing all preys is therefore $+ 3$ . Each agent observes a $5 \times 5$ grid centered around its position which contains information showing other agents and preys relative to its position. An episode ends if all preys have been captured or after 800 time steps. This task is similar to one proposed by Bohmer et al. (2020); Son et al. (2019), but significantly more complex in terms of the coordination ¨ required amongst agents as more agents need to coordinate simultaneously to capture the preys. We now prove Proposition 1 which states that:
+
+Proposition. For, the predator-prey game defined above, the optimal joint action reward function for any group of $2 \leq k \leq n$ predator agents surrounding a prey is nonmonotonic (as defined by Mahajan et al., 2019) iff $p > 0$ .
+
+Proof. Without loss of generality, we assume a single prey surrounded by three agents $( A _ { 1 } , A _ { 2 } , A _ { 3 } )$ in the environment. The joint reward function for this group of three agents is defined in Table 1.
+
+For the case $ { p } \mathrm { ~  ~ { ~ > ~ } ~ } 0$ the proposition can be easily verified using the definition of nonmonotonicity (Mahajan et al., 2019). For any $3 \leq k \leq n$ agents attempting to catch a prey in state $s$ , we fix the actions of any $k - 3$ agents to be “other” indicating either of up, down, left, right, and noop actions and represent it with $\mathbf { \Delta } u ^ { k - 3 }$ . Next we consider the rewards $r$ for two cases:
+
+• If we fix the action of any two of the remaining three agents as “other” represented as $\mathbf { \Delta } _ { \mathbf { \ b { u } } ^ { 2 } }$ , the action of the remaining agent becomes $\begin{array} { r } { \bar { u ^ { 1 } } = \mathrm { a r g } \operatorname* { m a x } _ { u \in \mathcal { U } } r ( s , \langle u , u ^ { \hat { 2 } } , u ^ { k - 3 } \rangle ) = } \end{array}$ “other”.   
+• If we fix the $\mathbf { \Delta } \mathbf { u } ^ { 2 }$ to be “capture”, we have : $u _ { 1 } \ = \ \arg \operatorname* { m a x } _ { u \in \mathcal { U } } r ( s , \langle u , u ^ { 2 } , u ^ { k - 3 } \rangle ) \ =$ “capture”.
+
+Thus the best action for agent $A _ { 1 }$ in state $s$ depends on the actions taken by the other agents and the rewards $R ( s )$ are non-monotonic. Finally for the equivalence, we note that for the case $p = 0$ we have that a default action of “capture” is always optimal for any group of $k$ predators surrounding the prey. Thus the rewards are monotonic as the best action for any agent is independent of the rest. □
+
+# C IMPLEMENTATION DETAILS
+
+# C.1 HYPER PARAMETERS
+
+All algorithms are implemented in the PyMARL framework (Samvelyan et al., 2019). All our experiments use $\epsilon$ -greedy scheme where $\epsilon$ is decayed from $\epsilon = 1$ to $\epsilon = 0 . 0 5$ over $2 5 0 k$ time steps. All our tasks use a discount factor of $\gamma = 0 . 9 9$ . We freeze the trained policy every $3 0 k$ timesteps and run 20 evaluation episodes with $\epsilon = 0$ . We use learning rate of 0.0005 with soft target updates for all experiments. We use a target network similar to Mnih et al. (2015) with “soft” target updates, rather than directly copying the weights: $\theta ^ { - }  \beta * \theta + ( 1 - \beta ) * \theta ^ { - }$ , where $\theta$ are the current network parameters. We use $\beta = 0 . 0 0 5$ for all experiments. This means that the target values are constrained to change slowly, greatly improving the stability of learning. All algorithms were trained with RMSprop optimizer by one gradient step on loss computed on a batch of 32 episodes sampled from a replay buffer containing last 1000 episodes. We also used gradient clipping to restrict the norm of the gradient to be $\leq 1 0$ .
+
+![](images/79642bac64219bbb6fed98da8aa95a7a5f68b6dd5c0b8960e4e7685a6f829964.jpg)  
+Figure 8: Additional Ablation results: Comparison between different action selection of UneVEn for $p \in$ $\{ 0 . 0 0 4 , 0 . 0 0 8 \}$ .
+
+![](images/bbf9866daac2c6c456085f82d1c54459008ffe15dcac638416cb83039f5987d8.jpg)  
+Figure 9: Additional Zero-shot generalization results for $p \in \{ 0 . 2 , 0 . 3 , 0 . 5 , 1 . 0 \}$ .
+
+The probability $\alpha$ of action selection based on target task in UneVEn with uniform and greedy action selection schemes increases from $\alpha = 0 . 3$ to $\alpha = 1 . 0$ over $2 5 0 k$ time steps. For sampling related tasks using normal distribution, we use $\mathcal { N } ( \pmb { w } , \sigma \mathbf { I } _ { d } )$ centered around target task $\pmb { w }$ with $\sigma \in$ $\{ 0 . 1 , 0 . 2 \}$ . At the beginning of each episode, we sample six related tasks, therefore $| \nu | = 6$ .
+
+# C.2 NN ARCHITECTURE
+
+Each agent’s local observation $o _ { t } ^ { a }$ are concatenated with agent’s last action $u _ { t - 1 } ^ { a }$ , and then passed through a fully-connected (FC) layers of 128 neurons, followed by ReLU activation, a GRU (Chung et al., 2014), and another FC of the same dimensionality to generate a action-observation history summary for the agent. Each agent’s task vector $z \in \mathcal { \dot { \nu } } \cup \{ w \}$ is passed through a FC layer of 128 neurons followed by ReLU activation to generate an internal task embedding. The history and task embedding are concatenated together and passed through two hidden FC-256 layers and ReLU activations to generate the outputs for each action. For methods with non-linear mixing such as QMIX (Rashid et al., 2020b), WQMIX (Rashid et al., 2020a), and MAVEN (Mahajan et al., 2019), we adopt the same hypernetworks from the original paper and test with either a single or double hypernet layers of $\mathrm { d i m 6 4 }$ utilizing an ELU non-linearity. For all baseline methods, we use the code shared publicly by the corresponding authors on Github.
+
+# D ADDITIONAL RESULTS
+
+Figure 8 presents additional ablation results for comparison between UneVEn with different action selection schemes for $p \in \{ 0 . 0 0 4 , 0 . 0 0 8 \}$ . Figure 9 presents additional zero-shot generalization results for policies trained on target task with penalty $p = 0 . 0 0 4$ tested on tasks with penalty $p \in \{ 0 . 2 , 0 . 3 , 0 . 5 , 1 . 0 \}$ . For UneVEn-Greedy-GPI, we can observe that the average number of miscoordinated capture attempts per episode actually drops with $p$ and converges around 1.5, i.e., for return $R _ { p }$ , average mistakes per episode is $\begin{array} { r } { \frac { 3 - R _ { p } } { p } = \{ 2 . 3 , 2 . 1 , 1 . 5 , 1 . 6 \} } \end{array}$ for $p \in \{ 0 . 2 , 0 . 3 , 0 . 5 , 1 . 0 \}$ .
+
+![](images/874ce5f79130bea695f3dcbefd5935eee7367d39fbe837514cf3cafbe639d8bd.jpg)  
+Figure 10: $m$ -step matrix game from Mahajan et al. (2019) for $m = 1 0$ . The red cross means that selecting that joint action will lead to termination of the episode.
+
+# E $m$ -STEP MATRIX GAMES
+
+Figure 10 shows the $m$ -step matrix game for $m = 1 0$ from Mahajan et al. (2019), where there are $m - 2$ intermediate steps, and selecting a joint-action with zero reward leads to termination of the episode.

parse/train/BJlzm64tDH/BJlzm64tDH.md

@@ -0,0 +1,258 @@
+# PRETRAINED ENCYCLOPEDIA: WEAKLY SUPERVISED KNOWLEDGE-PRETRAINED LANGUAGE MODEL
+
+Wenhan Xiong†, Jingfei $\mathbf { D } \mathbf { u } ^ { \mathrm { S } }$ , William Yang Wang†, Veselin Stoyanov§,
+
+† University of California, Santa Barbara § Facebook AI {xwhan, william}@cs.ucsb.edu, {jingfeidu, ves}@fb.com
+
+# ABSTRACT
+
+Recent breakthroughs of pretrained language models have shown the effectiveness of self-supervised learning for a wide range of natural language processing (NLP) tasks. In addition to standard syntactic and semantic NLP tasks, pretrained models achieve strong improvements on tasks that involve real-world knowledge, suggesting that large-scale language modeling could be an implicit method to capture knowledge. In this work, we further investigate the extent to which pretrained models such as BERT capture knowledge using a zero-shot fact completion task. Moreover, we propose a simple yet effective weakly supervised pretraining objective, which explicitly forces the model to incorporate knowledge about real-world entities. Models trained with our new objective yield significant improvements on the fact completion task. When applied to downstream tasks, our model consistently outperforms BERT on four entity-related question answering datasets (i.e., WebQuestions, TriviaQA, SearchQA and Quasar-T) with an average $2 . 7 \ \mathrm { F 1 }$ improvements and a standard fine-grained entity typing dataset (i.e., FIGER) with 5.7 accuracy gains.
+
+# 1 INTRODUCTION
+
+Language models pretrained on a large amount of text such as ELMo (Peters et al., 2018a)), BERT (Devlin et al., 2019) and XLNet (Yang et al., 2019c) have established new state of the art on a wide variety of NLP tasks. Researchers ascertain that pretraining allows models to learn syntactic and semantic information of language that is then transferred on other tasks (Peters et al., 2018b; Clark et al., 2019). Interestingly, pretrained models also perform well on tasks that require grounding language and reasoning about the real world. For instance, the new state-of-the-art for WNLI (Wang et al., 2019a), ReCoRD (Zhang et al., 2018) and SWAG (Zellers et al., 2018) is achieved by pretrained models. These tasks are carefully designed so that the text input alone does not convey the complete information for accurate predictions – external knowledge is required to fill the gap. These results suggest that large-scale pretrained models implicitly capture real-world knowledge. Logan et al. (2019) and Petroni et al. (2019) further validate this hypothesis through a zero-shot fact completion task that involves single-token entities, showing that pretrained models achieve much better performance than random guessing and can be on par with specifically-trained relation extraction models.
+
+As unstructured text encodes a great deal of information about the world, large-scale pretraining over text data holds the promise of simultaneously learning syntax, semantics and connecting them with knowledge about the real world within a single model. However, existing pretraining objectives are usually defined at the token level and do not explicitly model entity-centric knowledge. In this work, we investigate whether we can further enforce pretrained models to focus on encyclopedic knowledge about real-world entities, so that they can better capture entity information from natural language and be applied to improving entity-related NLP tasks. We evaluate the extent to which a pretrained model represents such knowledge by extending an existing fact completion evaluation to a cloze ranking setting that allows us to deal with a large number of multi-token entity names without manual judgments. Our experiments on 10 common Wikidata (Vrandeciˇ c & Kr ´ otzsch, 2014) ¨ relations reveal that existing pretrained models encode entity-level knowledge only to a limited degree. Thus, we propose a new weakly supervised knowledge learning objective that requires the model to distinguish between true and false knowledge expressed in natural language. Specifically, we replace entity mentions in the original documents with names of other entities of the same type and train the models to distinguish the correct entity mention from randomly chosen ones. Models trained with this objective demonstrates much stronger fact completion performance for most relations we test on. Compared with previous work (Zhang et al., 2019; Peters et al., 2019) that utilizes an external knowledge base to incorporate entity knowledge, our method is able to directly derive real-world knowledge from unstructured text. Moreover, our method requires no additional data processing, memory or modifications to the BERT model when fine-tuning for downstream tasks.
+
+![](images/e6619be00d1cafc8fea5ec749341b822c0b3263ae9dd4a44330f69cc690badb1.jpg)  
+Figure 1: Type-Constrained Entity Replacements for Knowledge Learning.
+
+We test our model on two practical NLP problems that require entity knowledge: Question Answering (QA) and fine-grained Entity Typing. We use four previously published datasets for open-domain QA and observe that questions in these datasets often concern entities. The Entity Typing task requires the model to recognize fine-grained types of specified entity mentions given short contexts. On three of the QA datasets, our pretrained model outperforms all previous methods that do not rely on memory-consuming inter-passage normalizations1. On the FIGER entity-typing dataset, our model sets a new state of the art. Through ablation analysis, we show that the new entity-centric training objective is instrumental for achieving state-of-the-art results.
+
+In summary, this paper makes the following contributions: 1) We extend existing fact completion evaluation settings to test pretrained models’ ability on encoding knowledge of common real-world entities; 2) We propose a new weakly supervised pretraining method which results in models that better capture knowledge about real-world entities from natural language text; 3) The model trained with our knowledge learning objective establishes new state of the art on three entity-related QA datasets and a standard fine-grained entity typing dataset.
+
+We begin by introducing our weakly supervised method for knowledge learning (§2) and then discuss experiment settings and evaluation protocols, compare our model to previously published work and perform ablation analysis. Finally, we review related work in §4 and conclude in §5.
+
+# 2 ENTITY REPLACEMENT TRAINING
+
+We design an entity-centric training objective that utilizes weakly supervised training signals to explicitly encourage knowledge learning during pretraining. Given an input document, we first recognize the entity mentions and link them to Wikipedia entities2. We consider the original texts as positive knowledge statements and create negative statements by randomly replacing the entity mentions $( { \mathcal { E } } ^ { + } )$ with the names of other random entities $( { \mathcal { E } } ^ { - } )$ that have the same entity type as the mentioned entity. This setup is similar in spirit to the type-constrained negative sampling technique used to train knowledge base representations (Bordes et al., 2013). The latter technique creates negative triples by replacing the subject or object entity with random entities of the same type. Instead of knowledge base triples, we treat unstructured texts as factual statements. For a certain entity $e$ mentioned in a context $\mathcal { C }$ , we train the model to make a binary prediction indicating whether the entity has been replaced:
+
+$$
+J _ { e , \mathcal { C } } = \mathbb { 1 } _ { e \in \mathcal { E } ^ { + } } \log P ( e | \mathcal { C } ) + ( 1 - \mathbb { 1 } _ { e \in \mathcal { E } ^ { + } } ) \log ( 1 - P ( e | \mathcal { C } ) ) .
+$$
+
+Compared to the language modeling objective, entity replacement is defined at the entity level and introduces stronger negative signals. When we enforce entities to be of the same type, we preserve the linguistic correctness of the original sentence while the system needs to learn to perform judgment based on the factual aspect of the sentence.
+
+We describe the implementation in more detail in the following paragraphs.
+
+Data Preparation We use the whole English Wikipedia dump as training data and rely on all Wikipedia entities3. Entities in documents are recognized based on Wikipedia anchor links and entity alias from Wikidata. That is, we first retrieve the entities annotated by anchor links and then find other mentions of these entities by string matching their Wikidata alias. We split each document into multiple text chunks with the same size (512 tokens). Although our experiments rely on the Wikipedia corpus, this setup can be easily extended to larger corpora with off-the-shelf entity linking tools. We leave the larger scope of the experiments to future work.
+
+Replacement Strategy When replacing entities, we first lookup type information4 from Wikidata and then randomly select other entities with the same type. We do not replace adjacent entities. In other words, there must be at least one unreplaced entity between any two replaced ones. This reduces cases where we replace all entities in the same sentence and the resulting sentences happen to introduce correct entities by chance. For replacement, we randomly sample a string from the entities’ alias set. For each text chunk, we replicate it 10 times with different negative entities for each replacement location. We show an illustration of the entity replacement method in Figure 1.
+
+Model Architecture We use the Transformer (Vaswani et al., 2017) model used by BERT (Devlin et al., 2019). We use the same architecture as BERT base: 12 Transformer layers, each with hidden dimension 768. We initialize the transformer with a model pretrained based on our own BERT reimplementations5. For each entity, we use the final representations of its boundary words (words before and after the entity mention) to make predictions. We simply concatenate the boundary words’ representations and add a linear layer for prediction. During training, we use 0.05 dropout at the final layer.
+
+Training Objectives Masked language model pretraining has been proven to be effective for downstream tasks. While training for entity replacement we also train with the masked language model objective in a multi-task set-up. When masking tokens, we restrict the masks to be outside the entity spans. We use a masking ratio of $5 \%$ instead of $1 5 \%$ in the original BERT to avoid masking out too much of the context. We train the model for approximately 1 million updates using a batch size of 128.
+
+# 3 EXPERIMENTS
+
+We first test our model on a fact completion task. This task resembles traditional knowledge base completion: it requires the model to complete missing entities in factual triples. We further test on two real-world downstream tasks that require entity-level knowledge – question answering and fine-grained entity typing. We describe the hyperparameter and training settings of all experiments in the appendix.
+
+# 3.1 ZERO-SHOT FACT COMPLETION
+
+In traditional knowledge base completion tasks models have access to a set of training triples. Instead, we utilize a zero-shot test to examine the model’s ability to automatically derive relational knowledge from natural language.
+
+Dataset We rely on factual triples from Wikidata. Each triple describes the relationship between two certain entities, e.g., {Paris, CapitalOf, France $\}$ . Following recent practices (Bosselut et al., 2019; Logan et al., 2019) that decode structured knowledge from language models, we first manually create templates to convert triples of 10 common relations into natural language expressions ({Paris, CapitalOf, France $\} $ the capital of France is Paris). We then create queries by removing the object entity in the expression and use pre-trained models to predict the missing entities, e.g., the capital of France is ?. We create 1000 cloze examples6 for each of the 10 relations.
+
+Evaluation Metrics Previous work (Logan et al., 2019; Petroni et al., 2019) either relies on human evaluation or only considers single-token entities for fact completion. In contrast, we consider an entity-ranking setup and create a set of candidate entities for each relation. This setting allows us to automatically evaluate a large number of queries that usually involve multi-token entities. We test pretrained models on their ability to recover the correct object entity from the candidate set. To create the negative choices, we select from the set of all object entities in the particular relation, which generally have the same type as the groundtruth and are more challenging to distinguish than entities with different types. Our evaluation strategy is similar to previous work on knowledge base completion (Nickel et al., 2011; Bordes et al., 2013; Xiong et al., 2017). We follow these studies and use Hits $@ 1 0$ as the evaluation metric.
+
+Baselines We compare our model with two pretrained language models BERT (Devlin et al., 2019) (both base and large) and GPT-2 (Radford et al., 2019). We make use of their output token probabilities to rank candidate entities. For BERT, we feed in the masked queries (e.g., $Q _ { m a s k e d } = \pm \mathrm { h e }$ capital of France is [MASK]). For multi-token candidates, we use the same number of [MASK] tokens in the query inputs. We use the average log probability of masked tokens for ranking. Given a multi-token entity $E _ { i } = [ e _ { i } ^ { 1 } , e _ { i } ^ { 2 } , . . . , e _ { i } ^ { | E _ { i } | } ]$ e|Ei|i ], the ranking score from BERT is calculated as
+
+$$
+S _ { E _ { i } } = \frac { 1 } { | E _ { i } | } \sum _ { k } \log P ( e _ { i } ^ { k } | Q _ { m a s k e d } ) .
+$$
+
+For GPT-2, we feed in the original query without the answer entity and use the first-token probability of candidate entities for ranking, which performs better than using average log probabilities. As our model learns to predict a plausible probability $( P ( e | \mathcal { C } ) )$ for each entity mention during entity replacement training, we can directly use these predicted probabilities to rank the candidates.
+
+Results Table 1 shows the fact completion results for all relations. We denote our method WKLM for (Weakly Supervised Knowledge-Pretrained Language Model). Overall, WKLM achieves the best results on 8 of the 10 relations. We also observe that GPT-2 outperforms BERT on average. We think this is because the fact completion task requires models to predict the missing entities using only a short context on the left, while BERT pretraining incorporates context from both directions. Interestingly, BERT achieves good performance on several geographical relations such as PlaceOfBirth, LocatedIn and PlaceOfDeath. We conjecture that this is because location entities usually appear at sentence ends in Wikipedia articles, e.g., Obama was born in
+
+Honolulu, Hawaii.. This sentence pattern is similar to our templates and BERT may learn to rely mostly on the left context to make predictions. For most relations that include answers that are person names, BERT lags behind both GPT-2 and our model.
+
+Comparing the top and bottom five relations, we observe that BERT’s performance is correlated with the size of the candidate set, while WKLM and GPT-2 are less sensitive to this number. A similar pattern exists between models’ performance and the cardinality of groundtruth answers, i.e., our model achieves similar performance on both single-answer and multiple-answer queries while BERT is usually better at single-answer queries. WKLM both outperforms BERT and GPT-2 and achieves robust performance across relations with different properties. Visualization of correlations between relation properties and model performance can be found in the appendix.
+
+Table 1: Zero-Shot Fact Completion Results.   
+
+<table><tr><td>Relation Name</td><td>#of Candidates</td><td>#of Answers</td><td>BERT-base</td><td>Model BERT-large</td><td>GPT-2</td><td>Ours</td></tr><tr><td>HASCHILD (P40)</td><td>906</td><td>3.8</td><td>9.00</td><td>6.00</td><td>20.5</td><td>63.5</td></tr><tr><td>NOTABLEWORK (P800)</td><td>901</td><td>5.2</td><td>1.88</td><td>2.56</td><td>2.39</td><td>4.10</td></tr><tr><td>CAPITALOF (P36)</td><td>820</td><td>2.2</td><td>1.87</td><td>1.55</td><td>15.8</td><td>49.1</td></tr><tr><td>FOUNDEDBY (P112)</td><td>798</td><td>3.7</td><td>2.44</td><td>1.93</td><td>8.65</td><td>24.2</td></tr><tr><td>CREATOR (P170)</td><td>536</td><td>3.6</td><td>4.57</td><td>4.57</td><td>7.27</td><td>9.84</td></tr><tr><td>PLACEOFBIRTH (P19)</td><td>497</td><td>1.8</td><td>19.2</td><td>30.9</td><td>8.95</td><td>23.2</td></tr><tr><td>LOCATEDIN (P131))</td><td>382</td><td>1.9</td><td>13.2</td><td>52.5</td><td>21.0</td><td>61.1</td></tr><tr><td>EDUCATEDAT (P69)</td><td>374</td><td>4.1</td><td>9.10</td><td>7.93</td><td>11.0</td><td>16.9</td></tr><tr><td>PLACEOFDEATH (P20)</td><td>313</td><td>1.7</td><td>43.0</td><td>42.6</td><td>8.83</td><td>26.5</td></tr><tr><td>OCCUPATION (P106)</td><td>190</td><td>1.4</td><td>8.58</td><td>10.7</td><td>9.17</td><td>10.7</td></tr><tr><td>Average Hits @ 10</td><td>1</td><td>-</td><td>11.3</td><td>16.1</td><td>16.3</td><td>28.9</td></tr></table>
+
+# 3.2 DOWNSTREAM TASKS
+
+Background knowledge is important for language understanding. We expect our pretraining approach to be beneficial to NLP applications where entity-level knowledge is essential. We consider two such applications: question answering and entity-typing. We find that a large portion of the questions in existing QA datasets are about entities and involve entity relations. In a way, our pretraining objective is analogous to question answering in a multiple-choice setting (Hermann et al., 2015). The entity-typing task requires the model to predict a set of correct types of entity mentions in a short context. The context itself can be insufficient and the training data for this task is small and noisy. We believe a model that encodes background entity knowledge can help in both cases.
+
+# 3.2.1 QUESTION ANSWERING
+
+Datasets We consider four question answering datasets:
+
+• WebQuestions (Berant et al., 2013) is originally a dataset for knowledge base question answering. The questions are collected using Google Suggest API and are all asking about simple relational facts of Freebase entities.   
+TriviaQA7 (Joshi et al., 2017) includes questions from trivia and quiz-league websites. Apart from a small portion of questions to which the answers are numbers and free texts, $9 2 . 8 5 \%$ of the answers are Wikipedia entities. Quasar-T (Dhingra et al., 2017) is another dataset that includes trivia questions. Most of the answers in this dataset are none phrases. According to our manual analysis on random samples, $8 8 \%$ of the answers are real-world entities8.   
+SearchQA (Dunn et al., 2017) uses questions from the television quiz show Jeopardy! and we also find that almost all of the answers are real-world entities.
+
+Questions in all three datasets are created without the context of a paragraph, which resembles the scenario of practical question answering applications. All the questions except WebQuestions are written by humans. This indicates that humans are generally interested to ask questions to seek information about entities. We show the statistics and example questions in Table 2. We split the training data (created by distant supervision) of WebQuestions with a ratio (9:1) for training and development. Since our model is based on our own BERT implementations, in addition to the aforementioned entity-related datasets, we first use the standard SQuAD (Rajpurkar et al., 2016) benchmark to validate our model’s answer extraction performance.
+
+Table 2: Properties of the QA Datasets.   
+
+<table><tr><td>Dataset</td><td>Train</td><td>Valid</td><td>Test</td><td>Example Questions</td></tr><tr><td>WebQuestions</td><td>3778</td><td></td><td>2032</td><td>Who plays Stewie Griffn on Family Guy?</td></tr><tr><td>TriviaQA</td><td>87291</td><td>11274</td><td>10790</td><td>What is the Japanese share index called?</td></tr><tr><td>SearchQA</td><td>99811</td><td>13893</td><td>27247</td><td>Hero several books 11 discover&#x27;s wizard?</td></tr><tr><td>Quasar-T</td><td>37012</td><td>3000</td><td>3000</td><td>Which vegetable isa Welsh emblem?</td></tr></table>
+
+Settings We adopt the fine-tuning approach to extract answer spans with pretrained models. We add linear layers over the last hidden states of the pretrained models to predict the start and end positions of the answer. Unlike $\mathrm { S Q u A D }$ , questions in the datasets we use are not paired with paragraphs that contain the answer. We follow previous work (Chen et al., 2017; Wang et al., 2018a) and retrieve context paragraphs with information retrieval systems. Details of the context retrieval process for each dataset can be found in the appendix. Reader models are trained with distantly supervised data, i.e., we treat any text span in any retrieved paragraph as ground truth as long as it matches the original answers. Since the reader model needs to read multiple paragraphs to predict a single answer at inference time, we also train a BERT based paragraph ranker with distant-supervised data to assign each paragraph a relevance score. The paragraph ranker takes question and paragraph pairs and predicts a score in the range [0, 1] for each pair. During inference, for each question and its evidence paragraph set, we first use the paragraph reader to extract the best answer from each paragraph. These answers are then ranked based on a linear combination of the answer extraction score (a log sum of the answer start and end scores) and the paragraph relevance score. We also evaluate model performance without using the relevance scores.
+
+Open-Domain QA Baselines We compare our QA model with the following systems:
+
+• DrQA (Chen et al., 2017) is an open-domain QA system which uses TF-IDF with bigram features for ranking and a simple attentive reader for answer extraction.   
+$\mathbf { R } ^ { 3 }$ (Wang et al., 2018a) is a reinforcement learning based system which jointly trains a paragraph ranker and a document reader. DSQA (Lin et al., 2018) uses RNN-based paragraph ranker and jointly trains the paragraph ranker and attentive paragraph ranker with a multi-task loss. Evidence Aggregation (Wang et al., 2018b) uses a hybrid answer reranking module to aggregate answer information from multiple paragraphs and rerank the answers extracted from multiple paragraphs. BERTserini (Yang et al., 2019a) is a BERT-based open-domain QA system, which uses BM25-based retriever to retrieve 100 paragraphs and a BERT-based reader to extract answers. The paragraph reader is either trained with SQuAD (Rajpurkar et al., 2016) data or distant-supervision data (Yang et al., 2019b) ORQA (Lee et al., 2019) replaces the traditional BM25 ranking with a BERT-based ranker. The ranker model is pretrained on the whole Wikipedia corpus with an inverse cloze task which simulates the matching between questions and paragraphs. All text blocks in Wikipedia are be pre-encoded as vectors and retrieved with Locality Sensitive Hashing.
+
+Results Table 3 shows the SQuAD results and Table 4 shows the open-domain results on the four datasets that are highly entity-related. From the SQuAD results, we observe that our BERT reimplementation performs better than the original model this is due to the fact that it is trained for twice as many updates: 2 million vs. 1 million for the original BERT. Although lots of the answers in SQuAD are non-entity spans, the WKLM model we propose achieves better performance than BERT. We believe the improvement is due to both the masked language model and entity replacement objectives. Ablation experiments on the training objectives will be discussed in $\ S 3 . 2 . 3$ .
+
+Having established that our BERT re-implementation performs better than the original model, we compare with only our own BERT for the following experiments. From Table 4, we see that our model produces consistent improvements across different datasets. Compared to the $0 . 8 \ : \mathrm { F 1 }$ improvements over BERT on SQuAD, we achieve an average of $2 . 7 ~ \mathrm { F 1 }$ improvements over BERT on entity-related datasets when the ranking scores are not used. On TriviaQA and Quasar-T, WKLM outperforms our BERT even when it uses ranking scores. Improvements in natural language question datasets (WebQuestions, TriviaQA, and Quasar-T) are more significant than SearchQA where the questions are informal queries. When we utilize ranking scores from a simple BERT based ranker, we are able to achieve the state-of-the-art on three of the four datasets.
+
+Table 3: SQuAD Dev Results.   
+
+<table><tr><td>Model</td><td>EM</td><td>F1</td></tr><tr><td>Google&#x27;s BERT-base</td><td>80.8</td><td>88.5</td></tr><tr><td>Google&#x27;s BERT-large</td><td>84.1</td><td>90.9</td></tr><tr><td>Our BERT-base</td><td>83.4</td><td>90.5</td></tr><tr><td>WKLM (base)</td><td>84.3</td><td>91.3</td></tr></table>
+
+Table 4: Open-domain QA Results.   
+
+<table><tr><td>Model</td><td>WebQuestions EM</td><td>F1</td><td>TriviaQA EM</td><td>F1</td><td>Quasar-T EM</td><td>F1</td><td>SearchQA EM</td><td>F1</td></tr><tr><td>DrQA (Chen et al., 2017)</td><td>20.7</td><td>1</td><td>-</td><td>1</td><td>-</td><td>-</td><td>-</td><td>1</td></tr><tr><td>R (Wang et al.,2018a)</td><td>-</td><td>1</td><td>50.6</td><td>57.3</td><td>42.3</td><td>49.6</td><td>57.0</td><td>63.2</td></tr><tr><td>DSQA (Lin et al., 2018)</td><td>18.5</td><td>25.6</td><td>48.7</td><td>56.3</td><td>42.2</td><td>49.3</td><td>49.0</td><td>55.3</td></tr><tr><td>Evidence Agg. (Wang et al.,2018b)</td><td>1</td><td>1</td><td>50.6</td><td>57.3</td><td>42.3</td><td>49.6</td><td>57.0</td><td>63.2</td></tr><tr><td>BERTserini (Yang et al.,2019a)</td><td>-</td><td>-</td><td>51.0</td><td>56.3</td><td>1</td><td>-</td><td>1</td><td>1</td></tr><tr><td>BERTserini+DS (Yang et al., 2019b)</td><td>=</td><td>=</td><td>54.4</td><td>60.2</td><td>1</td><td>=</td><td>-</td><td>1</td></tr><tr><td>ORQA (Lee et al., 2019)</td><td>36.4</td><td>1</td><td>45.0</td><td>-</td><td>-</td><td>-</td><td>-</td><td>1</td></tr><tr><td>Our BERT</td><td>29.2</td><td>35.5</td><td>48.7</td><td>53.2</td><td>40.4</td><td>46.1</td><td>57.1</td><td>61.9</td></tr><tr><td>Our BERT +Ranking score</td><td>32.2</td><td>38.9</td><td>52.1</td><td>56.5</td><td>43.2</td><td>49.2</td><td>60.6</td><td>65.9</td></tr><tr><td>WKLM</td><td>30.8</td><td>37.9</td><td>52.2</td><td>56.7</td><td>43.7</td><td>49.9</td><td>58.7</td><td>63.3</td></tr><tr><td>WKLM + Ranking score</td><td>34.6</td><td>41.8</td><td>58.1</td><td>63.1</td><td>45.8</td><td>52.2</td><td>61.7</td><td>66.7</td></tr></table>
+
+# 3.2.2 ENTITY TYPING
+
+To compare with an existing study (Zhang et al., 2019) that also attempts to incorporate entity knowledge into language models, we consider an additional entity typing task using the large FIGER dataset (Ling & Weld, 2012). The task is to assign a fine-grained type to entity mentions. We do that by adding two special tokens before and after the entity span to mark the entity position. We use the final representation of the start token ([CLS]) to predict the entity types. The model is fine-tuned on weakly-supervised training data with binary cross-entropy loss. We evaluate the models using strict accuracy, loose micro, and macro F1 scores.
+
+We show the results in Table 5. We compare our model with two non-BERT neural baselines (Inui et al., 2017) that integrate a set of hand-crafted features: LSTM $^ +$ Hand-crafted and Attentive $^ +$
+
+Table 5: Fine-grained Entity Typing Results on the FIGER dataset.   
+
+<table><tr><td>Model</td><td>Acc</td><td>Ma-F1</td><td>Mi-F1</td></tr><tr><td>LSTM+ Hand-crafted (Inui et al.,2017)</td><td>57.02</td><td>76.98</td><td>73.94</td></tr><tr><td>Attentive + Hand-crafted (Inui et al.,2017) BERT baseline (Zhang et al.,2019)</td><td>59.68 52.04</td><td>78.97 75.16</td><td>75.36 71.63</td></tr><tr><td>ERNIE (Zhang et al., 2019)</td><td>57.19</td><td>75.61</td><td>73.39</td></tr><tr><td>Our BERT</td><td>54.53</td><td></td><td></td></tr><tr><td>WKLM</td><td>60.21</td><td>79.57 81.99</td><td>74.74 77.00</td></tr></table>
+
+Hand-crafted; a vanilla BERT baseline and the ERNIE model (Zhang et al., 2019) that enhances BERT with knowledge base embeddings.
+
+First, we see that naively applying BERT is less effective than simple models combined with sparse hand-crafted features. Although the ERNIE model can improve over BERT by 5.15 points, its performance still lags behind models that make good use of hand-crafted features. In contrast, although based on a stronger BERT model, our model achieves larger absolute improvements (5.68 points) and sets a new state-of-the-art for this task. Given the larger improvement margin, we believe our model that directly learn knowledge from text is more effective than the ERNIE method.
+
+# 3.2.3 ABLATION STUDY: THE EFFECT OF MASKED LANGUAGE MODEL LOSS
+
+In view of a recent study (Liu et al., 2019b) showing simply extending the training time of BERT leads to stronger performance on various downstream tasks, we conduct further analysis to differentiate the effects of entity replacement training and masked language modeling. We compare our model with three variants: a model pretrained only with the knowledge learning objective (WKLM without MLM), a model trained with both knowledge learning and masked language modeling with more masked words (WKLM with $1 5 \%$ MLM) and a BERT model trained with additional 1 million updates on English Wikipedia $\mathbf { \left( B E R T + 1 M \right) }$ MLM updates) and no knowledge learning.
+
+The ablation results are shown in Table 6. The results of WKLM without MLM validate that adding the language model objective is essential for downstream performance. We also find that masking out too many words (i.e., $1 5 \%$ masking ratio as in the original BERT) leads to worse results. We conjecture that too many masked words outside entity mentions break parts of the context information and introduce noisy signals to knowledge learning. Results of continued BERT training show that more MLM updates are often beneficial, especially for SQuAD. However, on tasks that are more entity-centric, continued MLM training is less effective than our WKLM method. This suggests that our WKLM method could serve as an effective complementary recipe to masked language modeling when applied to entity-related NLP tasks.
+
+Table 6: Ablation Studies on Masked Language Model and Masking Ratios.   
+
+<table><tr><td>Model</td><td colspan="2">SQuAD EM F1</td><td colspan="2">TriviaQA EM F1</td><td colspan="2">Quasar-T EM F1</td><td>FIGER Acc</td></tr><tr><td>Our BERT</td><td>83.4</td><td>90.5</td><td>48.7</td><td>53.2</td><td>40.4</td><td>46.1</td><td>54.53</td></tr><tr><td>WKLM</td><td>84.3</td><td>91.3</td><td>52.2</td><td>56.7</td><td>43.7</td><td>49.9</td><td>60.21</td></tr><tr><td>WKLM without MLM</td><td>80.5</td><td>87.6</td><td>48.2</td><td>52.5</td><td>42.2</td><td>48.1</td><td>58.44</td></tr><tr><td>WKLM with 15% masking</td><td>84.1</td><td>91.0</td><td>51.0</td><td>55.3</td><td>42.9</td><td>49.0</td><td>59.68</td></tr><tr><td>Our BERT + 1MMLMupdates</td><td>84.4</td><td>91.1</td><td>52.0</td><td>56.3</td><td>42.3</td><td>48.2</td><td>54.17</td></tr></table>
+
+# 4 RELATED WORK
+
+Pretrained Language Representations Early research on language representations focused on static unsupervised word representations (Mikolov et al., 2013; Pennington et al., 2014). Word embeddings leverage co-occurrences to learn latent word vectors that approximately reflect word semantics. Given that words can have different meanings in different contexts, more recent studies (McCann et al., 2017; Peters et al., 2018a) show that contextual language representations can be more powerful than static word embeddings in downstream tasks. This direction has been further explored at a larger scale with efficient Transformer architectures (Radford et al., 2019; Devlin et al., 2019; Yang et al., 2019c). Our WKLM method is based on these techniques and we focus on improving the knowledge ability of pretrained models.
+
+Knowledge-Enhanced NLP Models Background knowledge has been considered an indispensable part of language understanding (Fillmore et al., 1976; Minsky, 1988). As standard language encoders usually do not explicitly model knowledge, recent studies (Ahn et al., 2016; Yang & Mitchell, 2017; Logan et al., 2019; Liu et al., 2019a) have explored methods to incorporate external knowledge into NLP models. Most of these methods rely on additional inputs such as entity representations from structured knowledge bases. With the breakthrough of large-scale pretrained language encoders (Devlin et al., 2019), Zhang et al. (2019) and Peters et al. (2019) adopt similar ideas and propose entity-level knowledge enhancement training objectives to incorporate knowledge into pretrained models. Other recent studies (Mihaylov & Frank, 2018; Xiong et al., 2019) leverage external knowledge bases to enhance text-based question answering models. In contrast to these methods, our method utilizes minimal external entity information and does not require additional memory or architectural changes when applied to downstream tasks.
+
+# 5 CONCLUSION
+
+We introduce a weakly supervised method to encourage pretrained language models to learn entitylevel knowledge. Our method uses minimal entity information during pretraining and does not introduce additional computation, memory or architectural overhead for downstream task fine-tuning. The trained model demonstrates strong performance on a probing fact completion task and two entity-related NLP tasks. Together, our results show the potential of directly learning entity-level knowledge from unstructured natural language and the benefits of large-scale knowledge-aware pretraining for downstream NLP tasks.
+
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+Wenhan Xiong, Mo Yu, Shiyu Chang, Xiaoxiao Guo, and William Yang Wang. Improving question answering over incomplete KBs with knowledge-aware reader. In Proceedings of the 57th Annual Meeting of the Association for Computational Linguistics, Florence, Italy, July 2019. Association for Computational Linguistics. doi: 10.18653/v1/P19-1417.
+
+Bishan Yang and Tom M. Mitchell. Leveraging knowledge bases in lstms for improving machine reading. In ACL (1), pp. 1436–1446. ACL, 2017.
+
+Wei Yang, Yuqing Xie, Aileen Lin, Xingyu Li, Luchen Tan, Kun Xiong, Ming Li, and Jimmy Lin. End-to-end open-domain question answering with bertserini. arXiv preprint arXiv:1902.01718, 2019a.
+
+Wei Yang, Yuqing Xie, Luchen Tan, Kun Xiong, Ming Li, and Jimmy Lin. Data augmentation for bert fine-tuning in open-domain question answering. arXiv preprint arXiv:1904.06652, 2019b.
+
+Zhilin Yang, Zihang Dai, Yiming Yang, Jaime Carbonell, Ruslan Salakhutdinov, and Quoc V Le. Xlnet: Generalized autoregressive pretraining for language understanding. arXiv preprint arXiv:1906.08237, 2019c.
+
+Rowan Zellers, Yonatan Bisk, Roy Schwartz, and Yejin Choi. SWAG: A large-scale adversarial dataset for grounded commonsense inference. In EMNLP, pp. 93–104. ACL, 2018.
+
+Sheng Zhang, Xiaodong Liu, Jingjing Liu, Jianfeng Gao, Kevin Duh, and Benjamin Van Durme. Record: Bridging the gap between human and machine commonsense reading comprehension. arXiv preprint arXiv:1810.12885, 2018.
+
+Zhengyan Zhang, Xu Han, Zhiyuan Liu, Xin Jiang, Maosong Sun, and Qun Liu. ERNIE: enhanced language representation with informative entities. In ACL (1), pp. 1441–1451. ACL, 2019.
+
+Yukun Zhu, Ryan Kiros, Richard S. Zemel, Ruslan Salakhutdinov, Raquel Urtasun, Antonio Torralba, and Sanja Fidler. Aligning books and movies: Towards story-like visual explanations by watching movies and reading books. In ICCV, pp. 19–27. IEEE Computer Society, 2015.
+
+# A APPENDIX
+
+Implementation Details and Hyperparameters We implement our method using Fairseq Ott et al. (2019) and the fact completion baselines are implemented with Huggingface’s PytorchTransformers9. We pretrain the models with 32 V100 GPUs for 3 days. We use at most 2 GPUs for fine-tuning the paragraph reader, use 8 GPUs for fine-tuning the paragraph ranker. The entity-typing experiments require larger batch sizes and take 8 GPUs for training.
+
+For the knowledge learning pretraining phase, we use the Adam optimizer (Kingma & Ba, 2014) with learning rate 1e-5, batch size 128 and weight decay 0.01. The model is pretrained on 32 V100 GPUs for 3 days. To train the paragraph reader for open-domain QA, we select the best learning rate from $\{ 1 \mathrm { e } { - } 6 , 5 \mathrm { e } { - } 6 , 1 \mathrm { e } { - } 5 , 2 \mathrm { e } { - } 5 \}$ and last layer dropout ratio from $\{ 0 . 1 , 0 . 2 \}$ . We set the maximum training epoch to be 10 and batch size to be 32. The maximal input sequence length is 512 for WebQuestions and 128 for the other three datasets that use sentence-level paragraphs. For the paragraph ranker, we choose learning rate from $\{ 1 \mathrm { e } { - } 5 , 2 \mathrm { e } { - } 5 , 5 \mathrm { e } { - } 6 \}$ , use dropout 0.1 and batch size 256. The maximal sequence length for each dataset is consistent with the one we used for training the paragraph reader. The linear combination of ranking and extraction scores is selected based on validation performance. For $\mathrm { S Q u A D }$ experiments, we select learning rate from {1e-5, 5e-6, 2e-5, 3e-5}, learning rate from $\{ 8 , 1 6 \}$ , last layer dropout ratio from $\{ 0 . \bar { 1 } , 0 . 2 \}$ . We set the maximal sequence length as 512 and the maximal training epoch as 5. For entity typing, we select learning rate from $\{ 1 \mathrm { e } { - } 5 , 2 \mathrm { e } { - } 5 , 3 \mathrm { e } { - } 5 , 5 \mathrm { e } { - } 5 \}$ and batch size from $\{ 1 2 8 , 2 5 6 \}$ . We set the maximal sequence length to be 256, the last layer dropout ratio to be 0.1. The model is fine-tuned for at most 3 epochs to prevent overfitting. The threshold for type prediction is selected on the validation set.
+
+Context Collection for QA Datasets For WebQuestions, we collect evidence context using the document retriever of DrQA (Chen et al., 2017), which uses TF-IDF based metric to retrieve the top 5 Wikipedia articles. For Quasar-T, we use Lucene ranked paragraphs. For SearchQA and TriviaQA, we use paragraphs ranked by search engines. Following existing research (Wang et al., 2018b; Lin et al., 2018), we use sentence-level paragraphs for SearchQA (50 sentences), TriviaQA (100 sentences) and SearchQA (100 sentences).
+
+Correlation between Fact Completion Results and Properties of Relations Figure 2 shows the fact completion results of BERT are unstable on different relations with different properties, i.e., BERT’s performance is strongly correlated with the size of candidate entity set and the number of groundtruth answers. Compared to BERT, WKLM is often less sensitive to these two factors.
+
+![](images/c4467ced3c563f98d90c351c77048841c6bfc2b0398c5d55d529d5aa4ca776ba.jpg)  
+Figure 2: Left: Correlation between candidate set size and hits $@ 1 0$ ; Right: Correlation between number of groundtruth answers and hits $@ 1 0$ .

parse/train/BJlzm64tDH/BJlzm64tDH_content_list.json

@@ -0,0 +1,1422 @@
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+    {
+        "type": "text",
+        "text": "PRETRAINED ENCYCLOPEDIA: WEAKLY SUPERVISED KNOWLEDGE-PRETRAINED LANGUAGE MODEL ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Wenhan Xiong†, Jingfei $\\mathbf { D } \\mathbf { u } ^ { \\mathrm { S } }$ , William Yang Wang†, Veselin Stoyanov§, ",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "† University of California, Santa Barbara § Facebook AI {xwhan, william}@cs.ucsb.edu, {jingfeidu, ves}@fb.com ",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "ABSTRACT ",
+        "text_level": 1,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Recent breakthroughs of pretrained language models have shown the effectiveness of self-supervised learning for a wide range of natural language processing (NLP) tasks. In addition to standard syntactic and semantic NLP tasks, pretrained models achieve strong improvements on tasks that involve real-world knowledge, suggesting that large-scale language modeling could be an implicit method to capture knowledge. In this work, we further investigate the extent to which pretrained models such as BERT capture knowledge using a zero-shot fact completion task. Moreover, we propose a simple yet effective weakly supervised pretraining objective, which explicitly forces the model to incorporate knowledge about real-world entities. Models trained with our new objective yield significant improvements on the fact completion task. When applied to downstream tasks, our model consistently outperforms BERT on four entity-related question answering datasets (i.e., WebQuestions, TriviaQA, SearchQA and Quasar-T) with an average $2 . 7 \\ \\mathrm { F 1 }$ improvements and a standard fine-grained entity typing dataset (i.e., FIGER) with 5.7 accuracy gains. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
+        "bbox": [
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+            334,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Language models pretrained on a large amount of text such as ELMo (Peters et al., 2018a)), BERT (Devlin et al., 2019) and XLNet (Yang et al., 2019c) have established new state of the art on a wide variety of NLP tasks. Researchers ascertain that pretraining allows models to learn syntactic and semantic information of language that is then transferred on other tasks (Peters et al., 2018b; Clark et al., 2019). Interestingly, pretrained models also perform well on tasks that require grounding language and reasoning about the real world. For instance, the new state-of-the-art for WNLI (Wang et al., 2019a), ReCoRD (Zhang et al., 2018) and SWAG (Zellers et al., 2018) is achieved by pretrained models. These tasks are carefully designed so that the text input alone does not convey the complete information for accurate predictions – external knowledge is required to fill the gap. These results suggest that large-scale pretrained models implicitly capture real-world knowledge. Logan et al. (2019) and Petroni et al. (2019) further validate this hypothesis through a zero-shot fact completion task that involves single-token entities, showing that pretrained models achieve much better performance than random guessing and can be on par with specifically-trained relation extraction models. ",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "As unstructured text encodes a great deal of information about the world, large-scale pretraining over text data holds the promise of simultaneously learning syntax, semantics and connecting them with knowledge about the real world within a single model. However, existing pretraining objectives are usually defined at the token level and do not explicitly model entity-centric knowledge. In this work, we investigate whether we can further enforce pretrained models to focus on encyclopedic knowledge about real-world entities, so that they can better capture entity information from natural language and be applied to improving entity-related NLP tasks. We evaluate the extent to which a pretrained model represents such knowledge by extending an existing fact completion evaluation to a cloze ranking setting that allows us to deal with a large number of multi-token entity names without manual judgments. Our experiments on 10 common Wikidata (Vrandeciˇ c & Kr ´ otzsch, 2014) ¨ relations reveal that existing pretrained models encode entity-level knowledge only to a limited degree. Thus, we propose a new weakly supervised knowledge learning objective that requires the model to distinguish between true and false knowledge expressed in natural language. Specifically, we replace entity mentions in the original documents with names of other entities of the same type and train the models to distinguish the correct entity mention from randomly chosen ones. Models trained with this objective demonstrates much stronger fact completion performance for most relations we test on. Compared with previous work (Zhang et al., 2019; Peters et al., 2019) that utilizes an external knowledge base to incorporate entity knowledge, our method is able to directly derive real-world knowledge from unstructured text. Moreover, our method requires no additional data processing, memory or modifications to the BERT model when fine-tuning for downstream tasks. ",
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+    },
+    {
+        "type": "image",
+        "img_path": "images/e6619be00d1cafc8fea5ec749341b822c0b3263ae9dd4a44330f69cc690badb1.jpg",
+        "image_caption": [
+            "Figure 1: Type-Constrained Entity Replacements for Knowledge Learning. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            181,
+            104,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "We test our model on two practical NLP problems that require entity knowledge: Question Answering (QA) and fine-grained Entity Typing. We use four previously published datasets for open-domain QA and observe that questions in these datasets often concern entities. The Entity Typing task requires the model to recognize fine-grained types of specified entity mentions given short contexts. On three of the QA datasets, our pretrained model outperforms all previous methods that do not rely on memory-consuming inter-passage normalizations1. On the FIGER entity-typing dataset, our model sets a new state of the art. Through ablation analysis, we show that the new entity-centric training objective is instrumental for achieving state-of-the-art results. ",
+        "bbox": [
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+            537,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In summary, this paper makes the following contributions: 1) We extend existing fact completion evaluation settings to test pretrained models’ ability on encoding knowledge of common real-world entities; 2) We propose a new weakly supervised pretraining method which results in models that better capture knowledge about real-world entities from natural language text; 3) The model trained with our knowledge learning objective establishes new state of the art on three entity-related QA datasets and a standard fine-grained entity typing dataset. ",
+        "bbox": [
+            174,
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "We begin by introducing our weakly supervised method for knowledge learning (§2) and then discuss experiment settings and evaluation protocols, compare our model to previously published work and perform ablation analysis. Finally, we review related work in §4 and conclude in §5. ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2 ENTITY REPLACEMENT TRAINING ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 1
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+    {
+        "type": "text",
+        "text": "We design an entity-centric training objective that utilizes weakly supervised training signals to explicitly encourage knowledge learning during pretraining. Given an input document, we first recognize the entity mentions and link them to Wikipedia entities2. We consider the original texts as positive knowledge statements and create negative statements by randomly replacing the entity mentions $( { \\mathcal { E } } ^ { + } )$ with the names of other random entities $( { \\mathcal { E } } ^ { - } )$ that have the same entity type as the mentioned entity. This setup is similar in spirit to the type-constrained negative sampling technique used to train knowledge base representations (Bordes et al., 2013). The latter technique creates negative triples by replacing the subject or object entity with random entities of the same type. Instead of knowledge base triples, we treat unstructured texts as factual statements. For a certain entity $e$ mentioned in a context $\\mathcal { C }$ , we train the model to make a binary prediction indicating whether the entity has been replaced: ",
+        "bbox": [
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+        "page_idx": 1
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+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/584310909bd4bc202b4ff2079d1deaccdb1ed418b79f5e676747d9147bde655d.jpg",
+        "text": "$$\nJ _ { e , \\mathcal { C } } = \\mathbb { 1 } _ { e \\in \\mathcal { E } ^ { + } } \\log P ( e | \\mathcal { C } ) + ( 1 - \\mathbb { 1 } _ { e \\in \\mathcal { E } ^ { + } } ) \\log ( 1 - P ( e | \\mathcal { C } ) ) .\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Compared to the language modeling objective, entity replacement is defined at the entity level and introduces stronger negative signals. When we enforce entities to be of the same type, we preserve the linguistic correctness of the original sentence while the system needs to learn to perform judgment based on the factual aspect of the sentence. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "We describe the implementation in more detail in the following paragraphs. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Data Preparation We use the whole English Wikipedia dump as training data and rely on all Wikipedia entities3. Entities in documents are recognized based on Wikipedia anchor links and entity alias from Wikidata. That is, we first retrieve the entities annotated by anchor links and then find other mentions of these entities by string matching their Wikidata alias. We split each document into multiple text chunks with the same size (512 tokens). Although our experiments rely on the Wikipedia corpus, this setup can be easily extended to larger corpora with off-the-shelf entity linking tools. We leave the larger scope of the experiments to future work. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Replacement Strategy When replacing entities, we first lookup type information4 from Wikidata and then randomly select other entities with the same type. We do not replace adjacent entities. In other words, there must be at least one unreplaced entity between any two replaced ones. This reduces cases where we replace all entities in the same sentence and the resulting sentences happen to introduce correct entities by chance. For replacement, we randomly sample a string from the entities’ alias set. For each text chunk, we replicate it 10 times with different negative entities for each replacement location. We show an illustration of the entity replacement method in Figure 1. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Model Architecture We use the Transformer (Vaswani et al., 2017) model used by BERT (Devlin et al., 2019). We use the same architecture as BERT base: 12 Transformer layers, each with hidden dimension 768. We initialize the transformer with a model pretrained based on our own BERT reimplementations5. For each entity, we use the final representations of its boundary words (words before and after the entity mention) to make predictions. We simply concatenate the boundary words’ representations and add a linear layer for prediction. During training, we use 0.05 dropout at the final layer. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Training Objectives Masked language model pretraining has been proven to be effective for downstream tasks. While training for entity replacement we also train with the masked language model objective in a multi-task set-up. When masking tokens, we restrict the masks to be outside the entity spans. We use a masking ratio of $5 \\%$ instead of $1 5 \\%$ in the original BERT to avoid masking out too much of the context. We train the model for approximately 1 million updates using a batch size of 128. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3 EXPERIMENTS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            102,
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We first test our model on a fact completion task. This task resembles traditional knowledge base completion: it requires the model to complete missing entities in factual triples. We further test on two real-world downstream tasks that require entity-level knowledge – question answering and fine-grained entity typing. We describe the hyperparameter and training settings of all experiments in the appendix. ",
+        "bbox": [
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+        "page_idx": 3
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+    {
+        "type": "text",
+        "text": "3.1 ZERO-SHOT FACT COMPLETION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            222,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In traditional knowledge base completion tasks models have access to a set of training triples. Instead, we utilize a zero-shot test to examine the model’s ability to automatically derive relational knowledge from natural language. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Dataset We rely on factual triples from Wikidata. Each triple describes the relationship between two certain entities, e.g., {Paris, CapitalOf, France $\\}$ . Following recent practices (Bosselut et al., 2019; Logan et al., 2019) that decode structured knowledge from language models, we first manually create templates to convert triples of 10 common relations into natural language expressions ({Paris, CapitalOf, France $\\} $ the capital of France is Paris). We then create queries by removing the object entity in the expression and use pre-trained models to predict the missing entities, e.g., the capital of France is ?. We create 1000 cloze examples6 for each of the 10 relations. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Evaluation Metrics Previous work (Logan et al., 2019; Petroni et al., 2019) either relies on human evaluation or only considers single-token entities for fact completion. In contrast, we consider an entity-ranking setup and create a set of candidate entities for each relation. This setting allows us to automatically evaluate a large number of queries that usually involve multi-token entities. We test pretrained models on their ability to recover the correct object entity from the candidate set. To create the negative choices, we select from the set of all object entities in the particular relation, which generally have the same type as the groundtruth and are more challenging to distinguish than entities with different types. Our evaluation strategy is similar to previous work on knowledge base completion (Nickel et al., 2011; Bordes et al., 2013; Xiong et al., 2017). We follow these studies and use Hits $@ 1 0$ as the evaluation metric. ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Baselines We compare our model with two pretrained language models BERT (Devlin et al., 2019) (both base and large) and GPT-2 (Radford et al., 2019). We make use of their output token probabilities to rank candidate entities. For BERT, we feed in the masked queries (e.g., $Q _ { m a s k e d } = \\pm \\mathrm { h e }$ capital of France is [MASK]). For multi-token candidates, we use the same number of [MASK] tokens in the query inputs. We use the average log probability of masked tokens for ranking. Given a multi-token entity $E _ { i } = [ e _ { i } ^ { 1 } , e _ { i } ^ { 2 } , . . . , e _ { i } ^ { | E _ { i } | } ]$ e|Ei|i ], the ranking score from BERT is calculated as ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/5d027965b695409721272dd4f66de07d6adc02981b0b91b07701cdb6f3204fa9.jpg",
+        "text": "$$\nS _ { E _ { i } } = \\frac { 1 } { | E _ { i } | } \\sum _ { k } \\log P ( e _ { i } ^ { k } | Q _ { m a s k e d } ) .\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "For GPT-2, we feed in the original query without the answer entity and use the first-token probability of candidate entities for ranking, which performs better than using average log probabilities. As our model learns to predict a plausible probability $( P ( e | \\mathcal { C } ) )$ for each entity mention during entity replacement training, we can directly use these predicted probabilities to rank the candidates. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Results Table 1 shows the fact completion results for all relations. We denote our method WKLM for (Weakly Supervised Knowledge-Pretrained Language Model). Overall, WKLM achieves the best results on 8 of the 10 relations. We also observe that GPT-2 outperforms BERT on average. We think this is because the fact completion task requires models to predict the missing entities using only a short context on the left, while BERT pretraining incorporates context from both directions. Interestingly, BERT achieves good performance on several geographical relations such as PlaceOfBirth, LocatedIn and PlaceOfDeath. We conjecture that this is because location entities usually appear at sentence ends in Wikipedia articles, e.g., Obama was born in ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Honolulu, Hawaii.. This sentence pattern is similar to our templates and BERT may learn to rely mostly on the left context to make predictions. For most relations that include answers that are person names, BERT lags behind both GPT-2 and our model. ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Comparing the top and bottom five relations, we observe that BERT’s performance is correlated with the size of the candidate set, while WKLM and GPT-2 are less sensitive to this number. A similar pattern exists between models’ performance and the cardinality of groundtruth answers, i.e., our model achieves similar performance on both single-answer and multiple-answer queries while BERT is usually better at single-answer queries. WKLM both outperforms BERT and GPT-2 and achieves robust performance across relations with different properties. Visualization of correlations between relation properties and model performance can be found in the appendix. ",
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+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/37815abb98f5a94ae584d39e8b31b9b8867be5e3b06ca0698e196d902c9ad025.jpg",
+        "table_caption": [
+            "Table 1: Zero-Shot Fact Completion Results. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Relation Name</td><td>#of Candidates</td><td>#of Answers</td><td>BERT-base</td><td>Model BERT-large</td><td>GPT-2</td><td>Ours</td></tr><tr><td>HASCHILD (P40)</td><td>906</td><td>3.8</td><td>9.00</td><td>6.00</td><td>20.5</td><td>63.5</td></tr><tr><td>NOTABLEWORK (P800)</td><td>901</td><td>5.2</td><td>1.88</td><td>2.56</td><td>2.39</td><td>4.10</td></tr><tr><td>CAPITALOF (P36)</td><td>820</td><td>2.2</td><td>1.87</td><td>1.55</td><td>15.8</td><td>49.1</td></tr><tr><td>FOUNDEDBY (P112)</td><td>798</td><td>3.7</td><td>2.44</td><td>1.93</td><td>8.65</td><td>24.2</td></tr><tr><td>CREATOR (P170)</td><td>536</td><td>3.6</td><td>4.57</td><td>4.57</td><td>7.27</td><td>9.84</td></tr><tr><td>PLACEOFBIRTH (P19)</td><td>497</td><td>1.8</td><td>19.2</td><td>30.9</td><td>8.95</td><td>23.2</td></tr><tr><td>LOCATEDIN (P131))</td><td>382</td><td>1.9</td><td>13.2</td><td>52.5</td><td>21.0</td><td>61.1</td></tr><tr><td>EDUCATEDAT (P69)</td><td>374</td><td>4.1</td><td>9.10</td><td>7.93</td><td>11.0</td><td>16.9</td></tr><tr><td>PLACEOFDEATH (P20)</td><td>313</td><td>1.7</td><td>43.0</td><td>42.6</td><td>8.83</td><td>26.5</td></tr><tr><td>OCCUPATION (P106)</td><td>190</td><td>1.4</td><td>8.58</td><td>10.7</td><td>9.17</td><td>10.7</td></tr><tr><td>Average Hits @ 10</td><td>1</td><td>-</td><td>11.3</td><td>16.1</td><td>16.3</td><td>28.9</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "3.2 DOWNSTREAM TASKS ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Background knowledge is important for language understanding. We expect our pretraining approach to be beneficial to NLP applications where entity-level knowledge is essential. We consider two such applications: question answering and entity-typing. We find that a large portion of the questions in existing QA datasets are about entities and involve entity relations. In a way, our pretraining objective is analogous to question answering in a multiple-choice setting (Hermann et al., 2015). The entity-typing task requires the model to predict a set of correct types of entity mentions in a short context. The context itself can be insufficient and the training data for this task is small and noisy. We believe a model that encodes background entity knowledge can help in both cases. ",
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+    {
+        "type": "text",
+        "text": "3.2.1 QUESTION ANSWERING ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Datasets We consider four question answering datasets: ",
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+    {
+        "type": "text",
+        "text": "• WebQuestions (Berant et al., 2013) is originally a dataset for knowledge base question answering. The questions are collected using Google Suggest API and are all asking about simple relational facts of Freebase entities.   \nTriviaQA7 (Joshi et al., 2017) includes questions from trivia and quiz-league websites. Apart from a small portion of questions to which the answers are numbers and free texts, $9 2 . 8 5 \\%$ of the answers are Wikipedia entities. Quasar-T (Dhingra et al., 2017) is another dataset that includes trivia questions. Most of the answers in this dataset are none phrases. According to our manual analysis on random samples, $8 8 \\%$ of the answers are real-world entities8.   \nSearchQA (Dunn et al., 2017) uses questions from the television quiz show Jeopardy! and we also find that almost all of the answers are real-world entities. ",
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+    },
+    {
+        "type": "text",
+        "text": "Questions in all three datasets are created without the context of a paragraph, which resembles the scenario of practical question answering applications. All the questions except WebQuestions are written by humans. This indicates that humans are generally interested to ask questions to seek information about entities. We show the statistics and example questions in Table 2. We split the training data (created by distant supervision) of WebQuestions with a ratio (9:1) for training and development. Since our model is based on our own BERT implementations, in addition to the aforementioned entity-related datasets, we first use the standard SQuAD (Rajpurkar et al., 2016) benchmark to validate our model’s answer extraction performance. ",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/237dcef3c93c1437051e3eaca6d77690a8bf9b594803ead5b6eb58d49adc1b82.jpg",
+        "table_caption": [
+            "Table 2: Properties of the QA Datasets. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Dataset</td><td>Train</td><td>Valid</td><td>Test</td><td>Example Questions</td></tr><tr><td>WebQuestions</td><td>3778</td><td></td><td>2032</td><td>Who plays Stewie Griffn on Family Guy?</td></tr><tr><td>TriviaQA</td><td>87291</td><td>11274</td><td>10790</td><td>What is the Japanese share index called?</td></tr><tr><td>SearchQA</td><td>99811</td><td>13893</td><td>27247</td><td>Hero several books 11 discover&#x27;s wizard?</td></tr><tr><td>Quasar-T</td><td>37012</td><td>3000</td><td>3000</td><td>Which vegetable isa Welsh emblem?</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Settings We adopt the fine-tuning approach to extract answer spans with pretrained models. We add linear layers over the last hidden states of the pretrained models to predict the start and end positions of the answer. Unlike $\\mathrm { S Q u A D }$ , questions in the datasets we use are not paired with paragraphs that contain the answer. We follow previous work (Chen et al., 2017; Wang et al., 2018a) and retrieve context paragraphs with information retrieval systems. Details of the context retrieval process for each dataset can be found in the appendix. Reader models are trained with distantly supervised data, i.e., we treat any text span in any retrieved paragraph as ground truth as long as it matches the original answers. Since the reader model needs to read multiple paragraphs to predict a single answer at inference time, we also train a BERT based paragraph ranker with distant-supervised data to assign each paragraph a relevance score. The paragraph ranker takes question and paragraph pairs and predicts a score in the range [0, 1] for each pair. During inference, for each question and its evidence paragraph set, we first use the paragraph reader to extract the best answer from each paragraph. These answers are then ranked based on a linear combination of the answer extraction score (a log sum of the answer start and end scores) and the paragraph relevance score. We also evaluate model performance without using the relevance scores. ",
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+    {
+        "type": "text",
+        "text": "Open-Domain QA Baselines We compare our QA model with the following systems: ",
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+    {
+        "type": "text",
+        "text": "• DrQA (Chen et al., 2017) is an open-domain QA system which uses TF-IDF with bigram features for ranking and a simple attentive reader for answer extraction.   \n$\\mathbf { R } ^ { 3 }$ (Wang et al., 2018a) is a reinforcement learning based system which jointly trains a paragraph ranker and a document reader. DSQA (Lin et al., 2018) uses RNN-based paragraph ranker and jointly trains the paragraph ranker and attentive paragraph ranker with a multi-task loss. Evidence Aggregation (Wang et al., 2018b) uses a hybrid answer reranking module to aggregate answer information from multiple paragraphs and rerank the answers extracted from multiple paragraphs. BERTserini (Yang et al., 2019a) is a BERT-based open-domain QA system, which uses BM25-based retriever to retrieve 100 paragraphs and a BERT-based reader to extract answers. The paragraph reader is either trained with SQuAD (Rajpurkar et al., 2016) data or distant-supervision data (Yang et al., 2019b) ORQA (Lee et al., 2019) replaces the traditional BM25 ranking with a BERT-based ranker. The ranker model is pretrained on the whole Wikipedia corpus with an inverse cloze task which simulates the matching between questions and paragraphs. All text blocks in Wikipedia are be pre-encoded as vectors and retrieved with Locality Sensitive Hashing. ",
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+    {
+        "type": "text",
+        "text": "Results Table 3 shows the SQuAD results and Table 4 shows the open-domain results on the four datasets that are highly entity-related. From the SQuAD results, we observe that our BERT reimplementation performs better than the original model this is due to the fact that it is trained for twice as many updates: 2 million vs. 1 million for the original BERT. Although lots of the answers in SQuAD are non-entity spans, the WKLM model we propose achieves better performance than BERT. We believe the improvement is due to both the masked language model and entity replacement objectives. Ablation experiments on the training objectives will be discussed in $\\ S 3 . 2 . 3$ . ",
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+    {
+        "type": "text",
+        "text": "",
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+    {
+        "type": "text",
+        "text": "Having established that our BERT re-implementation performs better than the original model, we compare with only our own BERT for the following experiments. From Table 4, we see that our model produces consistent improvements across different datasets. Compared to the $0 . 8 \\ : \\mathrm { F 1 }$ improvements over BERT on SQuAD, we achieve an average of $2 . 7 ~ \\mathrm { F 1 }$ improvements over BERT on entity-related datasets when the ranking scores are not used. On TriviaQA and Quasar-T, WKLM outperforms our BERT even when it uses ranking scores. Improvements in natural language question datasets (WebQuestions, TriviaQA, and Quasar-T) are more significant than SearchQA where the questions are informal queries. When we utilize ranking scores from a simple BERT based ranker, we are able to achieve the state-of-the-art on three of the four datasets. ",
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+    {
+        "type": "table",
+        "img_path": "images/1854d7a4ca65eaaf497369b4e325a9a8cdad84e041b310ba25a74e5ed00a7f0e.jpg",
+        "table_caption": [
+            "Table 3: SQuAD Dev Results. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>EM</td><td>F1</td></tr><tr><td>Google&#x27;s BERT-base</td><td>80.8</td><td>88.5</td></tr><tr><td>Google&#x27;s BERT-large</td><td>84.1</td><td>90.9</td></tr><tr><td>Our BERT-base</td><td>83.4</td><td>90.5</td></tr><tr><td>WKLM (base)</td><td>84.3</td><td>91.3</td></tr></table>",
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+        "type": "text",
+        "text": "",
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+    {
+        "type": "table",
+        "img_path": "images/8009850beb058acab121c395c79c8d81cf79e2f65963c628b1a7bb6c30196764.jpg",
+        "table_caption": [
+            "Table 4: Open-domain QA Results. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>WebQuestions EM</td><td>F1</td><td>TriviaQA EM</td><td>F1</td><td>Quasar-T EM</td><td>F1</td><td>SearchQA EM</td><td>F1</td></tr><tr><td>DrQA (Chen et al., 2017)</td><td>20.7</td><td>1</td><td>-</td><td>1</td><td>-</td><td>-</td><td>-</td><td>1</td></tr><tr><td>R (Wang et al.,2018a)</td><td>-</td><td>1</td><td>50.6</td><td>57.3</td><td>42.3</td><td>49.6</td><td>57.0</td><td>63.2</td></tr><tr><td>DSQA (Lin et al., 2018)</td><td>18.5</td><td>25.6</td><td>48.7</td><td>56.3</td><td>42.2</td><td>49.3</td><td>49.0</td><td>55.3</td></tr><tr><td>Evidence Agg. (Wang et al.,2018b)</td><td>1</td><td>1</td><td>50.6</td><td>57.3</td><td>42.3</td><td>49.6</td><td>57.0</td><td>63.2</td></tr><tr><td>BERTserini (Yang et al.,2019a)</td><td>-</td><td>-</td><td>51.0</td><td>56.3</td><td>1</td><td>-</td><td>1</td><td>1</td></tr><tr><td>BERTserini+DS (Yang et al., 2019b)</td><td>=</td><td>=</td><td>54.4</td><td>60.2</td><td>1</td><td>=</td><td>-</td><td>1</td></tr><tr><td>ORQA (Lee et al., 2019)</td><td>36.4</td><td>1</td><td>45.0</td><td>-</td><td>-</td><td>-</td><td>-</td><td>1</td></tr><tr><td>Our BERT</td><td>29.2</td><td>35.5</td><td>48.7</td><td>53.2</td><td>40.4</td><td>46.1</td><td>57.1</td><td>61.9</td></tr><tr><td>Our BERT +Ranking score</td><td>32.2</td><td>38.9</td><td>52.1</td><td>56.5</td><td>43.2</td><td>49.2</td><td>60.6</td><td>65.9</td></tr><tr><td>WKLM</td><td>30.8</td><td>37.9</td><td>52.2</td><td>56.7</td><td>43.7</td><td>49.9</td><td>58.7</td><td>63.3</td></tr><tr><td>WKLM + Ranking score</td><td>34.6</td><td>41.8</td><td>58.1</td><td>63.1</td><td>45.8</td><td>52.2</td><td>61.7</td><td>66.7</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "3.2.2 ENTITY TYPING ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "To compare with an existing study (Zhang et al., 2019) that also attempts to incorporate entity knowledge into language models, we consider an additional entity typing task using the large FIGER dataset (Ling & Weld, 2012). The task is to assign a fine-grained type to entity mentions. We do that by adding two special tokens before and after the entity span to mark the entity position. We use the final representation of the start token ([CLS]) to predict the entity types. The model is fine-tuned on weakly-supervised training data with binary cross-entropy loss. We evaluate the models using strict accuracy, loose micro, and macro F1 scores. ",
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+    {
+        "type": "text",
+        "text": "We show the results in Table 5. We compare our model with two non-BERT neural baselines (Inui et al., 2017) that integrate a set of hand-crafted features: LSTM $^ +$ Hand-crafted and Attentive $^ +$ ",
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+    {
+        "type": "table",
+        "img_path": "images/d02b780701e2abd4e6c8b6f2b30fdf34aee47bee8a735c6bfe1bb0f3379a1536.jpg",
+        "table_caption": [
+            "Table 5: Fine-grained Entity Typing Results on the FIGER dataset. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>Acc</td><td>Ma-F1</td><td>Mi-F1</td></tr><tr><td>LSTM+ Hand-crafted (Inui et al.,2017)</td><td>57.02</td><td>76.98</td><td>73.94</td></tr><tr><td>Attentive + Hand-crafted (Inui et al.,2017) BERT baseline (Zhang et al.,2019)</td><td>59.68 52.04</td><td>78.97 75.16</td><td>75.36 71.63</td></tr><tr><td>ERNIE (Zhang et al., 2019)</td><td>57.19</td><td>75.61</td><td>73.39</td></tr><tr><td>Our BERT</td><td>54.53</td><td></td><td></td></tr><tr><td>WKLM</td><td>60.21</td><td>79.57 81.99</td><td>74.74 77.00</td></tr></table>",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Hand-crafted; a vanilla BERT baseline and the ERNIE model (Zhang et al., 2019) that enhances BERT with knowledge base embeddings. ",
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+        "type": "text",
+        "text": "First, we see that naively applying BERT is less effective than simple models combined with sparse hand-crafted features. Although the ERNIE model can improve over BERT by 5.15 points, its performance still lags behind models that make good use of hand-crafted features. In contrast, although based on a stronger BERT model, our model achieves larger absolute improvements (5.68 points) and sets a new state-of-the-art for this task. Given the larger improvement margin, we believe our model that directly learn knowledge from text is more effective than the ERNIE method. ",
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+    {
+        "type": "text",
+        "text": "3.2.3 ABLATION STUDY: THE EFFECT OF MASKED LANGUAGE MODEL LOSS ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In view of a recent study (Liu et al., 2019b) showing simply extending the training time of BERT leads to stronger performance on various downstream tasks, we conduct further analysis to differentiate the effects of entity replacement training and masked language modeling. We compare our model with three variants: a model pretrained only with the knowledge learning objective (WKLM without MLM), a model trained with both knowledge learning and masked language modeling with more masked words (WKLM with $1 5 \\%$ MLM) and a BERT model trained with additional 1 million updates on English Wikipedia $\\mathbf { \\left( B E R T + 1 M \\right) }$ MLM updates) and no knowledge learning. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The ablation results are shown in Table 6. The results of WKLM without MLM validate that adding the language model objective is essential for downstream performance. We also find that masking out too many words (i.e., $1 5 \\%$ masking ratio as in the original BERT) leads to worse results. We conjecture that too many masked words outside entity mentions break parts of the context information and introduce noisy signals to knowledge learning. Results of continued BERT training show that more MLM updates are often beneficial, especially for SQuAD. However, on tasks that are more entity-centric, continued MLM training is less effective than our WKLM method. This suggests that our WKLM method could serve as an effective complementary recipe to masked language modeling when applied to entity-related NLP tasks. ",
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+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/d4568ab64b2ca24e5cde277fd34757bae39b25014cd616d7d127afbc3998a66f.jpg",
+        "table_caption": [
+            "Table 6: Ablation Studies on Masked Language Model and Masking Ratios. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td colspan=\"2\">SQuAD EM F1</td><td colspan=\"2\">TriviaQA EM F1</td><td colspan=\"2\">Quasar-T EM F1</td><td>FIGER Acc</td></tr><tr><td>Our BERT</td><td>83.4</td><td>90.5</td><td>48.7</td><td>53.2</td><td>40.4</td><td>46.1</td><td>54.53</td></tr><tr><td>WKLM</td><td>84.3</td><td>91.3</td><td>52.2</td><td>56.7</td><td>43.7</td><td>49.9</td><td>60.21</td></tr><tr><td>WKLM without MLM</td><td>80.5</td><td>87.6</td><td>48.2</td><td>52.5</td><td>42.2</td><td>48.1</td><td>58.44</td></tr><tr><td>WKLM with 15% masking</td><td>84.1</td><td>91.0</td><td>51.0</td><td>55.3</td><td>42.9</td><td>49.0</td><td>59.68</td></tr><tr><td>Our BERT + 1MMLMupdates</td><td>84.4</td><td>91.1</td><td>52.0</td><td>56.3</td><td>42.3</td><td>48.2</td><td>54.17</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "4 RELATED WORK ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Pretrained Language Representations Early research on language representations focused on static unsupervised word representations (Mikolov et al., 2013; Pennington et al., 2014). Word embeddings leverage co-occurrences to learn latent word vectors that approximately reflect word semantics. Given that words can have different meanings in different contexts, more recent studies (McCann et al., 2017; Peters et al., 2018a) show that contextual language representations can be more powerful than static word embeddings in downstream tasks. This direction has been further explored at a larger scale with efficient Transformer architectures (Radford et al., 2019; Devlin et al., 2019; Yang et al., 2019c). Our WKLM method is based on these techniques and we focus on improving the knowledge ability of pretrained models. ",
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+    {
+        "type": "text",
+        "text": "Knowledge-Enhanced NLP Models Background knowledge has been considered an indispensable part of language understanding (Fillmore et al., 1976; Minsky, 1988). As standard language encoders usually do not explicitly model knowledge, recent studies (Ahn et al., 2016; Yang & Mitchell, 2017; Logan et al., 2019; Liu et al., 2019a) have explored methods to incorporate external knowledge into NLP models. Most of these methods rely on additional inputs such as entity representations from structured knowledge bases. With the breakthrough of large-scale pretrained language encoders (Devlin et al., 2019), Zhang et al. (2019) and Peters et al. (2019) adopt similar ideas and propose entity-level knowledge enhancement training objectives to incorporate knowledge into pretrained models. Other recent studies (Mihaylov & Frank, 2018; Xiong et al., 2019) leverage external knowledge bases to enhance text-based question answering models. In contrast to these methods, our method utilizes minimal external entity information and does not require additional memory or architectural changes when applied to downstream tasks. ",
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+        "type": "text",
+        "text": "5 CONCLUSION ",
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+        "text": "A APPENDIX ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Implementation Details and Hyperparameters We implement our method using Fairseq Ott et al. (2019) and the fact completion baselines are implemented with Huggingface’s PytorchTransformers9. We pretrain the models with 32 V100 GPUs for 3 days. We use at most 2 GPUs for fine-tuning the paragraph reader, use 8 GPUs for fine-tuning the paragraph ranker. The entity-typing experiments require larger batch sizes and take 8 GPUs for training. ",
+        "bbox": [
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+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "For the knowledge learning pretraining phase, we use the Adam optimizer (Kingma & Ba, 2014) with learning rate 1e-5, batch size 128 and weight decay 0.01. The model is pretrained on 32 V100 GPUs for 3 days. To train the paragraph reader for open-domain QA, we select the best learning rate from $\\{ 1 \\mathrm { e } { - } 6 , 5 \\mathrm { e } { - } 6 , 1 \\mathrm { e } { - } 5 , 2 \\mathrm { e } { - } 5 \\}$ and last layer dropout ratio from $\\{ 0 . 1 , 0 . 2 \\}$ . We set the maximum training epoch to be 10 and batch size to be 32. The maximal input sequence length is 512 for WebQuestions and 128 for the other three datasets that use sentence-level paragraphs. For the paragraph ranker, we choose learning rate from $\\{ 1 \\mathrm { e } { - } 5 , 2 \\mathrm { e } { - } 5 , 5 \\mathrm { e } { - } 6 \\}$ , use dropout 0.1 and batch size 256. The maximal sequence length for each dataset is consistent with the one we used for training the paragraph reader. The linear combination of ranking and extraction scores is selected based on validation performance. For $\\mathrm { S Q u A D }$ experiments, we select learning rate from {1e-5, 5e-6, 2e-5, 3e-5}, learning rate from $\\{ 8 , 1 6 \\}$ , last layer dropout ratio from $\\{ 0 . \\bar { 1 } , 0 . 2 \\}$ . We set the maximal sequence length as 512 and the maximal training epoch as 5. For entity typing, we select learning rate from $\\{ 1 \\mathrm { e } { - } 5 , 2 \\mathrm { e } { - } 5 , 3 \\mathrm { e } { - } 5 , 5 \\mathrm { e } { - } 5 \\}$ and batch size from $\\{ 1 2 8 , 2 5 6 \\}$ . We set the maximal sequence length to be 256, the last layer dropout ratio to be 0.1. The model is fine-tuned for at most 3 epochs to prevent overfitting. The threshold for type prediction is selected on the validation set. ",
+        "bbox": [
+            173,
+            210,
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+            417
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Context Collection for QA Datasets For WebQuestions, we collect evidence context using the document retriever of DrQA (Chen et al., 2017), which uses TF-IDF based metric to retrieve the top 5 Wikipedia articles. For Quasar-T, we use Lucene ranked paragraphs. For SearchQA and TriviaQA, we use paragraphs ranked by search engines. Following existing research (Wang et al., 2018b; Lin et al., 2018), we use sentence-level paragraphs for SearchQA (50 sentences), TriviaQA (100 sentences) and SearchQA (100 sentences). ",
+        "bbox": [
+            174,
+            434,
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+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Correlation between Fact Completion Results and Properties of Relations Figure 2 shows the fact completion results of BERT are unstable on different relations with different properties, i.e., BERT’s performance is strongly correlated with the size of candidate entity set and the number of groundtruth answers. Compared to BERT, WKLM is often less sensitive to these two factors. ",
+        "bbox": [
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+        "page_idx": 12
+    },
+    {
+        "type": "image",
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+        "image_caption": [
+            "Figure 2: Left: Correlation between candidate set size and hits $@ 1 0$ ; Right: Correlation between number of groundtruth answers and hits $@ 1 0$ . "
+        ],
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parse/train/Hkex2a4FPr/Hkex2a4FPr.md

@@ -0,0 +1,349 @@
+# ON VARIATIONAL LEARNING OF CONTROLLABLE REPRESENTATIONS FOR TEXT WITHOUT SUPERVISION
+
+Anonymous authors Paper under double-blind review
+
+# ABSTRACT
+
+The variational autoencoder (VAE) has found success in modelling the manifold of natural images on certain datasets, allowing meaningful images to be generated while interpolating or extrapolating in the latent code space, but it is unclear whether similar capabilities are feasible for text considering its discrete nature. In this work, we investigate the reason why unsupervised learning of controllable representations fails for text. We find that traditional sequence VAEs can learn disentangled representations through their latent codes to some extent, but they often fail to properly decode when the latent factor is being manipulated, because the manipulated codes often land in holes or vacant regions in the aggregated posterior latent space, which the decoding network is not trained to process. Both as a validation of the explanation and as a fix to the problem, we propose to constrain the posterior mean to a learned probability simplex, and performs manipulation within this simplex. Our proposed method mitigates the latent vacancy problem and achieves the first success in unsupervised learning of controllable representations for text. Empirically, our method significantly outperforms unsupervised baselines and is competitive with strong supervised approaches on text style transfer. Furthermore, when switching the latent factor (e.g., topic) during a long sentence generation, our proposed framework can often complete the sentence in a seemingly natural way – a capability that has never been attempted by previous methods.
+
+# 1 INTRODUCTION
+
+High-dimensional data, such as images and text, are often causally generated through the interaction of many complex factors, such as lighting and pose in images or style and content in texts. Recently, VAEs and other unsupervised generative models have found successes in modelling the manifold of natural images (Higgins et al., 2017; Kumar et al., 2017; Chen et al., 2016). These models often discover controllable latent factors that allow manipulation of the images through conditional generation from interpolated or extrapolated latent codes, often with impressive quality. On the other hand, while various attributes of text such as sentiment and topic can be discovered in an unsupervised way, manipulating the text by changing these learned factors have not been possible with unsupervised generative models to the best of our knowledge. C´ıfka et al. (2018); Zhao et al. (2018) observed that text manipulation is generally more challenging compared to images, and the successes of these models cannot be directly transferred to texts.
+
+Controllable text generation aims at generating realistic text with control over various attributes including sentiment, topic and other high-level properties. Besides being a scientific curiosity, the possibility of unsupervised controllable text generation could help in a wide range of application, e.g., dialogues systems (Wen et al., 2016). Existing promising progress (Shen et al., 2017; Fu et al., 2018; Li et al., 2018; Sudhakar et al., 2019) all relies on supervised learning from annotated attributes to generate the text in a controllable fashion. The high cost of labelling large training corpora with attributes of interest limits the usage of these models, as pre-existing annotations often do not align with some downstream goal. Even if cheap labels are available, for example, review scores as a proxy for sentiment, the control is limited to the variation defined by the attributes.
+
+In this work, we examine the obstacles that prevent sequence VAEs from performing well in unsupervised controllable text generation. We empirically discover that manipulating the latent factors for typical semantic variations often leads to latent codes that reside in some low-density region of the aggregated posterior distribution. In other words, there are vacant regions in the latent code space (Makhzani et al., 2015; Rezende & Viola, 2018) not being considered by the decoding network, at least not at convergence. As a result, the decoding network is unable to process such manipulated latent codes, yielding unpredictable generation results of low quality.
+
+In order to mitigate the latent vacancy problem, we propose to constrain the posterior mean to a learned probability simplex and only perform manipulation within the probability simplex. Two regularizers are added to the original objective of VAE. The first enforces an orthogonal structure of the learned probability simplex; the other encourages this simplex to be filled without holes. Besides confirming that latent vacancy is indeed a cause of failure in previous sequence VAEs’, it is also the first successful attempt towards unsupervised learning of controllable representations for text to the best of our knowledge. Experimental results on text style transfer show that our approach significantly outperforms unsupervised baselines, and is competitive with strong supervised approaches across a wide range of evaluation metrics. Our proposed framework also enables finer-grained and more flexible control over text generation. In particular, we can switch the topic in the middle of sentence generation, and the model will often still find a way to complete the sentence in a natural way.
+
+# 2 BACKGROUND: VARIATIONAL AUTOENCODERS
+
+The variational autoencoder (VAE) (Kingma & Welling, 2013) is a generative model defined by a prior $p ( z )$ and a conditional distribution $p _ { \pmb { \theta } } ( \pmb { x } | \pmb { z } )$ . The VAE is trained to optimize a tractable variational lower bound of $\log p \pmb { \theta } ( \pmb { x } )$ :
+
+$$
+\begin{array} { r } { \mathcal { L } _ { \mathrm { V A E } } ( \pmb { x } ; \pmb { \theta } , \phi ) = \mathbf { E } _ { z \sim q _ { \phi } ( z | \pmb { x } ) } [ \log p _ { \pmb { \theta } } ( \pmb { x } | z ) ] - D _ { \mathrm { K L } } ( q _ { \phi } ( z | \pmb { x } ) | | p ( z ) ) , } \end{array}
+$$
+
+where $q _ { \phi } ( z | \pmb { x } )$ is a variational distribution parameterized by an encoding network with parameters $\phi$ , and $p _ { \pmb { \theta } } ( \pmb { x } | \pmb { z } )$ denotes the decoding network with parameters $\pmb \theta$ . This objective tries to minimize the reconstruction error to generate the data, and at the same time regularizes $q _ { \phi } ( { \pmb z } | { \pmb x } )$ towards the prior $p ( z )$ . In this paper, $p ( z )$ is chosen as $\mathcal { N } ( \mathbf { 0 } , I )$ . For text modelling, the input $\pmb { x }$ is some observed text. Both the encoding and decoding network are usually recurrent neural networks.
+
+Note that during learning, the decoding network $p _ { \pmb { \theta } }$ only learns to decode conditioned on $\textit { \textbf { z } }$ that are sampled from $q _ { \phi } ( z | \pmb { x } )$ . In other words, the decoding network only learns to process $_ { z }$ sampled from the aggregated posterior distribution $q _ { \phi } ( z ) = \mathbf { E } _ { \pmb { x } \sim p _ { d } ( \pmb { x } ) } q _ { \phi } ( z | \pmb { x } )$ , where $p _ { d } ( \pmb { x } )$ is the data distribution. If $q _ { \phi } ( z )$ has regions of low density, there is no guarantee that $p _ { \pmb { \theta } }$ would decode well in such regions. This is an important intuition that will become central to our analysis in Sec. 3.
+
+# 3 LATENT VACANCY PREVENTS EFFECTIVE MANIPULATION
+
+In this section, we take a deeper look into the aggregated posterior latent space of sequence VAE trained on text, and provide justification for the alternative solution we propose in Section 4.
+
+# 3.1 OBSERVATIONS FROM UNSUPERVISED SENTIMENT MANIPULATION
+
+As pointed out by Bowman et al. (2015), one of the motivations to apply VAEs on text is to allow generation of the sentences conditioned on extrinsic features by controlling the latent codes. Without annotated labels, no previous methods have successfully learned controllable latent factors as mentioned in Sec. 1. To understand what is missing, we conduct exploratory experiments to use VAE for unsupervised sentiment manipulation.
+
+We use the Yelp restaurant reviews dataset and the same data split following Li et al. (2018). We train a $\beta$ -VAE (Higgins et al., $2 0 1 7 ) ^ { 1 }$ with a latent space of 80 dimensions, an LSTM encoder, and an LSTM decoder. Details about this experiment are described in Appendix A.1.
+
+By inspecting the accuracy on the validation set, we find that there exists one dimension of latent code achieving higher than $9 0 \%$ sentiment classification accuracy by its value alone, while other latent codes get accuracy around $5 0 \%$ . Further details can be found in Appendix A.2. It means that this latent dimension is an effective sentiment indicator. Similar phenomena have been observed in large-scale language models (Radford et al., 2017). However, the direct influence on the generative process of the model observed in Radford et al. (2017) does not apply on the VAE. When we try to perform sentiment manipulation by modifying this latent dimension2, the decoding network fails to generate the desired outputs most of the time, as evidenced by the poor quantitative evaluation in Table. 1, and poor samples shown in Appendix A.3.
+
+![](images/f11826ce918d43826e0d0d542c73a7fdac2de1b3d7a07a63d866b55ecce23d72.jpg)  
+Figure 1: Illustration of why latent vacancy prevents effective manipulation in VAEs.
+
+![](images/166547c34d2bc45ed7e6d9dfa9ac8537ac6698379886be3248661cf906fba412.jpg)
+
+![](images/c13255d5d4570513678c7c4342ce695904e93e3f31bff68d001a4853a651a7b6.jpg)  
+Figure 2: CP-VAE, mapping the posterior to a probability simplex with orthogonal basis vectors.   
+Figure 3: (a) Comparisons between $\beta$ -VAE and CP-VAE considering density under the aggregated posterior distribution, the blue and green solid arrows match with the manipulation illustrated in Fig 1 and 2; (b) Histogram of original and modified latent codes’ NLL in $\beta$ -VAE; (c) Histogram of original and modified latent codes’ NLL in CP-VAE.
+
+# 3.2 LATENT VACANCY IN TEXT MODELLING
+
+One possible reason for the failure is that the decoding network is never trained on codes like the manipulated ones. This is the case if the aggregated posterior has holes or regions of low density, and the manipulated codes fall into such vacant regions. Supposing the aggregated posterior latent space possesses a shape as shown in Fig. 1, the direct manipulated latent codes will fall out of the aggregated posterior latent space for most input samples. Such latent codes are never seen by the model during training and possess a low density under the aggregated posterior distribution, leading to unpredictable behaviours during decoding.
+
+To verify our hypothesis demonstrated in Fig. 1, we empirically estimate the density of sentimentmanipulated codes under the aggregated posterior distribution of our trained VAE. Here, we approximate the data distribution $p _ { d } ( \pmb { x } )$ with the empirical distribution over all the training samples. As a result, the estimated aggregated posterior distribution is a large mixture of Gaussian distribution. For all 1000 test samples, we move the dimension of code capturing sentiment from $\mu - 2 \sigma$ to $\mu + 2 \sigma$ where $\mu$ and $\sigma$ are the mean and the standard deviation estimated on all the training samples and measure the averaged negative log-likelihood (NLL) under the aggregated posterior distribution. As depicted in Fig. 3 (a), the NLL plotted in blue dot curve rises sharply when moving away from $\mu$ even if there is only one dimension of code is changing, indicating the existence of the vacancy in the aggregated posterior latent space. In addition, we draw the histogram of all the test samples’ NLL considering their original latent codes and modified ones in Fig. 3 (b). The histogram shows that there is a large divergence in NLL between the original latent codes and the modified ones. Also, the modified latent codes have two separate modes, confirming the irregular shape of the aggregated posterior latent space. In order to resolve this issue, the approach proposed in this work is to constrain the posterior in a way that the manipulation only happens in a learned simplex, as depicted in Fig. 2. In this constrained subspace, the phenomenom of low density holes of aggregated posterior is significantly reduced, as Fig. 3 (a) and (c) empirically show that there is little change in NLL of original versus modified codes. The details of our method is presented in the next section.
+
+# 4 METHOD
+
+# 4.1 OVERVIEW
+
+The experiments conducted in Sec. 3 validates the existence of vacancy in the aggregated posterior latent space. One potential way to resolve the problem is to better match the aggregated posterior with the prior (Makhzani et al., 2015; Tomczak & Welling, 2017; Zhao et al., 2018). However, in terms of unsupervised learning of controllable representation for text, these previous methods have not shown successes; Zhao et al. (2018) only attempted supervised text style transfer, and also reported negative results from the AAE (Makhzani et al., 2015). Another way to resolve the vacancy issue is to directly enforce that the aggregated posterior itself has no vacant region anywhere where we would like to perform latent code manipulation. We propose to map the posterior Gaussian mean to a constrained space, more specifically a learned probability simplex, where we can encourage the constrained latent space to be filled without vacancy, and perform manipulation to be within this simplex. As illustrated in Fig. 2, we add an additional mapping function as part of the encoding network which maps the mean of the Gaussian posterior to a constrained space. Two regularization terms are introduced later to ensure the learned simplex is not degenerate and that this subspace is well filled.
+
+In addition, we separately model the relevant factors that we wish to control and the irrelevant factors by splitting $\textit { \textbf { z } }$ into two parts, $z ^ { ( 1 ) }$ and $\pmb { z } ^ { ( 2 ) }$ , following prior work (Bao et al., 2019). The first part captures the relevant factors that are dominant in the data without an inductive bias from external signals, while the second part learns to encode the remaining local information that is useful for reconstructing the source sentences. As a result, $q _ { \phi } ( { \pmb z } | { \pmb x } )$ is decomposed into $q _ { \phi _ { 1 } } ( { \pmb z } ^ { ( 1 ) } | { \pmb x } ) q _ { \phi _ { 2 } } ( { \pmb z } ^ { ( 2 ) } | { \pmb x } )$ where $\pmb { \phi } = \phi _ { 1 } \cup \phi _ { 2 }$ . With diagonal covariances the KL divergence term in Eq. 1 splits into two separate KL terms. In practice, we use a MLP encoding network to parametrize $\pmb { z } ^ { ( 1 ) }$ with some sentence representations as the input (e.g., averaging GloVe embeddings (Pennington et al., 2014) over the input tokens) and a LSTM encoding network to parametrize $z ^ { ( 2 ) }$ . We only constrain the posterior of $z ^ { ( 1 ) }$ and $\pmb { z } ^ { ( 2 ) }$ is optimized the same way as the traditional VAE.
+
+# 4.2 CONSTRAINING THE POSTERIOR
+
+We now describe how to map the mean $\pmb { \mu }$ of the Gaussian posterior for $z ^ { ( 1 ) } \in \mathbb { R } ^ { N }$ to a constrained latent space. We would like to constrain the mean $\pmb { \mu }$ to have a structure as follows:
+
+$$
+\mu = \sum _ { i = 1 } ^ { K } p _ { i } e _ { i } , \quad \sum _ { i = 1 } ^ { K } p _ { i } = 1 , \quad \langle e _ { i } , e _ { j } \rangle = 0 , i \neq j , \quad K \leq N
+$$
+
+where $e _ { i }$ are vectors representing the relevant factors, $p _ { i }$ is the proportion of $i$ th relevant factor encoded in $z ^ { ( 1 ) }$ and $K$ is a hyperparameter indicating the number of relevant factors to discover. In other words, the mean of the Gaussian posterior of $\pmb { z } ^ { ( \bar { 1 } ) }$ is constrained to be inside a $K$ -dimension probability simplex in $\mathbb { R } ^ { N }$ whose vertices are represented by the orthogonal basis vectors $\mathbf { \Delta } e _ { i } , i = 1 , \ldots , K$ . Given the outputs of the MLP encoder $\pmb { h }$ and $\log \pmb { \sigma } ^ { 2 }$ , we learn an additional mapping function $\pi$ which maps $\pmb { h }$ to the constrained posterior space, which can be treated as part of the encoding network:
+
+$$
+\pmb { \mu } = \pi ( \pmb { h } ) = \pmb { E } \cdot \mathrm { s o f t m a x } ( \pmb { W } \pmb { h } + \pmb { b } ) ,
+$$
+
+where $\pmb { { \cal E } } = [ \pmb { e } _ { 1 } , \dots , \pmb { e } _ { K } ]$ is a learnable embedding matrix representing the bases, $W$ is the learnable weight matrix, and $\pmb { b }$ is the learnable bias vector. As a result, the constrained posterior is parametrized by $\pmb { \mu }$ and $\log \sigma ^ { 2 }$ as a Gaussian distribution ${ \mathcal { N } } ( \mu , \mathrm { d i a g } ( \pmb { \sigma } ^ { 2 } ) )$ .
+
+With the mapping function alone, the proposed VAE suffers from posterior collapse (Bowman et al., 2015), a well-known problem where the model ignores the latent code $\textit { \textbf { z } }$ during the training. Further complicating matters is the fact that there is an abundance of signals for predicting the next token in the text, but the signals indicating high-level semantics are quite sparse. It is thus unlikely that the VAEs can capture useful relevant factors from raw text without collapse. For these reasons, we enforce orthogonality in the learnt basis vectors as defined in Eq. 2, which introduces a natural recipe to prevent posterior collapse for $\pmb { z } ^ { ( 1 ) }$ . Note that the KL divergence between $q _ { \phi _ { 1 } } ( \pmb { z } ^ { ( 1 ) } | \pmb { x } )$ and $p ( \pmb { z } ^ { ( 1 ) } )$ is
+
+$$
+D _ { \mathrm { K L } } \big ( q _ { \phi _ { 1 } } ( z ^ { ( 1 ) } | \pmb { x } ) \| p ( z ^ { ( 1 ) } ) \big ) = \frac { 1 } { 2 } \pmb { \mu } ^ { \top } \pmb { \mu } + \frac { 1 } { 2 } \left( \pmb { \sigma } ^ { \top } \pmb { \sigma } - \log \pmb { \sigma } ^ { \top } \pmb { \sigma } - 1 \right) .
+$$
+
+With orthogonality in the basis vectors, the first term in the above equation can be factorized into
+
+$$
+\pmb { \mu } ^ { \top } \pmb { \mu } = ( \sum _ { i } p _ { i } \pmb { e } _ { i } ) ^ { \top } ( \sum _ { i } p _ { i } \pmb { e } _ { i } ) = \sum _ { i } p _ { i } ^ { 2 } \pmb { e } _ { i } ^ { \top } \pmb { e } _ { i } .
+$$
+
+To encourage orthogonality in the basis vectors, a regularization term is added to the objective function:
+
+$$
+\begin{array} { r } { \mathcal { L } _ { \mathrm { R E G } } ( \pmb { x } ; \pmb { \phi } _ { 1 } ) = \| \pmb { E } ^ { \top } \pmb { E } - \alpha \pmb { I } \| , } \end{array}
+$$
+
+where $\pmb { I }$ is the identity matrix and $\alpha$ is a hyperparamter. When $\mathcal { L } _ { \mathrm { R E G } } = 0$ , $\pmb { e } _ { i } ^ { \top } \pmb { e } _ { i } = \alpha$ . In this case, $\begin{array} { r } { \pmb { \mu } ^ { \top } \pmb { \mu } = \alpha \sum _ { i } p _ { i } ^ { 2 } } \end{array}$ reaches its minimum $\frac { \alpha } { K }$ when $\pmb { p }$ is a uniform distribution. The proof can be found in Appendix C. In practice, $\mathcal { L } _ { \mathrm { R E G } }$ will quickly decrease to around 0, ensuring that the KL term will never fully collapse with the structural constraint. When it comes to controlled generation, one can choose a vertex or any desired point in the probability simplex, as illustrated in Fig. 2.
+
+Note that the constrained posterior also means that the aggregated posterior can never match the isotropic Gaussian prior. In other word, we achieve good controlled text generation potentially at the cost of poor uncontrolled generation from the prior, but such is not the focus of this current work, and could potentially be resolved by selecting or learning a better prior as in Tomczak & Welling (2017).
+
+# 4.3 FILLING THE CONSTRAINED SPACE
+
+Constraining the posterior inside a certain space does not guarantee that this space will be filled after training. In order to prevent this, we want the probability distribution over the relevant factors $\pmb { p }$ to cover as much of the constrained latent space as possible. We introduce a reconstruction error of the structured latent code in order to push $\pmb { p }$ away from a uniform distribution. For each input sentence, we randomly sample $m$ sentences from the training data as negative samples. By applying the same encoding process, we get the structured latent code $\pmb { \mu } _ { i } ^ { ( - ) }$ for each negative sample. Our goal is to make the raw latent code $\pmb { h }$ similar to the restructured latent code $\pmb { \mu }$ while different from latent codes $\pmb { \mu } _ { i } ^ { ( - ) }$ of the negative samples, so that $\pmb { p }$ is generally different for each input sample. The structured reconstruction loss is formulated as a margin loss as follows:
+
+$$
+\mathcal { L } _ { \mathrm { S - R E C } } ( \boldsymbol { x } ; \boldsymbol { \phi } _ { 1 } ) = \mathbb { E } _ { \boldsymbol { z } ^ { ( 1 ) } \sim q _ { \phi _ { 1 } } ( \boldsymbol { z } ^ { ( 1 ) } | \boldsymbol { x } ) } \left[ \frac { 1 } { m } \sum _ { i = 1 } ^ { m } \operatorname* { m a x } ( 0 , 1 - \boldsymbol { h } \cdot \boldsymbol { \mu } + \boldsymbol { h } \cdot \boldsymbol { \mu } _ { i } ^ { ( - ) } ) \right] .
+$$
+
+Our final objective function is defined as follows:
+
+$$
+\begin{array} { r } { \mathcal { L } (  { \boldsymbol { { x } } } ;  { \boldsymbol { { \theta } } } , \phi ) = \mathcal { L } _ { \mathrm { V A E } } + \mathcal { L } _ { \mathrm { R E G } } + \mathcal { L } _ { \mathrm { S - R E C } } . } \end{array}
+$$
+
+# 5 RELATED WORK
+
+# 5.1 UNSUPERVISED LEARNING OF DISENTANGLED REPRESENTATIONS
+
+Learning disentangled representations is an important step towards better representation learning (Bengio et al., 2013) which can be useful for (semi-)supervised learning of downstream tasks, transfer and few-shot learning (Peters et al., 2017). VAEs have achieved promising results for unsupervised learning of disentangled representations. Several variations of VAEs have been proposed to achieve better disentanglement (Higgins et al., 2017; Kumar et al., 2017; Chen et al., 2016; Razavi et al., 2019). However, most recent progress in this direction has been restricted to the domain of images.
+
+# 5.2 CONTROLLED TEXT GENERATION
+
+In order to perform controllable text generation, previous methods either assume annotated attributes or multiple text datasets with different known styles (Hu et al., 2017; Shen et al., 2017; Zhao et al., 2018; Fu et al., 2018; Li et al., 2018; Sudhakar et al., 2019; Logeswaran et al., 2018; Lample et al., 2018). The requirement of labelled data largely restricts the capabilities and the applications of these models. Instead, all our proposed framework needs is raw text without any annotated attribute. The dominant underlying relevant factors in the given corpus will be discovered and disentangled by our unsupervised method, which can in turn be used for controlled generation.
+
+# 6 EXPERIMENTS
+
+To demonstrate the effectiveness of our approach, we compare it to unsupervised baselines with traditional VAEs, considering the density under the aggregated posterior distribution and the performance on sentiment manipulation. Following evaluation protocols in text style transfer, we also compare our method to strong supervised approaches. Furthermore, we showcase the ability of finer-grained style discovery and transition possessed by our system, which has not been attempted in the literature.
+
+In this section, our proposed framework is referred as CP-VAE (Constrained Posterior VAE). Detailed configurations including the hyperparameters, model architecture, training regimes, and decoding strategy are found in Appendix B.
+
+# 6.1 COMPARISONS WITH UNSUPERVISED BASELINES
+
+Experimental setup: We use the same experimental setting and dataset as mentioned in Sec. 3. The 80D latent code is split into 16 and 64 dimensions for $\pmb { z } ^ { ( 1 ) }$ and $\pmb { z } ^ { ( 2 ) }$ respectively. The sentence representations used for $\bar { z } ^ { ( 1 ) }$ is the averaged GloVe embeddings over the input tokens and $K$ is chosen as 3. To decide which basis vector corresponds to which sentiment, we sample 10 positive and 10 negative sentences respectively in the development set, pass them to the encoder, and choose the basis vector with the highest average $p _ { i }$ in $\pmb { p } = \operatorname { s o f t m a x } ( W \pmb { h } + \pmb { b } )$ , yielding $v _ { p }$ as the positive basis and $v _ { n }$ as the negative basis. If $v _ { p }$ and $v _ { n }$ are chosen to be the same vector, we choose the index with the second highest $p _ { i }$ for $v _ { p }$ . To perform sentiment manipulation, we fix $z ^ { ( 1 ) }$ to be the chosen basis vector; that is, $v _ { p }$ or $v _ { n }$ .
+
+Comparisons on density under the aggregated posterior distribution: First, we do linear interpolation between the two discovered basis vectors $v _ { p }$ and $v _ { n }$ and estimate the averaged NLL under the aggregated posterior distribution the same way as introduced in Sec. 3. The green solid curve in Fig. 3 (a) shows that the NLL of CP-VAE is relatively stable for the whole range of the interpolation. In Fig. 3 (c), the original latent codes and the modified ones largely overlap with each other. Both observations validate the effectiveness of CP-VAE in resolving the latent vacancy problem, leading to significant improvements on unsupervised sentiment manipulation, as seen later.
+
+![](images/15bd119b3de22f152c98ce6fb35786f885a51154761db022a0eb35cfae7c392c.jpg)  
+Figure 4: Visualization of all training samples in the probability simplex: (A) With $\mathcal { L } _ { \mathrm { S } }$ -REC ;(B) Without $\mathcal { L } _ { \mathrm { S - R E C } }$
+
+Comparsions with metrics on text style transfer: For quantitative evaluation, we adopt automatic evaluation metrics used in text style transfer (Sudhakar et al., 2019) including classification accuracy (AC), BLEU score (BL), GLEU score (GL) and language model perplexity (PL), whose definitions are elaborated in the next section. We also report $\bar { D _ { \mathrm { K L } } ( q _ { \phi _ { 1 } } ( z ^ { ( 1 ) } | \bar { \pmb x } ) | | \bar { p } ( z ) ) }$ (KL) for $z ^ { ( 1 ) }$ of CP-VAE. As shown in Tab. 1, CP-VAE performs significantly better than $\beta$ -VAE in terms of accuracy, BLEU and GLEU. The lower perplexity of $\beta$ -VAE is due to mode collapse, which produces very short pivot sentences such as “great !”. The results match our observations from the experiments on density under the aggregated posterior distribution, confirming that latent vacancy prevents effective manipulation of the latent codes. We also conduct an ablation study by removing $\mathcal { L } _ { \mathrm { R E G } }$ and $\mathcal { L } _ { \mathrm { S } }$ -REC from the objective. The results demonstrate that both terms are crucial to the success of CP-VAE. Without $\mathcal { L } _ { \mathrm { { R E G } } }$ , CP-VAE experiences posterior collapse for $z ^ { ( 1 ) }$ . As a result, $v _ { p }$ and $v _ { n }$ collide with each other, leading to failure in disentangled representation learning. Since we choose $K$ as 3, it is convenient to visualize the samples during training with $\pmb { p }$ in the learnt probability simplex, as shown in Fig. 4. We can see that the whole simplex is mostly covered with samples with the help of $\mathcal { L } _ { \mathrm { S } }$ -REC. Without $\mathcal { L } _ { \mathrm { S - R E C } }$ , the decoding network fails to recognize the basis vectors due to the poor coverage of the probability simplex, causing the model to lose most of its transferring ability.
+
+Table 1: Comparisons with unsupervised baselines on Yelp dataset.   
+
+<table><tr><td>Model</td><td>AC个</td><td>BL个</td><td>GL个</td><td>PL↓</td><td>KL for z(1)</td></tr><tr><td>β-VAE</td><td>50.44± 2.04</td><td>7.68 ± 0.33</td><td>2.97 ± 0.14</td><td>24.63 ± 1.85</td><td>NA</td></tr><tr><td>CP-G(loVe)</td><td>60.22 ± 4.57</td><td>33.69 ± 1.47</td><td>6.78± 0.44</td><td>63.12 ±2.41</td><td>18.35 ± 0.15</td></tr><tr><td>-LREG</td><td>10.82 ± 0.91</td><td>33.27 ± 2.84</td><td>5.04± 0.27</td><td>37.25 ± 2.40</td><td>0.04± 0.01</td></tr><tr><td>- Ls-REC</td><td>12.28 ± 3.69</td><td>49.34 ± 2.65</td><td>6.22 ± 0.40</td><td>55.26 ± 2.46</td><td>17.57 ± 0.12</td></tr></table>
+
+# 6.2 COMPARISONS TO SUPERVISED APPROACHES ON TEXT STYLE TRANSFER
+
+Experimental setup: We choose two datasets, Yelp and Amazon, used in works (Li et al., 2018; Sudhakar et al., 2019) on text style transfer which provide human gold-standard references for the test set. The same train-dev-test splits are used in our experiments. Two different sentence representations are used in this experiment, averaged GloVe and BERT (Devlin et al., 2018), denoted as CP-G(loVe) and CP-B(ert) respectively. The remaining settings are as described in the above section.
+
+Compared supervised approaches: On the two datasets, we compare to three adversarially trained models: StyleEmbedding (SE) (Fu et al., 2018), MultiDecoder (MD) (Fu et al., 2018), CrossAligned (CA) (Shen et al., 2017) and two state-of-the-art models based on a “delete, transform, and generate” framework: DeleteAndRetrieve (D&R) (Li et al., 2018) and Blind-GenerativeStyleTransformer (B-GST) (Sudhakar et al., 2019).
+
+Evaluation protocols: Four different automatic evaluation metrics are used to measure the different perspectives of the transferring quality, following Sudhakar et al. (2019). To measure transferring ability, we use pre-trained CNN based classifiers achieving $98 \%$ and $84 \%$ accuracies on the test sets of Yelp and Amazon respectively. To measure content preservation, we use the BLEU (Papineni et al., 2002) score between the transferred sentences and the source sentences. To measure fluency, we finetune OpenAI GPT-2 (Radford et al., 2019) with 345 million parameters on the same trainingdev-test split to obtain the perplexity of generated sentences. The fine-tuned language models achieve perplexities of 26.6 and 34.5 on the test sets of Yelp and Amazon respectively. In addition, Sudhakar et al. (2019) argued that the Generalized Language Evaluation Understanding Metric (GLEU) has a better correlation with the human judgement. Here, we use the implementation of GLEU3 provided by Napoles et al. (2015) to calculate the GLEU score.
+
+Result Analysis: As observed by Li et al. (2018) and Sudhakar et al. (2019), accuracy, BLEU score and perplexity do not correlate well with human evaluations. Therefore, it is important to not consider them in isolation. Tab. 2 shows that our proposed approaches get similar scores on these metrics with human reference sentences on the second row, indicating that the generated sentences of our proposed approaches is reasonable considering the combination of these metrics. As seen by Sudhakar et al. (2019) and verified in Sec. 6.1, GLEU strike a balance between target style match and content retention and correlate well with the human evaluations. From Tab. 2, CP-VAE consistently outperforms the three adversarially trained models on GLEU by a noticeable margin and achieve competitive results as compared to the recent state-of-the-art models. By checking the samples generated from the models as shown in Tab. 3, B-GST, the current state-of-the-art, is more consistent to the source sentence, which can be expected, since it only makes necessary edits to flip the sentiment. CP-VAE tends to generate more diverse contents which may not be relevant sometimes, but the overall quality is reasonable considering it is trained without the label information. More samples can be found in Appendix E.
+
+Table 2: Comparisons with supervised approaches on Yelp and Amazon dataset.   
+
+<table><tr><td colspan="5"></td><td colspan="4">Amazon</td></tr><tr><td>Model</td><td>AC↑</td><td>Yelp BL↑</td><td>GL↑</td><td>PL↓</td><td>AC↑</td><td>BL↑</td><td>GL↑</td><td>PL↓</td></tr><tr><td>Source Human</td><td>1.8 70.1</td><td>100.0 25.3</td><td>8.4 100.0</td><td>26.6 63.7</td><td>16.3 41.2</td><td>100.0 45.7</td><td>22.8 100.0</td><td>34.5 68.6</td></tr><tr><td>CA SE MD</td><td>74.0 8.2 49.5</td><td>20.7 67.4 40.1</td><td>6.0 6.9 6.6</td><td>103.6 65.4 164.1</td><td>75.5 40.2 70.1</td><td>0.0 0.4 0.3</td><td>0.0 0.0 0.0</td><td>39.3 125.0 138.8</td></tr><tr><td>D&amp;R B-GST</td><td>88.1 85.6</td><td>36.7 45.2</td><td>7.9 12.7</td><td>85.5 49.6</td><td>49.2 55.2</td><td>0.6 52.3</td><td>0.0 18.1</td><td>46.3 48.2</td></tr><tr><td>CP-G CP-B</td><td>66.7 55.4</td><td>35.5 48.4</td><td>7.5 9.6</td><td>67.8 47.6</td><td>60.1 40.0</td><td>35.4 39.7</td><td>11.5 12.7</td><td>109.1 97.3</td></tr></table>
+
+Table 3: Samples of generated sentences. SRC is the input sentence and HUMAN is the human references.   
+
+<table><tr><td rowspan=1 colspan=1>Yelp</td><td rowspan=1 colspan=1>PositivetoNegative</td><td rowspan=1 colspan=1>Negativeto Positive</td></tr><tr><td rowspan=1 colspan=1>SRC</td><td rowspan=1 colspan=1>this place is super yummy !</td><td rowspan=1 colspan=1>but it probably sucks too !</td></tr><tr><td rowspan=1 colspan=1>HUMAN</td><td rowspan=1 colspan=1>this place is super yucky !</td><td rowspan=1 colspan=1>but it probably doesn&#x27;t suck too !</td></tr><tr><td rowspan=1 colspan=1>B-GST</td><td rowspan=1 colspan=1>thisplace is superbad！</td><td rowspan=1 colspan=1>but it tastes great too!</td></tr><tr><td rowspan=1 colspan=1>CP-G</td><td rowspan=1 colspan=1>thisplace is super slow andwatered down.</td><td rowspan=1 colspan=1>but it&#x27;struly funand insanelydelicious.</td></tr><tr><td rowspan=1 colspan=1>CP-B</td><td rowspan=1 colspan=1>this place is super greasy and gross!</td><td rowspan=1 colspan=1>butit &#x27;sprobablywonderfulwhen you!</td></tr><tr><td rowspan=1 colspan=1>Amazon</td><td rowspan=1 colspan=1>PositivetoNegative</td><td rowspan=1 colspan=1>NegativetoPositive</td></tr><tr><td rowspan=1 colspan=1>SRC</td><td rowspan=1 colspan=1>because it s made of cast iron, scorching isminimized.</td><td rowspan=1 colspan=1>they are cheerios,afterall,and we love theoriginal kind .</td></tr><tr><td rowspan=1 colspan=1>HUMAN</td><td rowspan=1 colspan=1>because itis made of cast iron, scorching ismaximized.</td><td rowspan=1 colspan=1>they are cheerios,and we love them.</td></tr><tr><td rowspan=1 colspan=1>B-GST</td><td rowspan=1 colspan=1>because it s cheaply made of cast iron, isuseless .</td><td rowspan=1 colspan=1>they are sturdy,afterall,sturdy and we lovethe original.</td></tr><tr><td rowspan=1 colspan=1>CP-G</td><td rowspan=1 colspan=1>because it s made of cast iron,vomitting.</td><td rowspan=1 colspan=1>theyare ripe,tastier,and we love them.</td></tr><tr><td rowspan=1 colspan=1>CP-B</td><td rowspan=1 colspan=1>because it s made of cast iron,limp .</td><td rowspan=1 colspan=1>theyare divine,fluffier,andwe love them.</td></tr></table>
+
+# 6.3 FINER-GRAINED STYLE DISCOVERY AND TRANSITION
+
+Table 4: Two pairs of samples generated without and with topic transition. The first sentence in the pair is generated with a topic fixed throughout the generation; while the second sentence is generated with topic transition, the generated outputs after switching are marked as bold.   
+
+<table><tr><td>World throughout</td><td>Afederal judge on Friday ordered a federal appeals court to overturn a federal appeals court ruling that the Visa and MasterCard credit card associations violated federal antitrust law by barring the names of the state .</td></tr><tr><td>WorldtoSci/Tech</td><td>Afederal judge on Friday ordered a federal appeals court to overturna decision by the Supreme Court to overturn a decision by the Federal Communications Commission to block the company&#x27;s antitrust case against Microsoft Corp .</td></tr><tr><td>Sports throughout</td><td>NEW YORK (Reuters) - RogerFederer, the world&#x27;sNo.1 player,will miss the rest of the season because of a sore quadriceps.</td></tr><tr><td>Sports to Business</td><td>NEW YORK (Reuters) - Roger Federer, the world&#x27;s No. 1 player, will miss the rest of the year because of a bid-rigging scandal .</td></tr></table>
+
+To further explore the potential of CP-VAE, we conduct the following exploratory experiments. We use the AG news dataset constructed by (Zhang et al., 2015), which contains four topic categories which are World, Sports, Business and Sci/Tech, with the title and description fields. Here, we drop the title and just use the description field to train CP-VAE and set $K = 1 0$ . All four topics are automatically discovered by CP-VAE and identified as described in Sec. 6.1. We also compare the results of our identified topics to standard baselines for unsupervised topic modelling, the details can be found in Appendix D. We choose a basis vector discovered by our model and generate a few tokens. Then, we switch the basis vector and continue the generation until the end-of-seq token is generated. Generated samples are shown in Table 4. We see that our model learns to transition from one topic to another in a natural and fluent way within the same sentence. Several observations can be made based on these samples: (1) it is good at detecting name entities and replacing them with the name entities related to the chosen topic; (2) there is no hard restriction on when to switch the topic; the model will determine an appropriate way to do the transition by itself. Such observations confirm that CP-VAE possesses a filled constrained latent space which make the latent code robust to manipulation across different time steps, which can be effectively reflected in the generation process. Due to space limitations, we put more samples in Appendix F.
+
+# 7 CONCLUSION
+
+In this work, we investigate latent vacancy as an important problem in unsupervised learning of controllable representations when modelling text with VAEs. To mitigate this, we propose to constrain the posterior within a learned probability simplex, achieving the first success towards controlled text generation without supervision.
+
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+
+# A DETAILS ABOUT EXPLORATORY EXPERIMENTS
+
+# A.1 MODEL DETAILS
+
+For the $\beta$ -VAE we used for the exploratory experiments, we use a LSTM encoding network and a LSTM decoding network. For the encoding network, the input size is 256, and the hidden size is 1,024. For the decoding network, the input size is 256, the hidden size is 1,024, and dropouts with probability 0.5 are applied on after the embedding layer and the LSTM layer in the decoding network. $\beta$ is chosen as 0.35, the dimension for the latent code is 80, and the batch size is 32. We use SGD with learning rate 1.0 to update the parameters for both the encoding and the decoding network. We train the model until the reconstruction loss stops decreasing.
+
+# A.2 IDENTIFYING THE LATENT FACTOR INDICATING THE SENTIMENT
+
+First, we normalize the value of each latent code by subtracting the mean estimated over all the training samples. Then we use the polarity of each latent code to classify the sentiment in the validation set. The one with the highest accuracy is identified as the latent factor indicating the sentiment.
+
+# A.3 SAMPLES GENERATED FROM $\beta$ -VAE
+
+Table 5: Samples of generated sentences from $\beta$ -VAE on Yelp.   
+
+<table><tr><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>Positive to Negative</td><td rowspan=1 colspan=1>Negativeto Positive</td></tr><tr><td rowspan=1 colspan=1>SRC</td><td rowspan=1 colspan=1>this place is super yummy!</td><td rowspan=1 colspan=1>but it probably sucks too ！</td></tr><tr><td rowspan=1 colspan=1>β-VAE</td><td rowspan=1 colspan=1>this place is perfect for all of us or so longand over priced !</td><td rowspan=1 colspan=1>thank you !</td></tr><tr><td rowspan=1 colspan=1>SRC</td><td rowspan=1 colspan=1>i will be going back and enjoying this greatplace</td><td rowspan=1 colspan=1>there is definitely not enough room in thatpart of the venue .</td></tr><tr><td rowspan=1 colspan=1>β-VAE</td><td rowspan=1 colspan=1>i will be going back and recommending thisplace to anyone who lives in the valley ！</td><td rowspan=1 colspan=1>there is great .</td></tr></table>
+
+# A.4 MANIPULATION STRATEGIES
+
+Following manipulation strategies have been attempted: (1) fixing the relevant factor to $\mu + 2 \sigma$ and $\mu - 2 \sigma$ ; (2) fixing the relevant factor to $\mu - \sigma$ and $\mu - \sigma$ ; (3) fixing the relevant factor to the maximum value and the minimum value of the relevant factor appearing in the training samples; (4) calculating a latent vector based on 10 manually constructed parallel sentences with opposite sentiment while keeping other factors unchanged. However, none of these four strategies is effective considering the generation results. We report the result with the first strategy in the paper, since it performs the best considering the accuracy and the BLEU score.
+
+# B DETAILS ABOUT EXPERIMENTS ON TEXT STYLE TRANSFER
+
+# B.1 TRAINING REGIMES
+
+Across all the datasets, we use Adam with learning rate 0.001 to update the parameters for the encoding network, while SGD with learning rate 1.0 to update the parameters for the decoding network. The batch size is chosen to be 32. Dropouts with drop probability 0.5 are applied on applied on after the embedding layer and the LSTM layer in the decoding network. We train the model until the reconstruction loss stops decreasing.
+
+# B.2 MITIGATING POSTERIOR COLLAPSE
+
+For the structured part $z ^ { ( 1 ) }$ , we use $\beta$ -VAE setting $\beta$ as 0.2 across all the datasets. For the unstructured part $z ^ { ( 2 ) }$ , different strategies are employed for each dataset:
+
+• Yelp: $\beta$ -VAE setting $\beta$ as 0.35.   
+• Amazon: $\beta$ -VAE setting $\beta$ as 0.35.   
+• AG-News: KL annealing, from 0.1 to 1.0 in 10 epochs.
+
+# B.3 HYPERPARAMETER SETTINGS
+
+Table 6: Hyperparameter settings.   
+
+<table><tr><td></td><td>Yelp</td><td>Amazon</td><td>AG-News</td></tr><tr><td>Numberof variationsK</td><td>3</td><td>3</td><td>10</td></tr><tr><td>Parameter to control the KL α</td><td>100</td><td>100</td><td>10</td></tr><tr><td>Input dimension forLSTM encoder</td><td>256</td><td>256</td><td>512</td></tr><tr><td>Hidden dimension forLSTM encoder</td><td>1024</td><td>1024</td><td>1024</td></tr><tr><td>Dimension for z(2)</td><td>64</td><td>64</td><td>96</td></tr><tr><td>Dimension for z(1)</td><td>16</td><td>16</td><td>32</td></tr><tr><td>Input dimension for LSTM decoder</td><td>128</td><td>128</td><td>512</td></tr><tr><td>Hidden dimension forLSTMdecoder</td><td>1024</td><td>1024</td><td>1024</td></tr></table>
+
+The hyperparameters are chosen by checking ${ \mathcal { L } } _ { \mathrm { V A E } }$ , KL, and the generated outputs on the development set for Yelp and AG-News. Amazon follows the same setting as Yelp without extra tuning.
+
+# B.4 DECODING STRATEGY
+
+For decoding, we use beam search with a beam size of 5.
+
+# C PROOF OF MINIMALIZATION OF EQ. 5
+
+The problem can be formulated as an optimization problem as follows:
+
+$$
+{ \mathrm { m a x i m i z e } } \sum _ { i = 1 } ^ { K } p _ { i } ^ { 2 } , \quad { \mathrm { s u b j e c t ~ t o } } \sum _ { i = 1 } ^ { K } p _ { i } = 1 .
+$$
+
+By introducing a Lagrange multiplier $\lambda$ , the Lagrange function is defined as
+
+$$
+\mathcal { L } ( p _ { 1 } , p _ { 2 } , . . . , p _ { K } , \lambda ) = \sum _ { i = 1 } ^ { K } p _ { i } ^ { 2 } - \lambda ( \sum _ { i = 1 } ^ { K } p _ { i } - 1 ) .
+$$
+
+In order to find the optimal point, we require that
+
+$$
+\frac { \partial } { \partial p _ { i } } \left( \sum _ { i = 1 } ^ { K } p _ { i } ^ { 2 } - \lambda ( \sum _ { i = 1 } ^ { K } p _ { i } - 1 ) \right) = 2 p _ { i } - \lambda = 0 , \quad i = 1 , 2 , \ldots , K ,
+$$
+
+which shows that all $p _ { i }$ are equal. By using the constraint $\textstyle \sum _ { i } p _ { i } \ = \ 1$ , we find $\begin{array} { r } { p _ { i } \ = \ \frac { 1 } { K } , i \ = \ } \end{array}$ $1 , 2 , \ldots , K$ . By plugging into the results, $\begin{array} { r } { \pmb { \mu } ^ { \top } \pmb { \mu } = \alpha \sum _ { i } p _ { i } ^ { 2 } } \end{array}$ reaches its minimum $\frac { \alpha } { K }$ .
+
+# D COMPARISONS WITH BASELINES ON TOPIC MODELLING
+
+Experimental setup: We use the AG news dataset for this task constructed by (Zhang et al., 2015). It contains four topic categories which are World, Sports, Business and Sci/Tech, with the title and description fields. For each category, there are 30, 000 training samples and 1, 900 test samples. In this paper, we drop the title and just use the description field. We compare our approach to two standard baselines for unsupervised topic modelling: (1) LDA (Blei et al., 2003), a standard implementation of LDA is used for this baseline4; (2) $k$ -means. To show the power of our approach beyond the pre-trained sentence representations, we perform $k$ -means clustering directly on the sentence representations. Following (Manning et al., 2010), we assign each inferred topic to one of the gold-standard topics with the optimal mapping and report the precision (a.k.a. purity), recall (a.k.a. collocation) and $F _ { 1 }$ score. The number of topics is chosen to be 10. The results reported for the baselines and our model are the average over 10 runs.
+
+Quantitative results: The results are shown in Table 7. We can see that our approach achieves comparable results to LDA while significantly outperforming $k$ -means in all four categories, indicating that our approach can go beyond just clustering on pre-trained sentence representations.
+
+Table 7: Results for topic identification.   
+
+<table><tr><td>Topic</td><td>Model</td><td>Precision</td><td>Recall</td><td>F1</td></tr><tr><td>World</td><td>LDA k-means Ours</td><td>69.73 67.64 80.83</td><td>75.32 47.63 70.55</td><td>72.14 55.90 74.59</td></tr><tr><td>Sports</td><td>LDA k-means Ours</td><td>79.17 47.66 81.14</td><td>82.50 89.50 78.88</td><td>80.22 62.04 79.49</td></tr><tr><td>Business</td><td>LDA k-means Ours</td><td>72.10 53.06 64.04</td><td>66.45 53.16 64.53</td><td>68.46 53.11 63.97</td></tr><tr><td>Sci/Tech</td><td>LDA k-means Ours</td><td>66.55 81.32 65.20</td><td>59.77 31.59 71.74</td><td>61.60 44.67 66.77</td></tr></table>
+
+# E TEXT TRANSFER EXAMPLES
+
+# E.1 SENTIMENT MANIPULATION ON YELP DATASET
+
+Table 8: Sentiment manipulation results from positive to negative   
+
+<table><tr><td rowspan=1 colspan=1>SRC</td><td rowspan=1 colspan=1>this was the besti have ever had !</td></tr><tr><td rowspan=1 colspan=1>B-GST</td><td rowspan=1 colspan=1>this was the worst place i have ever had !</td></tr><tr><td rowspan=1 colspan=1>CP-G</td><td rowspan=1 colspan=1>this was the worst pizza i have ever had !</td></tr><tr><td rowspan=1 colspan=1>CP-B</td><td rowspan=1 colspan=1>this was the worsti have ever had!</td></tr><tr><td rowspan=1 colspan=1>SRC</td><td rowspan=1 colspan=1>friendly and welcoming with a fun atmosphere and terrific food .</td></tr><tr><td rowspan=1 colspan=1>B-GST</td><td rowspan=1 colspan=1>the hummus is ridiculously bland and bland .</td></tr><tr><td rowspan=1 colspan=1>CP-G</td><td rowspan=1 colspan=1>rude and unorganized with a terrible atmosphere and coffee .</td></tr><tr><td rowspan=1 colspan=1>CP-B</td><td rowspan=1 colspan=1>the hummusisridiculously greasy and tasteless.</td></tr><tr><td rowspan=1 colspan=1>SRC</td><td rowspan=1 colspan=1>i ordered the carne asada steak and it was cooked perfectly !</td></tr><tr><td rowspan=1 colspan=1>B-GST</td><td rowspan=1 colspan=1>i ordered thecarneasadasteakanditwasjustasbad！</td></tr><tr><td rowspan=1 colspan=1>CP-G</td><td rowspan=1 colspan=1>i ordered the carne asada steak and it was n&#x27;t cooked and it was lacking .</td></tr><tr><td rowspan=1 colspan=1>CP-B</td><td rowspan=1 colspan=1>i ordered the carne asada burrito and it was mediocre .</td></tr><tr><td rowspan=1 colspan=1>SRC</td><td rowspan=1 colspan=1>the owner is a hoot and the facility is very accommodating .</td></tr><tr><td rowspan=1 colspan=1>B-GST</td><td rowspan=1 colspan=1>the ownerisa jerkand thefacilityisvery outdated.</td></tr><tr><td rowspan=1 colspan=1>CP-G</td><td rowspan=1 colspan=1>the owner is a hoot and the facility is empty and the layout is empty .</td></tr><tr><td rowspan=1 colspan=1>CP-B</td><td rowspan=1 colspan=1>the ownerisa riot and the facilityisveryclean.</td></tr><tr><td rowspan=1 colspan=1>SRC</td><td rowspan=1 colspan=1>i will be going back and enjoying this great place !</td></tr><tr><td rowspan=1 colspan=1>B-GST</td><td rowspan=1 colspan=1>i wo n&#x27;t be going back and this place is horrible !</td></tr><tr><td rowspan=1 colspan=1>CP-G</td><td rowspan=1 colspan=1>i will be going back and eat this pizza hut elsewhere .</td></tr><tr><td rowspan=1 colspan=1>CP-B</td><td rowspan=1 colspan=1>i will be going back and hated the worst dining experience .</td></tr></table>
+
+Table 9: Sentiment manipulation results from negative to positive   
+
+<table><tr><td rowspan=1 colspan=1>SRC</td><td rowspan=1 colspan=1>there is definitely not enough room in that part of the venue .</td></tr><tr><td rowspan=1 colspan=1>B-GST</td><td rowspan=1 colspan=1>there is plenty enough seating in that part of the venue .</td></tr><tr><td rowspan=1 colspan=1>CP-G</td><td rowspan=1 colspan=1>there is definitely an authentic dinner in that part .</td></tr><tr><td rowspan=1 colspan=1>CP-B</td><td rowspan=1 colspan=1>there is definitely a nice theatre in that part .</td></tr><tr><td rowspan=1 colspan=1>SRC</td><td rowspan=1 colspan=1>but it probably sucks too !</td></tr><tr><td rowspan=1 colspan=1>B-GST</td><td rowspan=1 colspan=1>but it tastes great too !</td></tr><tr><td rowspan=1 colspan=1>CP-G</td><td rowspan=1 colspan=1>but it &#x27;s truly fun and insanely delicious .</td></tr><tr><td rowspan=1 colspan=1>CP-B</td><td rowspan=1 colspan=1>but it&#x27;sprobablywonderful when u !</td></tr><tr><td rowspan=1 colspan=1>SRC</td><td rowspan=1 colspan=1>always rude in their tone and always have shitty customer service !</td></tr><tr><td rowspan=1 colspan=1>B-GST</td><td rowspan=1 colspan=1>always in tune with their tone and have great customer service .</td></tr><tr><td rowspan=1 colspan=1>CP-G</td><td rowspan=1 colspan=1>always great with theirbirthdaysand always excellent music.</td></tr><tr><td rowspan=1 colspan=1>CP-B</td><td rowspan=1 colspan=1>always accommodating and my dog is always on family .</td></tr><tr><td rowspan=1 colspan=1>SRC</td><td rowspan=1 colspan=1>i was very sick the night after.</td></tr><tr><td rowspan=1 colspan=1>B-GST</td><td rowspan=1 colspan=1>i was very happy the night after.</td></tr><tr><td rowspan=1 colspan=1>CP-G</td><td rowspan=1 colspan=1>i was very pleased with the night .</td></tr><tr><td rowspan=1 colspan=1>CP-B</td><td rowspan=1 colspan=1>i was very happy with the night .</td></tr><tr><td rowspan=1 colspan=1>SRC</td><td rowspan=1 colspan=1>this is a horrible venue.</td></tr><tr><td rowspan=1 colspan=1>B-GST</td><td rowspan=1 colspan=1>this is a wonderful venue.</td></tr><tr><td rowspan=1 colspan=1>CP-G</td><td rowspan=1 colspan=1>this is a great place for celebrating friends.</td></tr><tr><td rowspan=1 colspan=1>CP-B</td><td rowspan=1 colspan=1>this is a great place for beginners .</td></tr></table>
+
+# E.2 SENTIMENT MANIPULATION ON AMAZON DATASET
+
+Table 10: Sentiment manipulation results from positive to negative   
+
+<table><tr><td rowspan=1 colspan=1>SRC</td><td rowspan=1 colspan=1>most pizza wheels thative seen are much smaller.</td></tr><tr><td rowspan=1 colspan=1>B-GST</td><td rowspan=1 colspan=1>most pizza dough that i ve seen are much better .</td></tr><tr><td rowspan=1 colspan=1>CP-G</td><td rowspan=1 colspan=1>most pizza wheels that i ve seen are much more good and are much quality .</td></tr><tr><td rowspan=1 colspan=1>CP-B</td><td rowspan=1 colspan=1>most pizza wheels that i ve seen are much better than are much better</td></tr><tr><td rowspan=1 colspan=1>SRC</td><td rowspan=1 colspan=1>however, this is an example of how rosle got it right .</td></tr><tr><td rowspan=1 colspan=1>B-GST</td><td rowspan=1 colspan=1>however, this game is an example of how rosle loves it .</td></tr><tr><td rowspan=1 colspan=1>CP-G</td><td rowspan=1 colspan=1>however, this is an example of how toxic... sad... obviously .</td></tr><tr><td rowspan=1 colspan=1>CP-B</td><td rowspan=1 colspan=1>however, this is an example of how cheap .similar .cheap advice .cheapadvice.similar.</td></tr><tr><td rowspan=1 colspan=1>SRC</td><td rowspan=1 colspan=1>auto shut off after num_num hours,which is a good feature .</td></tr><tr><td rowspan=1 colspan=1>B-GST</td><td rowspan=1 colspan=1>auto shuts off after num _num hours,which is a shame.</td></tr><tr><td rowspan=1 colspan=1>CP-G</td><td rowspan=1 colspan=1>whipped mask off after num_num hours，which is slimy，which is disgusting .</td></tr><tr><td rowspan=1 colspan=1>CP-B</td><td rowspan=1 colspan=1>auto shut off after num_num hours,which is a stupid idea,which seems to bebad.</td></tr><tr><td rowspan=1 colspan=1>SRC</td><td rowspan=1 colspan=1>that said , the mic did pic up everything it could .</td></tr><tr><td rowspan=1 colspan=1>B-GST</td><td rowspan=1 colspan=1>that said, the game took up everything it could .</td></tr><tr><td rowspan=1 colspan=1>CP-G</td><td rowspan=1 colspan=1>that said, the shampoo did nt smell him well . stopped cleaning everything .ended up smelling sick</td></tr><tr><td rowspan=1 colspan=1>CP-B</td><td rowspan=1 colspan=1> that said, the mic did not fit everything on well , let me down it weren t cleaning</td></tr><tr><td rowspan=1 colspan=1>SRC</td><td rowspan=1 colspan=1>ialso prefered thabladeweightand thicknessof thewustof !</td></tr><tr><td rowspan=1 colspan=1>B-GST</td><td rowspan=1 colspan=1>i also like the blade weight and of the wustof.</td></tr><tr><td rowspan=1 colspan=1>CP-G</td><td rowspan=1 colspan=1>ialso disliked theblade weightand thicknessof the materials.</td></tr><tr><td rowspan=1 colspan=1>CP-B</td><td rowspan=1 colspan=1>ialso slammed the blade weight and thickness of the wide.</td></tr></table>
+
+Table 11: Sentiment manipulation results from negative to positive   
+
+<table><tr><td rowspan=1 colspan=1>SRC</td><td rowspan=1 colspan=1>the quality is declined quicklybyheat exposure .</td></tr><tr><td rowspan=1 colspan=1>B-GST</td><td rowspan=1 colspan=1>thewaterisquicklydrained byhead exposure .</td></tr><tr><td rowspan=1 colspan=1>CP-G</td><td rowspan=1 colspan=1>the quality is utilitarian so grinding or sandwiches .</td></tr><tr><td rowspan=1 colspan=1>CP-B</td><td rowspan=1 colspan=1>the quality is priceless quickly by heat rises .</td></tr><tr><td rowspan=1 colspan=1>SRC</td><td rowspan=1 colspan=1>the directions were easy to follow but the quality of the easel was pathetic .</td></tr><tr><td rowspan=1 colspan=1>B-GST</td><td rowspan=1 colspan=1>the directions were easy to follow but the quality of the product was excellent .</td></tr><tr><td rowspan=1 colspan=1>CP-G</td><td rowspan=1 colspan=1>the directions were easy to follow but the quality is good for the quality and is</td></tr><tr><td rowspan=1 colspan=1>CP-B</td><td rowspan=1 colspan=1>the directions were easy to follow but the quality is what the quality is like thebest quality of</td></tr><tr><td rowspan=1 colspan=1>SRC</td><td rowspan=1 colspan=1>multiplayer is just as bad, though thankfully not worse .</td></tr><tr><td rowspan=1 colspan=1>B-GST</td><td rowspan=1 colspan=1>quality is just as good , though thankfully not perfect .</td></tr><tr><td rowspan=1 colspan=1>CP-G</td><td rowspan=1 colspan=1>besides it is just good, though.those..usually...usually...</td></tr><tr><td rowspan=1 colspan=1>CP-B</td><td rowspan=1 colspan=1>multiplayer is just as bad, though somebody s also so far not so far but noproblem .</td></tr><tr><td rowspan=1 colspan=1>SRC</td><td rowspan=1 colspan=1> another energy product that simply wastes our money .</td></tr><tr><td rowspan=1 colspan=1>B-GST</td><td rowspan=1 colspan=1>another energy product that simply saves our money .</td></tr><tr><td rowspan=1 colspan=1>CP-G</td><td rowspan=1 colspan=1> another energy product that simply glides your pasta .</td></tr><tr><td rowspan=1 colspan=1>CP-B</td><td rowspan=1 colspan=1>another energyproduct that simplywastes this money.</td></tr><tr><td rowspan=1 colspan=1>SRC</td><td rowspan=1 colspan=1>i received the wrong color and it shreds easily .</td></tr><tr><td rowspan=1 colspan=1>B-GST</td><td rowspan=1 colspan=1>i received the color and it works easily.</td></tr><tr><td rowspan=1 colspan=1>CP-G</td><td rowspan=1 colspan=1>i low the new color and it closes easily.</td></tr><tr><td rowspan=1 colspan=1>CP-B</td><td rowspan=1 colspan=1>i received the wrong color and it pours easily from dishwasher and dries easilyon garlic easily .</td></tr></table>
+
+# F TEXT TRANSITION EXAMPLES ON AG NEWS
+
+Table 12: Topic transition examples.   
+
+<table><tr><td rowspan=1 colspan=1>World throughout</td><td rowspan=1 colspan=1>BAGHDAD (Reuters) - Iraq ’s interim prime minister, Iyad Allwi , said on Monday that the United States had no intention of withdrawingfrom the country to end the violence in Iraq .</td></tr><tr><td rowspan=1 colspan=1>World to Sports</td><td rowspan=1 colspan=1>BAGHDAD (Reuters) - Iraq &#x27;s interim prime minister, Iyad Allawi, said on Monday that the United States had no intention of withdrawing its troops from the country to the end of the year .</td></tr><tr><td rowspan=1 colspan=1>World to Business</td><td rowspan=1 colspan=1>BAGHDAD (Reuters) - Iraq &#x27;s interim prime minister, Iyad Allawi , said on Monday that the United States had no intention of withdrawing itstroops from the country to the country .</td></tr><tr><td rowspan=1 colspan=1>World to Sci/Tech</td><td rowspan=1 colspan=1>BAGHDAD (Reuters) - Iraq &#x27;s interim prime minister, Iyad Allawi, saidon Monday that the United States had no intention of withdrawing itsuranium enrichment program to the United States .</td></tr><tr><td rowspan=1 colspan=1>Sports throughout</td><td rowspan=1 colspan=1>For the first time in four years , the US men &#x27;s basketball team won the gold medal in the men &#x27;s 40O-meter medley relay .</td></tr><tr><td rowspan=1 colspan=1>Sports to World</td><td rowspan=1 colspan=1>For the first time in four years， the US men &#x27;s basketball team wonthe gold medal at the Athens Olympics in Athens,where the UnitedStates and the United States have agreed to a peace deal .</td></tr><tr><td rowspan=1 colspan=1>Sports to Business</td><td rowspan=1 colspan=1>For the first time in four years , the US men &#x27;s basketball team won the gold medal at the Athens Olympics on Wednesday ,with a surge incrude oil prices .</td></tr><tr><td rowspan=1 colspan=1>Sports to Sci/Tech</td><td rowspan=1 colspan=1>For the first time in four years , the US men &#x27;s basketball team won the gold medal in the men &#x27;s Olympic basketball tournament in Beijingon Tuesday.</td></tr><tr><td rowspan=1 colspan=1>Business throughout</td><td rowspan=1 colspan=1>NEW YORK (Reuters) - U.S. stocks opened higher on Friday , as oil prices climbed above $48 a barrel and the Federal Reserve raised interestrates by a quarter percentage point .</td></tr><tr><td rowspan=1 colspan=1>Businessto World</td><td rowspan=1 colspan=1>NEW YORK (Reuters) - U.S. stocks opened higher on Friday ,as oilprices climbed above $48 a barrel and the Federal Reserve raisedinterest rates by a quarter percentage point .</td></tr><tr><td rowspan=1 colspan=1>Business to Sports</td><td rowspan=1 colspan=1>NEW YORK (Reuters) - U.S. stocks opened higher on Friday, as oilprices climbed above $48 a barrel and the Federal Reserve raised interest rates by a quarter percentage point .</td></tr><tr><td rowspan=1 colspan=1>Business to Sci/Tech</td><td rowspan=1 colspan=1>NEW YORK (Reuters) - U.S. stocks opened higher on Friday , as oil prices climbed above $48 a barrel and the Federal CommunicationsCommission said it would allow the companies to use mobile phones</td></tr><tr><td rowspan=1 colspan=1>Sci/Tech throughout</td><td rowspan=1 colspan=1>SINGAPORE (Reuters) - South Korea &#x27;s Hynix Semiconductor Inc. saidon Tuesday it had developed a prototype micro fuel cell recharger for arange of security vulnerabilities in India .</td></tr><tr><td rowspan=1 colspan=1>Sci/Tech to World</td><td rowspan=1 colspan=1>SINGAPORE (Reuters) - South Korea &#x27;s Hynix Semiconductor Inc. said on Tuesday it had developed a prototype micro fuel cell aimed at endinga standoff with North Korea.</td></tr><tr><td rowspan=1 colspan=1>Sci/Tech to Sports</td><td rowspan=1 colspan=1>SINGAPORE (Reuters) - South Korea &#x27;s Hynix Semiconductor Inc.said on Tuesday it had developed a prototype micro fuel cell aimed atprotecting the world ’s biggest gold medal .</td></tr><tr><td rowspan=1 colspan=1>Sci/Tech to Business</td><td rowspan=1 colspan=1>SINGAPORE (Reuters) - South Korea &#x27;s Hynix Semiconductor Inc. said on Tuesday it had developed a prototype micro fuel cell aimed atprotecting the world &#x27;s largest oil producer .</td></tr></table>

parse/train/S1gmrxHFvB/S1gmrxHFvB.md

@@ -0,0 +1,308 @@
+# AUGMIX: A SIMPLE DATA PROCESSING METHOD TO IMPROVE ROBUSTNESS AND UNCERTAINTY
+
+Dan Hendrycks∗   
+DeepMind   
+hendrycks@berkeley.edu   
+Norman Mu∗   
+Google   
+normanmu@google.com
+
+Ekin D. Cubuk Google cubuk@google.com
+
+Barret Zoph   
+Google   
+barretzoph@google.com
+
+Justin Gilmer Google gilmer@google.com
+
+Balaji Lakshminarayanan† DeepMind balajiln@google.com
+
+# ABSTRACT
+
+Modern deep neural networks can achieve high accuracy when the training distribution and test distribution are identically distributed, but this assumption is frequently violated in practice. When the train and test distributions are mismatched, accuracy can plummet. Currently there are few techniques that improve robustness to unforeseen data shifts encountered during deployment. In this work, we propose a technique to improve the robustness and uncertainty estimates of image classifiers. We propose AUGMIX, a data processing technique that is simple to implement, adds limited computational overhead, and helps models withstand unforeseen corruptions. AUGMIX significantly improves robustness and uncertainty measures on challenging image classification benchmarks, closing the gap between previous methods and the best possible performance in some cases by more than half.
+
+# 1 INTRODUCTION
+
+Current machine learning models depend on the ability of training data to faithfully represent the data encountered during deployment. In practice, data distributions evolve (Lipton et al., 2018), models encounter new scenarios (Hendrycks & Gimpel, 2017), and data curation procedures may capture only a narrow slice of the underlying data distribution (Torralba & Efros, 2011). Mismatches between the train and test data are commonplace, yet the study of this problem is not. As it stands, models do not robustly generalize across shifts in the data distribution. If models could identify when they are likely to be mistaken, or estimate uncertainty accurately, then the impact of such fragility might be ameliorated. Unfortunately, modern models already produce overconfident predictions when the training examples are independent and identically distributed to the test distribution. This overconfidence and miscalibration is greatly exacerbated by mismatched training and testing distributions.
+
+Small corruptions to the data distribution are enough to subvert existing classifiers, and techniques to improve corruption robustness remain few in number. Hendrycks & Dietterich (2019) show that classification error of modern models rises from $22 \%$ on the usual ImageNet test set to $64 \%$ on ImageNet-C, a test set consisting of various corruptions applied to ImageNet test images. Even methods which aim to explicitly quantify uncertainty, such as probabilistic and Bayesian neural networks, struggle under data shift, as recently demonstrated by Ovadia et al. (2019). Improving performance in this setting has been difficult. One reason is that training against corruptions only encourages networks to memorize the specific corruptions seen during training and leaves models unable to generalize to new corruptions (Vasiljevic et al., 2016; Geirhos et al., 2018). Further, networks trained on translation augmentations remain highly sensitive to images shifted by a single pixel (Gu et al., 2019; Hendrycks & Dietterich, 2019). Others have proposed aggressive data augmentation schemes (Cubuk et al., 2018), though at the cost of a computational increase. Chun et al. (2019) demonstrates that many techniques may improve clean accuracy at the cost of robustness while many techniques which improve robustness harm uncertainty, and contrariwise. In all, existing techniques have considerable trade-offs.
+
+![](images/83b7e856f0dd9d03c3943a76c56f051a39a07d25b37598ba7a1811b7ca2ec8b8.jpg)  
+Figure 1: A visual comparison of data augmentation techniques. AUGMIX produces images with variety while preserving much of the image semantics and local statistics.
+
+In this work, we propose a technique to improve both the robustness and uncertainty estimates of classifiers under data shift. We propose AUGMIX, a method which simultaneously achieves new state-of-the-art results for robustness and uncertainty estimation while maintaining or improving accuracy on standard benchmark datasets. AUGMIX utilizes stochasticity and diverse augmentations, a Jensen-Shannon Divergence consistency loss, and a formulation to mix multiple augmented images to achieve state-of-the-art performance. On CIFAR-10 and CIFAR-100, our method roughly halves the corruption robustness error of standard training procedures from $2 8 . 4 \%$ to $1 2 . 4 \%$ and $5 4 . 3 \%$ to $3 7 . 8 \%$ error, respectively. On ImageNet, AUGMIX also achieves state-of-the-art corruption robustness and decreases perturbation instability from $5 7 . 2 \%$ to $3 7 . 4 \%$ . Code is available at https://github.com/google-research/augmix.
+
+# 2 RELATED WORK
+
+Robustness under Data Shift. Geirhos et al. (2018) show that training against distortions can often fail to generalize to unseen distortions, as networks have a tendency to memorize properties of the specific training distortion. Vasiljevic et al. (2016) show training with various blur augmentations can fail to generalize to unseen blurs or blurs with different parameter settings. Hendrycks & Dietterich (2019) propose measuring generalization to unseen corruptions and provide benchmarks for doing so. Kang et al. (2019) construct an adversarial version of the aforementioned benchmark. Gilmer et al. (2018); Gilmer & Hendrycks (2019) argue that robustness to data shift is a pressing problem which greatly affects the reliability of real-world machine learning systems.
+
+Calibration under Data Shift. Guo et al. (2017); Nguyen & O’Connor (2015) propose metrics for determining the calibration of machine learning models. Lakshminarayanan et al. (2017) find that simply ensembling classifier predictions improves prediction calibration. Hendrycks et al. (2019a) show that pre-training can also improve calibration. Ovadia et al. (2019) demonstrate that model calibration substantially deteriorates under data shift.
+
+Data Augmentation. Data augmentation can greatly improve generalization performance. For image data, random left-right flipping and cropping are commonly used He et al. (2015). Random occlusion techniques such as Cutout can also improve accuracy on clean data (Devries & Taylor, 2017; Zhong et al., 2017). Rather than occluding a portion of an image, CutMix replaces a portion of an image with a portion of a different image (Yun et al., 2019). Mixup also use information from two images. Rather than implanting one portion of an image inside another, Mixup produces an elementwise convex combination of two images (Zhang et al., 2017; Tokozume et al.
+
+![](images/26ec12a0be68e3d389af8bd4cd008b2f8c72cb8aae9f3a60cb87e3113ea1da0c.jpg)  
+ImageNet-C Corruptions   
+Figure 2: Example ImageNet-C corruptions. These corruptions are encountered only at test time and not during training.
+
+![](images/195cfa71f2ca86610e0cbc94d9680b99afa27ef52edff09d0d7e783760de3e83.jpg)  
+Figure 3: A cascade of successive compositions can produce images which drift far from the original image, and lead to unrealistic images. However, this divergence can be balanced by controlling the number of steps. To increase variety, we generate multiple augmented images and mix them.
+
+2018). Guo et al. (2019) show that Mixup can be improved with an adaptive mixing policy, so as to prevent manifold intrusion. Separate from these approaches are learned augmentation methods such as AutoAugment (Cubuk et al., 2018), where a group of augmentations is tuned to optimize performance on a downstream task. Patch Gaussian augments data with Gaussian noise applied to a randomly chosen portion of an image (Lopes et al., 2019). A popular way to make networks robust to $\ell _ { p }$ adversarial examples is with adversarial training (Madry et al., 2018), which we use in this paper. However, this tends to increase training time by an order of magnitude and substantially degrades accuracy on non-adversarial images (Raghunathan et al., 2019).
+
+# 3 AUGMIX
+
+AUGMIX is a data augmentation technique which improves model robustness and uncertainty estimates, and slots in easily to existing training pipelines. At a high level, AugMix is characterized by its utilization of simple augmentation operations in concert with a consistency loss. These augmentation operations are sampled stochastically and layered to produce a high diversity of augmented images. We then enforce a consistent embedding by the classifier across diverse augmentations of the same input image through the use of Jensen-Shannon divergence as a consistency loss.
+
+Mixing augmentations allows us to generate diverse transformations, which are important for inducing robustness, as a common failure mode of deep models in the arena of corruption robustness is the memorization of fixed augmentations (Vasiljevic et al., 2016; Geirhos et al., 2018). Previous methods have attempted to increase diversity by directly composing augmentation primitives in a chain, but this can cause the image to quickly degrade and drift off the data manifold, as depicted in Figure 3. Such image degradation can be mitigated and the augmentation diversity can be maintained by mixing together the results of several augmentation chains in convex combinations. A concrete account of the algorithm is given in the pseudocode below.
+
+# Algorithm AUGMIX Pseudocode
+
+1: Input: Model $\hat { p }$ , Classification Loss $\mathcal { L }$ , Image $x _ { \mathrm { o r i g } }$ , Operations $\mathcal { O } = \{ \mathrm { r o t a t e } , \dots , \mathrm { p o s t e r i z e } \}$   
+2: function AugmentAndMix $\cdot { x } _ { \mathrm { o r i g } }$ , $k = 3 , \alpha = 1 ,$ )   
+3: Fill $x _ { \mathrm { a u g } }$ with zeros   
+4: Sample mixing weights $( w _ { 1 } , w _ { 2 } , \ldots , w _ { k } ) \sim { \mathrm { D i r i c h l e t } } ( \alpha , \alpha , \ldots , \alpha )$   
+5: for $i = 1 , \ldots , k$ do   
+6: Sample operations $\begin{array} { r } { \boldsymbol { \mathrm { o p } } _ { 1 } , \boldsymbol { \mathrm { o p } } _ { 2 } , \boldsymbol { \mathrm { o p } } _ { 3 } \sim \mathcal { O } } \end{array}$   
+7: Compose operations with varying depth $\mathrm { o p _ { 1 2 } = o p _ { 2 } \circ o p _ { 1 } }$ and $\mathrm { o p _ { 1 2 3 } = o p _ { 3 } \circ o p _ { 2 } \circ o p _ { 1 } }$   
+8: Sample uniformly from one of these operations chain $\sim \{ \boldsymbol { \mathrm { o p } } _ { 1 } , \boldsymbol { \mathrm { o p } } _ { 1 2 } , \boldsymbol { \mathrm { o p } } _ { 1 2 3 } \}$   
+9: $x _ { \mathrm { a u g } } + = w _ { i } \cdot \mathrm { c h a i n } ( x _ { \mathrm { o r i g } } )$ . Addition is elementwise   
+10: end for   
+11: Sample weight $m \sim \operatorname { B e t a } ( \alpha , \alpha )$   
+12: Interpolate with rule $x _ { \mathrm { a u g m i x } } = m x _ { \mathrm { o r i g } } + ( 1 - m ) x _ { \mathrm { a u g } }$   
+13: return xaugmix   
+14: end function   
+15: xaugmix1 = AugmentAndMix(xorig) . xaugmix1 is stochastically generated   
+16: $x _ { \mathrm { a u g m i x 2 } } = \mathrm { A u g m e n t A n d M i x } ( x _ { \mathrm { o r i g } } )$ $\triangleright x _ { a u g m i x I } \neq x _ { a u g m i x 2 }$   
+17: Loss Output: $\mathcal { L } ( \hat { p } ( y \mid x _ { \mathrm { o r i g } } ) , y ) \breve { + } \lambda$ Jensen-Shannon $1 \big ( \hat { p } ( y \mid x _ { \mathrm { o r i g } } ) ; \hat { p } ( y \vert x _ { \mathrm { a u g m i x 1 } } ) ; \hat { p } ( y \vert x _ { \mathrm { a u g m i x 2 } } ) \big )$
+
+![](images/6af8a2b0286d0af5a7558f66612d2889ff1f4ce091aedf77dedbdb557a78cab2.jpg)  
+Figure 4: A realization of AUGMIX. Augmentation operations such as translate x and weights such as $m$ are randomly sampled. Randomly sampled operations and their compositions allow us to explore the semantically equivalent input space around an image. Mixing these images together produces a new image without veering too far from the original.
+
+Augmentations. Our method consists of mixing the results from augmentation chains or compositions of augmentation operations. We use operations from AutoAugment. Each operation is visualized in Appendix C. Crucially, we exclude operations which overlap with ImageNet- $C$ corruptions. In particular, we remove the contrast, color, brightness, sharpness, and Cutout operations so that our set of operations and the ImageNet-C corruptions are disjoint. In turn, we do not use any image noising nor image blurring operations so that ImageNet-C corruptions are encountered only at test time. Operations such as rotate can be realized with varying severities, like $2 ^ { \circ }$ or $- 1 5 ^ { \circ }$ . For operations with varying severities, we uniformly sample the severity upon each application. Next, we randomly sample $k$ augmentation chains, where $k = 3$ by default. Each augmentation chain is constructed by composing from one to three randomly selected augmentation operations.
+
+Mixing. The resulting images from these augmentation chains are combined by mixing. While we considered mixing by alpha compositing, we chose to use elementwise convex combinations for simplicity. The $k$ -dimensional vector of convex coefficients is randomly sampled from a Dirichle $( \alpha , \ldots , \alpha )$ distribution. Once these images are mixed, we use a “skip connection” to combine the result of the augmentation chain and the original image through a second random convex combination sampled from a Beta $( \alpha , \alpha )$ distribution. The final image incorporates several sources of randomness from the choice of operations, the severity of these operations, the lengths of the augmentation chains, and the mixing weights.
+
+Jensen-Shannon Divergence Consistency Loss. We couple with this augmentation scheme a loss that enforces smoother neural network responses. Since the semantic content of an image is approximately preserved with AUGMIX, we should like the model to embed $x _ { \mathrm { o r i g } }$ , $x _ { \mathrm { a u g m i x 1 } }$ , xaugmix2 similarly. Toward this end, we minimize the Jensen-Shannon divergence among the posterior distributions of the original sample $x _ { \mathrm { o r i g } }$ and its augmented variants. That is, for $p _ { \mathrm { o r i g } } ~ = ~ { \hat { p } } ( y ~ |$ $x _ { \mathrm { o r i g } } ) , p _ { \mathrm { a u g m i x 1 } } = \hat { p } ( y \mid \bar { x } _ { \mathrm { a u g m i x 1 } } ) , \bar { p } _ { \mathrm { a u g m i x 2 } } \stackrel { \sim } { = } \hat { p } ( y | x _ { \mathrm { a u g m i x 2 } } )$ , we replace the original loss $\mathcal { L }$ with the loss
+
+$$
+\mathcal { L } ( p _ { \mathrm { o r i g } } , y ) + \lambda \operatorname { J S } ( p _ { \mathrm { o r i g } } ; p _ { \mathrm { a u g m i x 1 } } ; p _ { \mathrm { a u g m i x 2 } } ) .
+$$
+
+To interpret this loss, imagine a sample from one of the three distributions $p _ { \mathrm { o r i g } } , p _ { \mathrm { a u g m i x 1 } } , p _ { \mathrm { a u g m i x 2 } }$ . The Jensen-Shannon divergence can be understood to measure the average information that the sample reveals about the identity of the distribution from which it was sampled.
+
+This loss can be computed by first obtaining $M = ( p _ { \mathrm { o r i g } } + p _ { \mathrm { a u g m i x 1 } } + p _ { \mathrm { a u g m i x 2 } } ) / 3$ and then computing
+
+$$
+\mathrm { J S } \big ( p _ { \mathrm { o r i g } } ; p _ { \mathrm { a u g m i x 1 } } ; p _ { \mathrm { a u g m i x 2 } } \big ) = \frac { 1 } { 3 } \Big ( \mathrm { K L } \big [ p _ { \mathrm { o r i g } } \| M \big ] + \mathrm { K L } \big [ p _ { \mathrm { a u g m i x 1 } } \| M \big ] + \mathrm { K L } \big [ p _ { \mathrm { a u g m i x 2 } } \| M \big ] \Big ) .
+$$
+
+Unlike an arbitrary KL Divergence between $p _ { \mathrm { o r i g } }$ and $p _ { \mathrm { a u g m i x } }$ , the Jensen-Shannon divergence is upper bounded, in this case by the logarithm of the number of classes. Note that we could instead compute $\mathbf { J } \mathbf { S } ( p _ { \mathrm { o r i g } } ; p _ { \mathrm { a u g m i x 1 } } )$ , though this does not perform as well. The gain of training with JS $p _ { \mathrm { o r i g } }$ ; paugmix1; paugmix2; paugmix3) is marginal. The Jensen-Shannon Consistency Loss impels to model to be stable, consistent, and insensitive across to a diverse range of inputs (Zheng et al., 2016; Kannan et al., 2018; Xie et al., 2019). Ablations are in Section 4.3 and Appendix A.
+
+# 4 EXPERIMENTS
+
+Datasets. The two CIFAR (Krizhevsky & Hinton, 2009) datasets contain small $3 2 \times 3 2 \times 3$ color natural images, both with 50,000 training images and 10,000 testing images. CIFAR-10 has 10 categories, and CIFAR-100 has 100. The ImageNet (Deng et al., 2009) dataset contains 1,000 classes of approximately 1.2 million large-scale color images.
+
+In order to measure a model’s resilience to data shift, we evaluate on the CIFAR-10-C, CIFAR-100- $C$ , and ImageNet- $C$ datasets (Hendrycks & Dietterich, 2019). These datasets are constructed by corrupting the original CIFAR and ImageNet test sets. For each dataset, there are a total of 15 noise, blur, weather, and digital corruption types, each appearing at 5 severity levels or intensities. Since these datasets are used to measure network behavior under data shift, we take care not to introduce these 15 corruptions into the training procedure.
+
+The CIFAR-10-P, CIFAR-100- ${ \bf \nabla } \cdot { \cal P }$ , and ImageNet- $P$ datasets also modify the original CIFAR and ImageNet datasets. These datasets contain smaller perturbations than CIFAR-C and are used to measure the classifier’s prediction stability. Each example in these datasets is a video. For instance, a video with the brightness perturbation shows an image getting progressively brighter over time. We should like the network not to give inconsistent or volatile predictions between frames of the video as the brightness increases. Thus these datasets enable the measurement of the “jaggedness” (Azulay & Weiss, 2018) of a network’s prediction stream.
+
+Metrics. The Clean Error is the usual classification error on the clean or uncorrupted test data. In our experiments, corrupted test data appears at five different intensities or severity levels $1 \leq s \leq 5$ . For a given corruption $c$ , the error rate at corruption severity $s$ is $E _ { c , s }$ . We can compute the average error across these severities to create the unnormalized corruption error $\begin{array} { r } { \mathbf { u C E } _ { c } = \sum _ { s = 1 } ^ { 5 } E _ { c , s } } \end{array}$ . On CIFAR-10- C and CIFAR-100-C we average these values over all 15 corruptions. Meanwhile, on ImageNet we follow the convention of normaet al., 2012). We compute $\begin{array} { r } { \mathrm { C E } _ { c } = \sum _ { s = 1 } ^ { 5 } \bar { E } _ { c , s } / \sum _ { s = 1 } ^ { 5 } E _ { c , s } ^ { \mathrm { A l e x N e t } } } \end{array}$ ruption error of AlexNet (Kriz. The average of the 15 cor errors CEGaussian Noise, CEShot Noise, . . . , CEPixelate, CEJPEG gives us the Mean Corruption Error $( m C E )$ .
+
+Perturbation robustness is not measured by accuracy but whether video frame predictions match. Consequently we compute what is called the flip probability. Concretely, for videos such as those with steadily increasing brightness, we determine the probability that two adjacent frames, or two frames with slightly different brightness levels, have “flipped” or mismatched predictions. There are 10 different perturbation types, and the mean across these is the mean Flip Probability $( m F P )$ . As with ImageNet-C, we can normalize by AlexNet’s flip probabilities and obtain the mean Flip Rate $( m F R )$ .
+
+In order to assess a model’s uncertainty estimates, we measure its miscalibration. Classifiers capable of reliably forecasting their accuracy are considered “calibrated.” For instance, a calibrated classifier should be correct $70 \%$ of the time on examples to which it assigns $70 \%$ confidence. Let the classifier’s confidence that its prediction $\hat { Y }$ is correct be written $C$ . Then the idealized RMS Calibration Error is $\sqrt { \mathbb { E } _ { C } [ ( \mathbb { P } ( Y = \hat { Y } | C = c ) - c ) ^ { 2 } ] } ,$ , which is the squared difference between the accuracy at a given confidence level and actual the confidence level. In Appendix E, we show how to empirically estimate this quantity and calculate the Brier Score.
+
+# 4.1 CIFAR-10 AND CIFAR-100
+
+Training Setup. In the following experiments we show that AUGMIX endows robustness to various architectures including an All Convolutional Network (Springenberg et al., 2014; Salimans & Kingma, 2016), a DenseNet-BC $( k = 1 2 , d = 1 0 0 )$ ) (Huang et al., 2017) , a 40-2 Wide ResNet (Zagoruyko & Komodakis, 2016), and a ResNeXt-29 $( 3 2 \times 4 )$ (Xie et al., 2016). All networks use an initial learning rate of 0.1 which decays following a cosine learning rate (Loshchilov & Hutter, 2016). All input images are pre-processed with standard random left-right flipping and cropping prior to any augmentations. We do not change AUGMIX parameters across CIFAR-10 and CIFAR-100 experiments for consistency. The All Convolutional Network and Wide ResNet train for 100 epochs, and the DenseNet and ResNeXt require 200 epochs for convergence. We optimize with stochastic gradient descent using Nesterov momentum. Following Zhang et al. (2017); Guo et al. (2019), we use a weight decay of 0.0001 for Mixup and 0.0005 otherwise.
+
+![](images/413822b829d4661106d29927637b1d4289291955a82fe9e9f1b5d858f495d6f1.jpg)  
+Figure 5: Error rates of various methods on CIFAR-10-C using a ResNeXt backbone. Observe that AUGMIX halves the error rate of prior methods and approaches the clean error rate.
+
+Table 1: Average classification error as percentages. Across several architectures, AUGMIX obtains CIFAR-10-C and CIFAR-100-C corruption robustness that exceeds the previous state of the art.   
+
+<table><tr><td></td><td></td><td>Standard</td><td>Cutout</td><td>Mixup</td><td></td><td>CutMix AutoAugment* Adv Training AUGMIX</td><td></td><td></td></tr><tr><td rowspan="4">CIFAR-10-C</td><td>AllConvNet</td><td>30.8</td><td>32.9</td><td>24.6</td><td>31.3</td><td>29.2</td><td>28.1</td><td>15.0</td></tr><tr><td>DenseNet</td><td>30.7</td><td>32.1</td><td>24.6</td><td>33.5</td><td>26.6</td><td>27.6</td><td>12.7</td></tr><tr><td>WideResNet</td><td>26.9</td><td>26.8</td><td>22.3</td><td>27.1</td><td>23.9</td><td>26.2</td><td>11.2</td></tr><tr><td>ResNeXt</td><td>27.5</td><td>28.9</td><td>22.6</td><td>29.5</td><td>24.2</td><td>27.0</td><td>10.9</td></tr><tr><td colspan="2">Mean</td><td>29.0</td><td>30.2</td><td>23.5</td><td>30.3</td><td>26.0</td><td>27.2</td><td>12.5</td></tr><tr><td rowspan="4">CIFAR-100-C</td><td>AllConvNet</td><td>56.4</td><td>56.8</td><td>53.4</td><td>56.0</td><td>55.1</td><td>56.0</td><td>42.7</td></tr><tr><td>DenseNet</td><td>59.3</td><td>59.6</td><td>55.4</td><td>59.2</td><td>53.9</td><td>55.2</td><td>39.6</td></tr><tr><td>WideResNet</td><td>53.3</td><td>53.5</td><td>50.4</td><td>52.9</td><td>49.6</td><td>55.1</td><td>35.9</td></tr><tr><td>ResNeXt</td><td>53.4</td><td>54.6</td><td>51.4</td><td>54.1</td><td>51.3</td><td>54.4</td><td>34.9</td></tr><tr><td colspan="2">Mean</td><td>55.6</td><td>56.1</td><td>52.6</td><td>55.5</td><td>52.5</td><td>55.2</td><td>38.3</td></tr></table>
+
+Results. Simply mixing random augmentations and using the Jensen-Shannon loss substantially improves robustness and uncertainty estimates. Compared to the “Standard” data augmentation baseline ResNeXt on CIFAR-10-C, AUGMIX achieves $1 6 . 6 \%$ lower absolute corruption error as shown in Figure 5. In addition to surpassing numerous other data augmentation techniques, Table 1 demonstrates that these gains directly transfer across architectures and on CIFAR-100-C with zero additional tuning. Crucially, the robustness gains do not only exist when measured in aggregate. Figure 12 shows that AUGMIX improves corruption robustness across every individual corruption and severity level. Our method additionally achieves the lowest mFP on CIFAR-10-P across three different models all while maintaining accuracy on clean CIFAR-10, as shown in Figure 6 (left) and Table 6. Finally, we demonstrate that AUGMIX improves the RMS calibration error on CIFAR-10 and CIFAR-10-C, as shown in Figure 6 (right) and Table 5. Expanded CIFAR-10-P and calibration results are in Appendix D, and Fourier Sensitivity analysis is in Appendix B.
+
+![](images/c4e2d37dfd75cceb92cbe45f608f245c84a3a80c4bb2d5a26eacb828660bb96a.jpg)  
+Figure 6: CIFAR-10-P prediction stability and Root Mean Square Calibration Error values for ResNeXt. AUGMIX simultaneously reduces flip probabilities and calibration error.
+
+# 4.2 IMAGENET
+
+Baselines. To demonstrate the utility of AUGMIX on ImageNet, we compare to many techniques designed for large-scale images. While techniques such as Cutout (Devries & Taylor, 2017) have not been demonstrated to help on the ImageNet scale, and while few have had success training adversarially robust models on ImageNet (Engstrom et al., 2018), other techniques such as Stylized ImageNet have been demonstrated to help on ImageNet-C. Patch Uniform (Lopes et al., 2019) is similar to Cutout except that randomly chosen regions of the image are injected with uniform noise; the original paper uses Gaussian noise, but that appears in the ImageNet-C test set so we use uniform noise. We tune Patch Uniform over 30 hyperparameter settings. Next, AutoAugment (Cubuk et al., 2018) searches over data augmentation policies to find a high-performing data augmentation policy. We denote AutoAugment results with AutoAugment\* since we remove augmentation operations that overlap with ImageNet-C corruptions, as with AUGMIX. We also test with Random AutoAugment\*, an augmentation scheme where each image has a randomly sampled augmentation policy using AutoAugment\* operations. In contrast to AutoAugment, Random AutoAugment\* and AUGMIX require far less computation and provide more augmentation variety, which can offset their lack of optimization. Note that Random AutoAugment\* is different from RandAugment introduced recently by Cubuk et al. (2019): RandAugment uses AutoAugment operations and optimizes a single distortion magnitude hyperparameter for all operations, while Random AutoAugment\* randomly samples magnitudes for each operation and uses the same operations as AUGMIX. MaxBlur Pooling (Zhang, 2019) is a recently proposed architectural modification which smooths the results of pooling. Now, Stylized ImageNet (SIN) is a technique where models are trained with the original ImageNet images and also ImageNet images with style transfer applied. Whereas the original Stylized ImageNet technique pretrains on ImageNet-C and performs style transfer with a content loss coefficient of 0 and a style loss coefficient of 1, we find that using 0.5 content and style loss coefficients decreases the mCE by $0 . 6 \%$ . Later, we show that SIN and AUGMIX can be combined. All models are trained from scratch, except MaxBlur Pooling models which has trained models available.
+
+Training Setup. Methods are trained with ResNet-50 and we follow the standard training scheme of Goyal et al. (2017), in which we linearly scale the learning rate with the batch size, and use a learning rate warm-up for the first 5 epochs, and AutoAugment and AUGMIX train for 180 epochs. All input images are first pre-processed with standard random cropping horizontal mirroring.
+
+Table 2: Clean Error, Corruption Error (CE), and mCE values for various methods on ImageNet-C. The mCE value is computed by averaging across all $1 5 \mathrm { C E }$ values. AUGMIX reduces corruption error while improving clean accuracy, and it can be combined with SIN for greater corruption robustness.   
+
+<table><tr><td></td><td></td><td></td><td>Noise</td><td></td><td></td><td>Blur</td><td></td><td></td><td></td><td></td><td>Weather</td><td></td><td></td><td>Digital</td><td></td><td></td><td></td></tr><tr><td>Network</td><td>Clean</td><td>Gauss.Shot Impulse</td><td></td><td></td><td>Defocus Glass Motion Zoom</td><td></td><td></td><td></td><td></td><td></td><td>SnowFrostFog</td><td>Bright</td><td></td><td>Contrast Elastic Pixel JPEG</td><td></td><td></td><td>mCE</td></tr><tr><td>Standard</td><td>23.9</td><td>79</td><td>80</td><td>82</td><td>82</td><td>90</td><td>84</td><td>80</td><td>86</td><td>81</td><td>75</td><td>65</td><td>79</td><td>91</td><td>77</td><td>80</td><td>80.6</td></tr><tr><td>Patch Uniform</td><td>24.5</td><td>67</td><td>68</td><td>70</td><td>74</td><td>83</td><td>81</td><td>77</td><td>80</td><td>74</td><td>75</td><td>62</td><td>77</td><td>84</td><td>71</td><td>71</td><td>74.3</td></tr><tr><td>AutoAugment* (AA)</td><td>22.8</td><td>69</td><td>68</td><td>72</td><td>77</td><td>83</td><td>80</td><td>81</td><td>79</td><td>75</td><td>64</td><td>56</td><td>70</td><td>88</td><td>57</td><td>71</td><td>72.7</td></tr><tr><td>Random AA*</td><td>23.6</td><td>70</td><td>71</td><td>72</td><td>80</td><td>86</td><td>82</td><td>81</td><td>81</td><td>77</td><td>72</td><td>61</td><td>75</td><td>88</td><td>73</td><td>72</td><td>76.1</td></tr><tr><td>MaxBlur pool</td><td>23.0</td><td>73</td><td>74</td><td>76</td><td>74</td><td>86</td><td>78</td><td>77</td><td>77</td><td>72</td><td>63</td><td>56</td><td>68</td><td>86</td><td>71</td><td>71</td><td>73.4</td></tr><tr><td>SIN</td><td>27.2</td><td>69</td><td>70</td><td>70</td><td>77</td><td>84</td><td>76</td><td>82</td><td>74</td><td>75</td><td>69</td><td>65</td><td>69</td><td>80</td><td>64</td><td>77</td><td>73.3</td></tr><tr><td>AUGMIX</td><td>22.4</td><td>65</td><td>66</td><td>67</td><td>70</td><td>80</td><td>66</td><td>66</td><td>75</td><td>72</td><td>67</td><td>58</td><td>58</td><td>79</td><td>69</td><td>69</td><td>68.4</td></tr><tr><td>AUGMIX+SIN</td><td>25.2</td><td>61</td><td>62</td><td>61</td><td>69</td><td>77</td><td>63</td><td>72</td><td>66</td><td>68</td><td>63</td><td>59</td><td>52</td><td>74</td><td>60</td><td>67</td><td>64.9</td></tr></table>
+
+Results. Our method achieves $6 8 . 4 \%$ mCE as shown in Table 2, down from the baseline $8 0 . 6 \%$ mCE. Additionally, we note that AUGMIX allows straightforward stacking with other methods such as SIN to achieve an even lower corruption error of $6 4 . 1 \%$ mCE. Other techniques such as AutoAugment\* require much tuning, while ours does not. Across increasing severities of corruptions, our method also produces much more calibrated predictions measured by both the Brier Score and RMS Calibration Error as shown in Figure 7. As shown in Table 3, AUGMIX also achieves a state-of-the art result on ImageNet-P at with an mFR of $3 7 . 4 \%$ , down from $5 7 . 2 \%$ . We demonstrate that scaling up AUGMIX from CIFAR to ImageNet also leads to state-of-the-art results in robustness and uncertainty estimation.
+
+# 4.3 ABLATIONS
+
+We locate the utility of AUGMIX in three factors: training set diversity, our Jensen-Shannon divergence consistency loss, and mixing. Improving training set diversity via increased variety of augmentations can greatly improve robustness. For instance, augmenting each example with a
+
+<table><tr><td></td><td></td><td colspan="2">Noise</td><td colspan="2">Blur</td><td colspan="2">Weather</td><td colspan="5">Digital</td></tr><tr><td>Network</td><td>Clean</td><td>Gaussian Shot</td><td></td><td>Motion Zoom</td><td></td><td>Snow</td><td>Bright</td><td>TranslateRotate</td><td></td><td>TiltScale</td><td></td><td>mFR</td></tr><tr><td>Standard</td><td>23.9</td><td>57</td><td>55</td><td>62</td><td>65</td><td>66</td><td>65</td><td>43</td><td>53</td><td>57</td><td>49</td><td>57.2</td></tr><tr><td>Patch Uniform</td><td>24.5</td><td>32</td><td>25</td><td>50</td><td>52</td><td>54</td><td>57</td><td>40</td><td>48</td><td>49</td><td>46</td><td>45.3</td></tr><tr><td>AutoAugment* (AA)</td><td>22.8</td><td>50</td><td>45</td><td>57</td><td>68</td><td>63</td><td>53</td><td>40</td><td>44</td><td>50</td><td>46</td><td>51.7</td></tr><tr><td>Random AA*</td><td>23.6</td><td>53</td><td>46</td><td>53</td><td>63</td><td>59</td><td>57</td><td>42</td><td>48</td><td>54</td><td>47</td><td>52.2</td></tr><tr><td>SIN</td><td>27.2</td><td>53</td><td>50</td><td>57</td><td>72</td><td>51</td><td>62</td><td>43</td><td>53</td><td>57</td><td>53</td><td>55.0</td></tr><tr><td>MaxBlur pool</td><td>23.0</td><td>52</td><td>51</td><td>59</td><td>63</td><td>57</td><td>64</td><td>34</td><td>43</td><td>49</td><td>40</td><td>51.2</td></tr><tr><td>AUGMIX</td><td>22.4</td><td>46</td><td>41</td><td>30</td><td>47</td><td>38</td><td>46</td><td>25</td><td>32</td><td>35</td><td>33</td><td>37.4</td></tr><tr><td>AUGMIX+SIN</td><td>25.2</td><td>45</td><td>40</td><td>30</td><td>54</td><td>32</td><td>48</td><td>27</td><td>35</td><td>38</td><td>39</td><td>38.9</td></tr></table>
+
+Table 3: ImageNet-P results. The mean flipping rate is the average of the flipping rates across all 10 perturbation types. AUGMIX improves perturbation stability by approximately $20 \%$ .
+
+![](images/0f95f31726e708fda8050e5871180a33c4fc38dd8f9929d9ee99690701b9528e.jpg)  
+Figure 7: Uncertainty results on ImageNet-C. Observe that under severe data shifts, the RMS calibration error with ensembles and AUGMIX is remarkably steady. Even though classification error increases, calibration is roughly preserved. Severity zero denotes clean data.
+
+randomly sampled augmentation chain decreases the error rate of Wide ResNet on CIFAR-10-C from $2 6 . 9 \%$ to $1 7 . 0 \%$ Table 4. Adding in the Jensen-Shannon divergence consistency loss drops error rate further to $1 4 . 7 \%$ . Mixing random augmentations without the Jenson-Shannon divergence loss gives us an error rate of $1 3 . 1 \%$ . Finally, re-introducing the Jensen-Shannon divergence gives us AUGMIX with an error rate of $1 1 . 2 \%$ . Note that adding even more mixing is not necessarily beneficial. For instance, applying AUGMIX on top of Mixup increases the error rate to $1 3 . 3 \%$ , possibly due to an increased chance of manifold intrusion (Guo et al., 2019). Hence AUGMIX’s careful combination of variety, consistency loss, and mixing explain its performance.
+
+Table 4: Ablating components of AUGMIX on CIFAR-10-C and CIFAR-100-C. Variety through randomness, the Jensen-Shannon divergence (JSD) loss, and augmentation mixing confer robustness.   
+
+<table><tr><td>Method</td><td>CIFAR-10-C Error Rate</td><td>CIFAR-100-C ErrorRate</td></tr><tr><td>Standard</td><td>26.9</td><td>53.3</td></tr><tr><td>AutoAugment*</td><td>23.9</td><td>49.6</td></tr><tr><td>Random AutoAugment*</td><td>17.0</td><td>43.6</td></tr><tr><td>Random AutoAugment* + JSDLoss</td><td>14.7</td><td>40.8</td></tr><tr><td>AugmentAndMix (No JSD Loss)</td><td>13.1</td><td>39.8</td></tr><tr><td>AUGMIX (Mixing + JSD Loss)</td><td>11.2</td><td>35.9</td></tr></table>
+
+# 5 CONCLUSION
+
+AUGMIX is a data processing technique which mixes randomly generated augmentations and uses a Jensen-Shannon loss to enforce consistency. Our simple-to-implement technique obtains state-of-the-art performance on CIFAR-10/100-C, ImageNet-C, CIFAR-10/100-P, and ImageNet-P. AUGMIX models achieve state-of-the-art calibration and can maintain calibration even as the distribution shifts. We hope that AUGMIX will enable more reliable models, a necessity for models deployed in safety-critical environments.
+
+# REFERENCES
+
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+
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+
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+
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+
+# A HYPERPARAMETER ABLATIONS
+
+In this section we demonstrate that AUGMIX’s hyperparameters are not highly sensitive, so that AUGMIX performs reliably without careful tuning. For this set of experiments, the baseline AUGMIX model trains for 90 epochs, has a mixing coefficient of $\alpha = 0 . 5$ , has 3 examples per Jensen-Shannon Divergence (1 clean image, 2 augmented images), has a chain depth stochastically varying from 1 to 3, and has $k = 3$ augmentation chains. Figure 8 shows that the performance of various AUGMIX models with different hyperparameters. Under these hyperparameter changes, the mCE does not change substantially.
+
+![](images/1cfcf05e745f24551323e62d6d3864d7681b43516d3591a80175e06aba0058eb.jpg)  
+AugMix ImageNet-C Ablations
+
+![](images/b2387776be0bcd6855c4139892a559b790e6134a8974823eeea4312a5b9f0b35.jpg)  
+Figure 8: AUGMIX hyperparameter ablations on ImageNet-C. ImageNet-C classification performance is stable changes to AUGMIX’s hyperparameters.   
+Figure 9: Fourier Sensitivity Heatmap of the baseline Wide ResNet, Cutout, and AUGMIX CIFAR-10 models. All Fourier basis perturbations are added to clean CIFAR-10 test images. AUGMIX maintains robustness at low frequencies and is far more robust to mid and high frequency modifications. Example perturbed images are shown above, with black pointer lines indicating the Fourier basis vector used to perturb the image. For each basis vector we compute the error rate of the model after perturbing the entire test set.
+
+# B FOURIER ANALYSIS
+
+A commonly mentioned hypothesis (Gilmer & Hendrycks, 2019) for the lack of robustness of deep neural networks is that they readily latch onto spurious high-frequency correlations that exist in the data. In order to better understand the reliance of models to such correlations, we measure model sensitivity to additive noise at differing frequencies. We create a $3 2 \times 3 2$ sensitivity heatmap. That is, we add a total of $3 2 \times 3 2$ Fourier basis vectors to the CIFAR-10 test set, one at a time, and record the resulting error rate after adding each Fourier basis vector. Each point in the heatmap shows the error rate on the CIFAR-10 test set after it has been perturbed by a single Fourier basis vector. Points corresponding to low frequency vectors are shown in the center of the heatmap, whereas high frequency vectors are farther from the center. For further details on Fourier sensitivity analysis, we refer the reader to Section 2 of Yin et al. (2019). In Figure 9 we observe that the baseline model is robust to low frequency perturbations but severely lacks robustness to high frequency perturbations, where error rates exceed $80 \%$ . The model trained with Cutout shows a similar lack of robustness. In contrast, the model trained with AUGMIX maintains robustness to low frequency perturbations, and on the mid and high frequencies AUGMIX is conspicuously more robust.
+
+# C AUGMENTATION OPERATIONS
+
+The augmentation operations we use for AUGMIX are shown in Figure 10.
+
+![](images/7748e858401f577400d8e8329defa78203fec7a848cb47c79b85b290d10a48b5.jpg)  
+Figure 10: Illustration of augmentation operations applied to the same image. Some operation severities have been increased to show detail.
+
+We do not use augmentations such as contrast, color, brightness, sharpness, and Cutout as they may overlap with ImageNet-C test set corruptions. We should note that augmentation choice requires additional care. Guo et al. (2019) show that blithely applying augmentations can potentially cause augmented images to take different classes. Figure 11 shows how histogram color swapping augmentation may change a bird’s class, leading to a manifold intrusion.
+
+![](images/c459b1b2d285197ceac76a323861e94a9afd455ba855528c9f1baa820dd32885.jpg)  
+Figure 11: An illustration of manifold intrusion (Guo et al., 2019), where histogram color augmentation can change the image’s class.
+
+# D ADDITIONAL RESULTS
+
+We include various additional results for CIFAR-10, CIFAR-10-C and CIFAR-10-P below. Figure 12 reports accuracy for each corruption, Table 5 reports calibration results for various architectures and Table 6 reports clean error and mFR. We refer to Section 4.1 for details about the architecture and training setup.
+
+![](images/3ffcf7ca776f94b1bbae00d39894de3c48178b50545e4390eb343ce3213fe832.jpg)  
+Figure 12: AUGMIX improves corruption robustness across all CIFAR-10-C noise, blur, weather, and digital corruptions, despite the model never having seen these corruptions during training.
+
+Table 5: RMS Calibration Error of various models and data augmentation methods across CIFAR-10 and CIFAR-10-C. All values are reported as percentages.   
+
+<table><tr><td></td><td></td><td>Standard Cutout</td><td>Mixup</td><td></td><td></td><td>CutMix AutoAugment* Adv Training AUGMIX</td><td></td><td></td></tr><tr><td rowspan="4">CIFAR-10</td><td>AllConvNet</td><td>5.4</td><td>4.0</td><td>12.6</td><td>3.1</td><td>4.2</td><td>11.1</td><td>2.2</td></tr><tr><td>DenseNet</td><td>7.5</td><td>6.4</td><td>15.6</td><td>5.4</td><td>6.0</td><td>16.2</td><td>5.0</td></tr><tr><td>WideResNet</td><td>6.8</td><td>3.8</td><td>14.0</td><td>5.0</td><td>4.7</td><td>10.7</td><td>4.2</td></tr><tr><td>ResNeXt</td><td>3.0</td><td>4.4</td><td>13.5</td><td>3.5</td><td>3.3</td><td>5.8</td><td>3.0</td></tr><tr><td colspan="2">Mean</td><td>5.7</td><td>4.7</td><td>13.9</td><td>4.2</td><td>4.6</td><td>11.0</td><td>3.6</td></tr><tr><td rowspan="4">CIFAR-10-C</td><td>AllConvNet</td><td>21.2</td><td>21.3</td><td>9.7</td><td>15.4</td><td>16.2</td><td>10.4</td><td>5.2</td></tr><tr><td>DenseNet</td><td>26.7</td><td>27.8</td><td>12.9</td><td>25.6</td><td>21.1</td><td>15.0</td><td>11.7</td></tr><tr><td>WideResNet</td><td>27.6</td><td>19.6</td><td>11.1</td><td>17.8</td><td>17.1</td><td>10.6</td><td>8.7</td></tr><tr><td>ResNeXt</td><td>16.4</td><td>21.4</td><td>11.7</td><td>19.6</td><td>15.1</td><td>11.6</td><td>8.3</td></tr><tr><td colspan="2">Mean</td><td>23.0</td><td>22.5</td><td>11.4</td><td>19.6</td><td>17.4</td><td>11.9</td><td>8.5</td></tr></table>
+
+Table 6: CIFAR-10 Clean Error and CIFAR-10-P mean Flip Probability. All values are percentages. While adversarial training performs well on CIFAR-10-P, it induces a substantial drop in accuracy (increase in error) on clean CIFAR-10 where AUGMIX does not.   
+
+<table><tr><td colspan="2"></td><td colspan="7">Standard Cutout Mixup CutMix AutoAugment* Adv Training AUGMIX</td></tr><tr><td rowspan="4">CIFAR-10</td><td>AllConvNet</td><td>6.1</td><td>6.1</td><td>6.3</td><td>6.4</td><td>6.6</td><td>18.9</td><td>6.5</td></tr><tr><td>DenseNet</td><td>5.8</td><td>4.8</td><td>5.5</td><td>5.3</td><td>4.8</td><td>17.9</td><td>4.9</td></tr><tr><td>WideResNet</td><td>5.2</td><td>4.4</td><td>4.9</td><td>4.6</td><td>4.8</td><td>17.1</td><td>4.9</td></tr><tr><td>ResNeXt</td><td>4.3</td><td>4.4</td><td>4.2</td><td>3.9</td><td>3.8</td><td>15.4</td><td>4.2</td></tr><tr><td colspan="2">Mean</td><td>5.4</td><td>4.9</td><td>5.2</td><td>5.0</td><td>5.0</td><td>17.3</td><td>5.1</td></tr><tr><td rowspan="4">CIFAR-10-P</td><td>AllConvNet</td><td>4.2</td><td>5.0</td><td>3.9</td><td>4.5</td><td>4.0</td><td>2.0</td><td>1.5</td></tr><tr><td>DenseNet</td><td>5.0</td><td>5.7</td><td>3.9</td><td>6.3</td><td>4.8</td><td>2.1</td><td>1.8</td></tr><tr><td>WideResNet</td><td>4.2</td><td>4.3</td><td>3.4</td><td>4.6</td><td>4.2</td><td>2.2</td><td>1.6</td></tr><tr><td>ResNeXt</td><td>4.0</td><td>4.5</td><td>3.2</td><td>5.2</td><td>4.2</td><td>2.5</td><td>1.5</td></tr><tr><td colspan="2">Mean</td><td>4.3</td><td>4.9</td><td>3.6</td><td>5.2</td><td>4.3</td><td>2.2</td><td>1.6</td></tr></table>
+
+# E CALIBRATION METRICS
+
+Due to the finite size of empirical test sets, the RMS Calibration Error must be estimated by partitioning all $n$ test set examples into $b$ contiguous bins $\{ B _ { 1 } , B _ { 2 } , \dots , B _ { b } \}$ ordered by prediction confidence. In this work we use bins which contain 100 predictions, so that we adaptively partition confidence scores on the interval [0, 1] (Nguyen & O’Connor, 2015; Hendrycks et al., 2019b). Other works partition the interval $[ 0 , 1 ]$ with 15 bins of uniform length (Guo et al., 2017). With these $b$ bins, we estimate the RMS Calibration Error empirically with the formula
+
+$$
+\sqrt { \sum _ { i = 1 } ^ { b } \frac { | B _ { i } | } { n } \biggl ( \frac { 1 } { | B _ { i } | } \sum _ { k \in B _ { i } } \mathbb { 1 } \bigl ( y _ { k } = \hat { y } _ { k } \bigr ) - \frac { 1 } { | B _ { i } | } \sum _ { k \in B _ { i } } c _ { k } \biggr ) ^ { 2 ^ { \top } } } .
+$$
+
+This is separate from classification error because a random classifier with an approximately uniform posterior distribution is approximately calibrated. Also note that adding the “refinement” $\mathbb { E } _ { C } [ ( \mathbb { P } ( Y =$ $\hat { Y } | C = c ) ( 1 - ( \mathbb { P } ( Y = \hat { Y } | C = c ) ) ]$ to the square of the RMS Calibration Error gives us the Brier Score (Nguyen & O’Connor, 2015).

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+    {
+        "type": "text",
+        "text": "AUGMIX: A SIMPLE DATA PROCESSING METHOD TO IMPROVE ROBUSTNESS AND UNCERTAINTY ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            98,
+            823,
+            146
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Dan Hendrycks∗   \nDeepMind   \nhendrycks@berkeley.edu   \nNorman Mu∗   \nGoogle   \nnormanmu@google.com ",
+        "bbox": [
+            183,
+            170,
+            380,
+            212
+        ],
+        "page_idx": 0
+    },
+    {
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Ekin D. Cubuk Google cubuk@google.com ",
+        "bbox": [
+            666,
+            170,
+            810,
+            212
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Barret Zoph   \nGoogle   \nbarretzoph@google.com ",
+        "bbox": [
+            183,
+            234,
+            372,
+            275
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Justin Gilmer Google gilmer@google.com ",
+        "bbox": [
+            411,
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+            566,
+            276
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Balaji Lakshminarayanan† DeepMind balajiln@google.com ",
+        "bbox": [
+            606,
+            234,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "ABSTRACT ",
+        "text_level": 1,
+        "bbox": [
+            454,
+            313,
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+            327
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Modern deep neural networks can achieve high accuracy when the training distribution and test distribution are identically distributed, but this assumption is frequently violated in practice. When the train and test distributions are mismatched, accuracy can plummet. Currently there are few techniques that improve robustness to unforeseen data shifts encountered during deployment. In this work, we propose a technique to improve the robustness and uncertainty estimates of image classifiers. We propose AUGMIX, a data processing technique that is simple to implement, adds limited computational overhead, and helps models withstand unforeseen corruptions. AUGMIX significantly improves robustness and uncertainty measures on challenging image classification benchmarks, closing the gap between previous methods and the best possible performance in some cases by more than half. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            517,
+            336,
+            534
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Current machine learning models depend on the ability of training data to faithfully represent the data encountered during deployment. In practice, data distributions evolve (Lipton et al., 2018), models encounter new scenarios (Hendrycks & Gimpel, 2017), and data curation procedures may capture only a narrow slice of the underlying data distribution (Torralba & Efros, 2011). Mismatches between the train and test data are commonplace, yet the study of this problem is not. As it stands, models do not robustly generalize across shifts in the data distribution. If models could identify when they are likely to be mistaken, or estimate uncertainty accurately, then the impact of such fragility might be ameliorated. Unfortunately, modern models already produce overconfident predictions when the training examples are independent and identically distributed to the test distribution. This overconfidence and miscalibration is greatly exacerbated by mismatched training and testing distributions. ",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Small corruptions to the data distribution are enough to subvert existing classifiers, and techniques to improve corruption robustness remain few in number. Hendrycks & Dietterich (2019) show that classification error of modern models rises from $22 \\%$ on the usual ImageNet test set to $64 \\%$ on ImageNet-C, a test set consisting of various corruptions applied to ImageNet test images. Even methods which aim to explicitly quantify uncertainty, such as probabilistic and Bayesian neural networks, struggle under data shift, as recently demonstrated by Ovadia et al. (2019). Improving performance in this setting has been difficult. One reason is that training against corruptions only encourages networks to memorize the specific corruptions seen during training and leaves models unable to generalize to new corruptions (Vasiljevic et al., 2016; Geirhos et al., 2018). Further, networks trained on translation augmentations remain highly sensitive to images shifted by a single pixel (Gu et al., 2019; Hendrycks & Dietterich, 2019). Others have proposed aggressive data augmentation schemes (Cubuk et al., 2018), though at the cost of a computational increase. Chun et al. (2019) demonstrates that many techniques may improve clean accuracy at the cost of robustness while many techniques which improve robustness harm uncertainty, and contrariwise. In all, existing techniques have considerable trade-offs. ",
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+    },
+    {
+        "type": "image",
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+        "image_caption": [
+            "Figure 1: A visual comparison of data augmentation techniques. AUGMIX produces images with variety while preserving much of the image semantics and local statistics. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In this work, we propose a technique to improve both the robustness and uncertainty estimates of classifiers under data shift. We propose AUGMIX, a method which simultaneously achieves new state-of-the-art results for robustness and uncertainty estimation while maintaining or improving accuracy on standard benchmark datasets. AUGMIX utilizes stochasticity and diverse augmentations, a Jensen-Shannon Divergence consistency loss, and a formulation to mix multiple augmented images to achieve state-of-the-art performance. On CIFAR-10 and CIFAR-100, our method roughly halves the corruption robustness error of standard training procedures from $2 8 . 4 \\%$ to $1 2 . 4 \\%$ and $5 4 . 3 \\%$ to $3 7 . 8 \\%$ error, respectively. On ImageNet, AUGMIX also achieves state-of-the-art corruption robustness and decreases perturbation instability from $5 7 . 2 \\%$ to $3 7 . 4 \\%$ . Code is available at https://github.com/google-research/augmix. ",
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+    {
+        "type": "text",
+        "text": "2 RELATED WORK ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            462,
+            344,
+            478
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Robustness under Data Shift. Geirhos et al. (2018) show that training against distortions can often fail to generalize to unseen distortions, as networks have a tendency to memorize properties of the specific training distortion. Vasiljevic et al. (2016) show training with various blur augmentations can fail to generalize to unseen blurs or blurs with different parameter settings. Hendrycks & Dietterich (2019) propose measuring generalization to unseen corruptions and provide benchmarks for doing so. Kang et al. (2019) construct an adversarial version of the aforementioned benchmark. Gilmer et al. (2018); Gilmer & Hendrycks (2019) argue that robustness to data shift is a pressing problem which greatly affects the reliability of real-world machine learning systems. ",
+        "bbox": [
+            176,
+            492,
+            575,
+            672
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Calibration under Data Shift. Guo et al. (2017); Nguyen & O’Connor (2015) propose metrics for determining the calibration of machine learning models. Lakshminarayanan et al. (2017) find that simply ensembling classifier predictions improves prediction calibration. Hendrycks et al. (2019a) show that pre-training can also improve calibration. Ovadia et al. (2019) demonstrate that model calibration substantially deteriorates under data shift. ",
+        "bbox": [
+            174,
+            680,
+            575,
+            791
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Data Augmentation. Data augmentation can greatly improve generalization performance. For image data, random left-right flipping and cropping are commonly used He et al. (2015). Random occlusion techniques such as Cutout can also improve accuracy on clean data (Devries & Taylor, 2017; Zhong et al., 2017). Rather than occluding a portion of an image, CutMix replaces a portion of an image with a portion of a different image (Yun et al., 2019). Mixup also use information from two images. Rather than implanting one portion of an image inside another, Mixup produces an elementwise convex combination of two images (Zhang et al., 2017; Tokozume et al. ",
+        "bbox": [
+            174,
+            799,
+            578,
+            882
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "image",
+        "img_path": "images/26ec12a0be68e3d389af8bd4cd008b2f8c72cb8aae9f3a60cb87e3113ea1da0c.jpg",
+        "image_caption": [
+            "ImageNet-C Corruptions ",
+            "Figure 2: Example ImageNet-C corruptions. These corruptions are encountered only at test time and not during training. "
+        ],
+        "image_footnote": [],
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+        "text": "",
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+    {
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+        "img_path": "images/195cfa71f2ca86610e0cbc94d9680b99afa27ef52edff09d0d7e783760de3e83.jpg",
+        "image_caption": [
+            "Figure 3: A cascade of successive compositions can produce images which drift far from the original image, and lead to unrealistic images. However, this divergence can be balanced by controlling the number of steps. To increase variety, we generate multiple augmented images and mix them. "
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "2018). Guo et al. (2019) show that Mixup can be improved with an adaptive mixing policy, so as to prevent manifold intrusion. Separate from these approaches are learned augmentation methods such as AutoAugment (Cubuk et al., 2018), where a group of augmentations is tuned to optimize performance on a downstream task. Patch Gaussian augments data with Gaussian noise applied to a randomly chosen portion of an image (Lopes et al., 2019). A popular way to make networks robust to $\\ell _ { p }$ adversarial examples is with adversarial training (Madry et al., 2018), which we use in this paper. However, this tends to increase training time by an order of magnitude and substantially degrades accuracy on non-adversarial images (Raghunathan et al., 2019). ",
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+        "type": "text",
+        "text": "3 AUGMIX ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "AUGMIX is a data augmentation technique which improves model robustness and uncertainty estimates, and slots in easily to existing training pipelines. At a high level, AugMix is characterized by its utilization of simple augmentation operations in concert with a consistency loss. These augmentation operations are sampled stochastically and layered to produce a high diversity of augmented images. We then enforce a consistent embedding by the classifier across diverse augmentations of the same input image through the use of Jensen-Shannon divergence as a consistency loss. ",
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+    {
+        "type": "text",
+        "text": "Mixing augmentations allows us to generate diverse transformations, which are important for inducing robustness, as a common failure mode of deep models in the arena of corruption robustness is the memorization of fixed augmentations (Vasiljevic et al., 2016; Geirhos et al., 2018). Previous methods have attempted to increase diversity by directly composing augmentation primitives in a chain, but this can cause the image to quickly degrade and drift off the data manifold, as depicted in Figure 3. Such image degradation can be mitigated and the augmentation diversity can be maintained by mixing together the results of several augmentation chains in convex combinations. A concrete account of the algorithm is given in the pseudocode below. ",
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+        "type": "text",
+        "text": "Algorithm AUGMIX Pseudocode ",
+        "text_level": 1,
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+        "text": "1: Input: Model $\\hat { p }$ , Classification Loss $\\mathcal { L }$ , Image $x _ { \\mathrm { o r i g } }$ , Operations $\\mathcal { O } = \\{ \\mathrm { r o t a t e } , \\dots , \\mathrm { p o s t e r i z e } \\}$   \n2: function AugmentAndMix $\\cdot { x } _ { \\mathrm { o r i g } }$ , $k = 3 , \\alpha = 1 ,$ )   \n3: Fill $x _ { \\mathrm { a u g } }$ with zeros   \n4: Sample mixing weights $( w _ { 1 } , w _ { 2 } , \\ldots , w _ { k } ) \\sim { \\mathrm { D i r i c h l e t } } ( \\alpha , \\alpha , \\ldots , \\alpha )$   \n5: for $i = 1 , \\ldots , k$ do   \n6: Sample operations $\\begin{array} { r } { \\boldsymbol { \\mathrm { o p } } _ { 1 } , \\boldsymbol { \\mathrm { o p } } _ { 2 } , \\boldsymbol { \\mathrm { o p } } _ { 3 } \\sim \\mathcal { O } } \\end{array}$   \n7: Compose operations with varying depth $\\mathrm { o p _ { 1 2 } = o p _ { 2 } \\circ o p _ { 1 } }$ and $\\mathrm { o p _ { 1 2 3 } = o p _ { 3 } \\circ o p _ { 2 } \\circ o p _ { 1 } }$   \n8: Sample uniformly from one of these operations chain $\\sim \\{ \\boldsymbol { \\mathrm { o p } } _ { 1 } , \\boldsymbol { \\mathrm { o p } } _ { 1 2 } , \\boldsymbol { \\mathrm { o p } } _ { 1 2 3 } \\}$   \n9: $x _ { \\mathrm { a u g } } + = w _ { i } \\cdot \\mathrm { c h a i n } ( x _ { \\mathrm { o r i g } } )$ . Addition is elementwise   \n10: end for   \n11: Sample weight $m \\sim \\operatorname { B e t a } ( \\alpha , \\alpha )$   \n12: Interpolate with rule $x _ { \\mathrm { a u g m i x } } = m x _ { \\mathrm { o r i g } } + ( 1 - m ) x _ { \\mathrm { a u g } }$   \n13: return xaugmix   \n14: end function   \n15: xaugmix1 = AugmentAndMix(xorig) . xaugmix1 is stochastically generated   \n16: $x _ { \\mathrm { a u g m i x 2 } } = \\mathrm { A u g m e n t A n d M i x } ( x _ { \\mathrm { o r i g } } )$ $\\triangleright x _ { a u g m i x I } \\neq x _ { a u g m i x 2 }$   \n17: Loss Output: $\\mathcal { L } ( \\hat { p } ( y \\mid x _ { \\mathrm { o r i g } } ) , y ) \\breve { + } \\lambda$ Jensen-Shannon $1 \\big ( \\hat { p } ( y \\mid x _ { \\mathrm { o r i g } } ) ; \\hat { p } ( y \\vert x _ { \\mathrm { a u g m i x 1 } } ) ; \\hat { p } ( y \\vert x _ { \\mathrm { a u g m i x 2 } } ) \\big )$ ",
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+        "page_idx": 2
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+    {
+        "type": "image",
+        "img_path": "images/6af8a2b0286d0af5a7558f66612d2889ff1f4ce091aedf77dedbdb557a78cab2.jpg",
+        "image_caption": [
+            "Figure 4: A realization of AUGMIX. Augmentation operations such as translate x and weights such as $m$ are randomly sampled. Randomly sampled operations and their compositions allow us to explore the semantically equivalent input space around an image. Mixing these images together produces a new image without veering too far from the original. "
+        ],
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+        "text": "Augmentations. Our method consists of mixing the results from augmentation chains or compositions of augmentation operations. We use operations from AutoAugment. Each operation is visualized in Appendix C. Crucially, we exclude operations which overlap with ImageNet- $C$ corruptions. In particular, we remove the contrast, color, brightness, sharpness, and Cutout operations so that our set of operations and the ImageNet-C corruptions are disjoint. In turn, we do not use any image noising nor image blurring operations so that ImageNet-C corruptions are encountered only at test time. Operations such as rotate can be realized with varying severities, like $2 ^ { \\circ }$ or $- 1 5 ^ { \\circ }$ . For operations with varying severities, we uniformly sample the severity upon each application. Next, we randomly sample $k$ augmentation chains, where $k = 3$ by default. Each augmentation chain is constructed by composing from one to three randomly selected augmentation operations. ",
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+    {
+        "type": "text",
+        "text": "Mixing. The resulting images from these augmentation chains are combined by mixing. While we considered mixing by alpha compositing, we chose to use elementwise convex combinations for simplicity. The $k$ -dimensional vector of convex coefficients is randomly sampled from a Dirichle $( \\alpha , \\ldots , \\alpha )$ distribution. Once these images are mixed, we use a “skip connection” to combine the result of the augmentation chain and the original image through a second random convex combination sampled from a Beta $( \\alpha , \\alpha )$ distribution. The final image incorporates several sources of randomness from the choice of operations, the severity of these operations, the lengths of the augmentation chains, and the mixing weights. ",
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+        "type": "text",
+        "text": "Jensen-Shannon Divergence Consistency Loss. We couple with this augmentation scheme a loss that enforces smoother neural network responses. Since the semantic content of an image is approximately preserved with AUGMIX, we should like the model to embed $x _ { \\mathrm { o r i g } }$ , $x _ { \\mathrm { a u g m i x 1 } }$ , xaugmix2 similarly. Toward this end, we minimize the Jensen-Shannon divergence among the posterior distributions of the original sample $x _ { \\mathrm { o r i g } }$ and its augmented variants. That is, for $p _ { \\mathrm { o r i g } } ~ = ~ { \\hat { p } } ( y ~ |$ $x _ { \\mathrm { o r i g } } ) , p _ { \\mathrm { a u g m i x 1 } } = \\hat { p } ( y \\mid \\bar { x } _ { \\mathrm { a u g m i x 1 } } ) , \\bar { p } _ { \\mathrm { a u g m i x 2 } } \\stackrel { \\sim } { = } \\hat { p } ( y | x _ { \\mathrm { a u g m i x 2 } } )$ , we replace the original loss $\\mathcal { L }$ with the loss ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/bf3c9224895a302eabce5bab3ea4358fce3587abb20de9811422cb6af3be4975.jpg",
+        "text": "$$\n\\mathcal { L } ( p _ { \\mathrm { o r i g } } , y ) + \\lambda \\operatorname { J S } ( p _ { \\mathrm { o r i g } } ; p _ { \\mathrm { a u g m i x 1 } } ; p _ { \\mathrm { a u g m i x 2 } } ) .\n$$",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "To interpret this loss, imagine a sample from one of the three distributions $p _ { \\mathrm { o r i g } } , p _ { \\mathrm { a u g m i x 1 } } , p _ { \\mathrm { a u g m i x 2 } }$ . The Jensen-Shannon divergence can be understood to measure the average information that the sample reveals about the identity of the distribution from which it was sampled. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "This loss can be computed by first obtaining $M = ( p _ { \\mathrm { o r i g } } + p _ { \\mathrm { a u g m i x 1 } } + p _ { \\mathrm { a u g m i x 2 } } ) / 3$ and then computing ",
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+    {
+        "type": "equation",
+        "img_path": "images/01069549b45f39875f8238df7be568ca49e1340eea9f51da879777ec9e8553db.jpg",
+        "text": "$$\n\\mathrm { J S } \\big ( p _ { \\mathrm { o r i g } } ; p _ { \\mathrm { a u g m i x 1 } } ; p _ { \\mathrm { a u g m i x 2 } } \\big ) = \\frac { 1 } { 3 } \\Big ( \\mathrm { K L } \\big [ p _ { \\mathrm { o r i g } } \\| M \\big ] + \\mathrm { K L } \\big [ p _ { \\mathrm { a u g m i x 1 } } \\| M \\big ] + \\mathrm { K L } \\big [ p _ { \\mathrm { a u g m i x 2 } } \\| M \\big ] \\Big ) .\n$$",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "Unlike an arbitrary KL Divergence between $p _ { \\mathrm { o r i g } }$ and $p _ { \\mathrm { a u g m i x } }$ , the Jensen-Shannon divergence is upper bounded, in this case by the logarithm of the number of classes. Note that we could instead compute $\\mathbf { J } \\mathbf { S } ( p _ { \\mathrm { o r i g } } ; p _ { \\mathrm { a u g m i x 1 } } )$ , though this does not perform as well. The gain of training with JS $p _ { \\mathrm { o r i g } }$ ; paugmix1; paugmix2; paugmix3) is marginal. The Jensen-Shannon Consistency Loss impels to model to be stable, consistent, and insensitive across to a diverse range of inputs (Zheng et al., 2016; Kannan et al., 2018; Xie et al., 2019). Ablations are in Section 4.3 and Appendix A. ",
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+    {
+        "type": "text",
+        "text": "4 EXPERIMENTS ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Datasets. The two CIFAR (Krizhevsky & Hinton, 2009) datasets contain small $3 2 \\times 3 2 \\times 3$ color natural images, both with 50,000 training images and 10,000 testing images. CIFAR-10 has 10 categories, and CIFAR-100 has 100. The ImageNet (Deng et al., 2009) dataset contains 1,000 classes of approximately 1.2 million large-scale color images. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In order to measure a model’s resilience to data shift, we evaluate on the CIFAR-10-C, CIFAR-100- $C$ , and ImageNet- $C$ datasets (Hendrycks & Dietterich, 2019). These datasets are constructed by corrupting the original CIFAR and ImageNet test sets. For each dataset, there are a total of 15 noise, blur, weather, and digital corruption types, each appearing at 5 severity levels or intensities. Since these datasets are used to measure network behavior under data shift, we take care not to introduce these 15 corruptions into the training procedure. ",
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+    {
+        "type": "text",
+        "text": "The CIFAR-10-P, CIFAR-100- ${ \\bf \\nabla } \\cdot { \\cal P }$ , and ImageNet- $P$ datasets also modify the original CIFAR and ImageNet datasets. These datasets contain smaller perturbations than CIFAR-C and are used to measure the classifier’s prediction stability. Each example in these datasets is a video. For instance, a video with the brightness perturbation shows an image getting progressively brighter over time. We should like the network not to give inconsistent or volatile predictions between frames of the video as the brightness increases. Thus these datasets enable the measurement of the “jaggedness” (Azulay & Weiss, 2018) of a network’s prediction stream. ",
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+    {
+        "type": "text",
+        "text": "Metrics. The Clean Error is the usual classification error on the clean or uncorrupted test data. In our experiments, corrupted test data appears at five different intensities or severity levels $1 \\leq s \\leq 5$ . For a given corruption $c$ , the error rate at corruption severity $s$ is $E _ { c , s }$ . We can compute the average error across these severities to create the unnormalized corruption error $\\begin{array} { r } { \\mathbf { u C E } _ { c } = \\sum _ { s = 1 } ^ { 5 } E _ { c , s } } \\end{array}$ . On CIFAR-10- C and CIFAR-100-C we average these values over all 15 corruptions. Meanwhile, on ImageNet we follow the convention of normaet al., 2012). We compute $\\begin{array} { r } { \\mathrm { C E } _ { c } = \\sum _ { s = 1 } ^ { 5 } \\bar { E } _ { c , s } / \\sum _ { s = 1 } ^ { 5 } E _ { c , s } ^ { \\mathrm { A l e x N e t } } } \\end{array}$ ruption error of AlexNet (Kriz. The average of the 15 cor errors CEGaussian Noise, CEShot Noise, . . . , CEPixelate, CEJPEG gives us the Mean Corruption Error $( m C E )$ . ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Perturbation robustness is not measured by accuracy but whether video frame predictions match. Consequently we compute what is called the flip probability. Concretely, for videos such as those with steadily increasing brightness, we determine the probability that two adjacent frames, or two frames with slightly different brightness levels, have “flipped” or mismatched predictions. There are 10 different perturbation types, and the mean across these is the mean Flip Probability $( m F P )$ . As with ImageNet-C, we can normalize by AlexNet’s flip probabilities and obtain the mean Flip Rate $( m F R )$ . ",
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+    {
+        "type": "text",
+        "text": "In order to assess a model’s uncertainty estimates, we measure its miscalibration. Classifiers capable of reliably forecasting their accuracy are considered “calibrated.” For instance, a calibrated classifier should be correct $70 \\%$ of the time on examples to which it assigns $70 \\%$ confidence. Let the classifier’s confidence that its prediction $\\hat { Y }$ is correct be written $C$ . Then the idealized RMS Calibration Error is $\\sqrt { \\mathbb { E } _ { C } [ ( \\mathbb { P } ( Y = \\hat { Y } | C = c ) - c ) ^ { 2 } ] } ,$ , which is the squared difference between the accuracy at a given confidence level and actual the confidence level. In Appendix E, we show how to empirically estimate this quantity and calculate the Brier Score. ",
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+    {
+        "type": "text",
+        "text": "4.1 CIFAR-10 AND CIFAR-100 ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Training Setup. In the following experiments we show that AUGMIX endows robustness to various architectures including an All Convolutional Network (Springenberg et al., 2014; Salimans & Kingma, 2016), a DenseNet-BC $( k = 1 2 , d = 1 0 0 )$ ) (Huang et al., 2017) , a 40-2 Wide ResNet (Zagoruyko & Komodakis, 2016), and a ResNeXt-29 $( 3 2 \\times 4 )$ (Xie et al., 2016). All networks use an initial learning rate of 0.1 which decays following a cosine learning rate (Loshchilov & Hutter, 2016). All input images are pre-processed with standard random left-right flipping and cropping prior to any augmentations. We do not change AUGMIX parameters across CIFAR-10 and CIFAR-100 experiments for consistency. The All Convolutional Network and Wide ResNet train for 100 epochs, and the DenseNet and ResNeXt require 200 epochs for convergence. We optimize with stochastic gradient descent using Nesterov momentum. Following Zhang et al. (2017); Guo et al. (2019), we use a weight decay of 0.0001 for Mixup and 0.0005 otherwise. ",
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+    {
+        "type": "image",
+        "img_path": "images/413822b829d4661106d29927637b1d4289291955a82fe9e9f1b5d858f495d6f1.jpg",
+        "image_caption": [
+            "Figure 5: Error rates of various methods on CIFAR-10-C using a ResNeXt backbone. Observe that AUGMIX halves the error rate of prior methods and approaches the clean error rate. "
+        ],
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+    {
+        "type": "table",
+        "img_path": "images/fb8faeda72e28b6b30b1b75eb56be41c89bcd10dc9055081b92fa7ff1b87d55b.jpg",
+        "table_caption": [
+            "Table 1: Average classification error as percentages. Across several architectures, AUGMIX obtains CIFAR-10-C and CIFAR-100-C corruption robustness that exceeds the previous state of the art. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td></td><td>Standard</td><td>Cutout</td><td>Mixup</td><td></td><td>CutMix AutoAugment* Adv Training AUGMIX</td><td></td><td></td></tr><tr><td rowspan=\"4\">CIFAR-10-C</td><td>AllConvNet</td><td>30.8</td><td>32.9</td><td>24.6</td><td>31.3</td><td>29.2</td><td>28.1</td><td>15.0</td></tr><tr><td>DenseNet</td><td>30.7</td><td>32.1</td><td>24.6</td><td>33.5</td><td>26.6</td><td>27.6</td><td>12.7</td></tr><tr><td>WideResNet</td><td>26.9</td><td>26.8</td><td>22.3</td><td>27.1</td><td>23.9</td><td>26.2</td><td>11.2</td></tr><tr><td>ResNeXt</td><td>27.5</td><td>28.9</td><td>22.6</td><td>29.5</td><td>24.2</td><td>27.0</td><td>10.9</td></tr><tr><td colspan=\"2\">Mean</td><td>29.0</td><td>30.2</td><td>23.5</td><td>30.3</td><td>26.0</td><td>27.2</td><td>12.5</td></tr><tr><td rowspan=\"4\">CIFAR-100-C</td><td>AllConvNet</td><td>56.4</td><td>56.8</td><td>53.4</td><td>56.0</td><td>55.1</td><td>56.0</td><td>42.7</td></tr><tr><td>DenseNet</td><td>59.3</td><td>59.6</td><td>55.4</td><td>59.2</td><td>53.9</td><td>55.2</td><td>39.6</td></tr><tr><td>WideResNet</td><td>53.3</td><td>53.5</td><td>50.4</td><td>52.9</td><td>49.6</td><td>55.1</td><td>35.9</td></tr><tr><td>ResNeXt</td><td>53.4</td><td>54.6</td><td>51.4</td><td>54.1</td><td>51.3</td><td>54.4</td><td>34.9</td></tr><tr><td colspan=\"2\">Mean</td><td>55.6</td><td>56.1</td><td>52.6</td><td>55.5</td><td>52.5</td><td>55.2</td><td>38.3</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Results. Simply mixing random augmentations and using the Jensen-Shannon loss substantially improves robustness and uncertainty estimates. Compared to the “Standard” data augmentation baseline ResNeXt on CIFAR-10-C, AUGMIX achieves $1 6 . 6 \\%$ lower absolute corruption error as shown in Figure 5. In addition to surpassing numerous other data augmentation techniques, Table 1 demonstrates that these gains directly transfer across architectures and on CIFAR-100-C with zero additional tuning. Crucially, the robustness gains do not only exist when measured in aggregate. Figure 12 shows that AUGMIX improves corruption robustness across every individual corruption and severity level. Our method additionally achieves the lowest mFP on CIFAR-10-P across three different models all while maintaining accuracy on clean CIFAR-10, as shown in Figure 6 (left) and Table 6. Finally, we demonstrate that AUGMIX improves the RMS calibration error on CIFAR-10 and CIFAR-10-C, as shown in Figure 6 (right) and Table 5. Expanded CIFAR-10-P and calibration results are in Appendix D, and Fourier Sensitivity analysis is in Appendix B. ",
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+    {
+        "type": "image",
+        "img_path": "images/c4e2d37dfd75cceb92cbe45f608f245c84a3a80c4bb2d5a26eacb828660bb96a.jpg",
+        "image_caption": [
+            "Figure 6: CIFAR-10-P prediction stability and Root Mean Square Calibration Error values for ResNeXt. AUGMIX simultaneously reduces flip probabilities and calibration error. "
+        ],
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+    {
+        "type": "text",
+        "text": "4.2 IMAGENET ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Baselines. To demonstrate the utility of AUGMIX on ImageNet, we compare to many techniques designed for large-scale images. While techniques such as Cutout (Devries & Taylor, 2017) have not been demonstrated to help on the ImageNet scale, and while few have had success training adversarially robust models on ImageNet (Engstrom et al., 2018), other techniques such as Stylized ImageNet have been demonstrated to help on ImageNet-C. Patch Uniform (Lopes et al., 2019) is similar to Cutout except that randomly chosen regions of the image are injected with uniform noise; the original paper uses Gaussian noise, but that appears in the ImageNet-C test set so we use uniform noise. We tune Patch Uniform over 30 hyperparameter settings. Next, AutoAugment (Cubuk et al., 2018) searches over data augmentation policies to find a high-performing data augmentation policy. We denote AutoAugment results with AutoAugment\\* since we remove augmentation operations that overlap with ImageNet-C corruptions, as with AUGMIX. We also test with Random AutoAugment\\*, an augmentation scheme where each image has a randomly sampled augmentation policy using AutoAugment\\* operations. In contrast to AutoAugment, Random AutoAugment\\* and AUGMIX require far less computation and provide more augmentation variety, which can offset their lack of optimization. Note that Random AutoAugment\\* is different from RandAugment introduced recently by Cubuk et al. (2019): RandAugment uses AutoAugment operations and optimizes a single distortion magnitude hyperparameter for all operations, while Random AutoAugment\\* randomly samples magnitudes for each operation and uses the same operations as AUGMIX. MaxBlur Pooling (Zhang, 2019) is a recently proposed architectural modification which smooths the results of pooling. Now, Stylized ImageNet (SIN) is a technique where models are trained with the original ImageNet images and also ImageNet images with style transfer applied. Whereas the original Stylized ImageNet technique pretrains on ImageNet-C and performs style transfer with a content loss coefficient of 0 and a style loss coefficient of 1, we find that using 0.5 content and style loss coefficients decreases the mCE by $0 . 6 \\%$ . Later, we show that SIN and AUGMIX can be combined. All models are trained from scratch, except MaxBlur Pooling models which has trained models available. ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Training Setup. Methods are trained with ResNet-50 and we follow the standard training scheme of Goyal et al. (2017), in which we linearly scale the learning rate with the batch size, and use a learning rate warm-up for the first 5 epochs, and AutoAugment and AUGMIX train for 180 epochs. All input images are first pre-processed with standard random cropping horizontal mirroring. ",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/8352fbc214b2f6d78170d7a72b719668fb62b8defc9d25a1fb465eefeb083d79.jpg",
+        "table_caption": [
+            "Table 2: Clean Error, Corruption Error (CE), and mCE values for various methods on ImageNet-C. The mCE value is computed by averaging across all $1 5 \\mathrm { C E }$ values. AUGMIX reduces corruption error while improving clean accuracy, and it can be combined with SIN for greater corruption robustness. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td></td><td></td><td>Noise</td><td></td><td></td><td>Blur</td><td></td><td></td><td></td><td></td><td>Weather</td><td></td><td></td><td>Digital</td><td></td><td></td><td></td></tr><tr><td>Network</td><td>Clean</td><td>Gauss.Shot Impulse</td><td></td><td></td><td>Defocus Glass Motion Zoom</td><td></td><td></td><td></td><td></td><td></td><td>SnowFrostFog</td><td>Bright</td><td></td><td>Contrast Elastic Pixel JPEG</td><td></td><td></td><td>mCE</td></tr><tr><td>Standard</td><td>23.9</td><td>79</td><td>80</td><td>82</td><td>82</td><td>90</td><td>84</td><td>80</td><td>86</td><td>81</td><td>75</td><td>65</td><td>79</td><td>91</td><td>77</td><td>80</td><td>80.6</td></tr><tr><td>Patch Uniform</td><td>24.5</td><td>67</td><td>68</td><td>70</td><td>74</td><td>83</td><td>81</td><td>77</td><td>80</td><td>74</td><td>75</td><td>62</td><td>77</td><td>84</td><td>71</td><td>71</td><td>74.3</td></tr><tr><td>AutoAugment* (AA)</td><td>22.8</td><td>69</td><td>68</td><td>72</td><td>77</td><td>83</td><td>80</td><td>81</td><td>79</td><td>75</td><td>64</td><td>56</td><td>70</td><td>88</td><td>57</td><td>71</td><td>72.7</td></tr><tr><td>Random AA*</td><td>23.6</td><td>70</td><td>71</td><td>72</td><td>80</td><td>86</td><td>82</td><td>81</td><td>81</td><td>77</td><td>72</td><td>61</td><td>75</td><td>88</td><td>73</td><td>72</td><td>76.1</td></tr><tr><td>MaxBlur pool</td><td>23.0</td><td>73</td><td>74</td><td>76</td><td>74</td><td>86</td><td>78</td><td>77</td><td>77</td><td>72</td><td>63</td><td>56</td><td>68</td><td>86</td><td>71</td><td>71</td><td>73.4</td></tr><tr><td>SIN</td><td>27.2</td><td>69</td><td>70</td><td>70</td><td>77</td><td>84</td><td>76</td><td>82</td><td>74</td><td>75</td><td>69</td><td>65</td><td>69</td><td>80</td><td>64</td><td>77</td><td>73.3</td></tr><tr><td>AUGMIX</td><td>22.4</td><td>65</td><td>66</td><td>67</td><td>70</td><td>80</td><td>66</td><td>66</td><td>75</td><td>72</td><td>67</td><td>58</td><td>58</td><td>79</td><td>69</td><td>69</td><td>68.4</td></tr><tr><td>AUGMIX+SIN</td><td>25.2</td><td>61</td><td>62</td><td>61</td><td>69</td><td>77</td><td>63</td><td>72</td><td>66</td><td>68</td><td>63</td><td>59</td><td>52</td><td>74</td><td>60</td><td>67</td><td>64.9</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Results. Our method achieves $6 8 . 4 \\%$ mCE as shown in Table 2, down from the baseline $8 0 . 6 \\%$ mCE. Additionally, we note that AUGMIX allows straightforward stacking with other methods such as SIN to achieve an even lower corruption error of $6 4 . 1 \\%$ mCE. Other techniques such as AutoAugment\\* require much tuning, while ours does not. Across increasing severities of corruptions, our method also produces much more calibrated predictions measured by both the Brier Score and RMS Calibration Error as shown in Figure 7. As shown in Table 3, AUGMIX also achieves a state-of-the art result on ImageNet-P at with an mFR of $3 7 . 4 \\%$ , down from $5 7 . 2 \\%$ . We demonstrate that scaling up AUGMIX from CIFAR to ImageNet also leads to state-of-the-art results in robustness and uncertainty estimation. ",
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+    {
+        "type": "text",
+        "text": "4.3 ABLATIONS ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We locate the utility of AUGMIX in three factors: training set diversity, our Jensen-Shannon divergence consistency loss, and mixing. Improving training set diversity via increased variety of augmentations can greatly improve robustness. For instance, augmenting each example with a ",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/c71d5251e57f3e189805ccf034aae0fbe8627d0203833f98e268e37bee5bd4a8.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td></td><td colspan=\"2\">Noise</td><td colspan=\"2\">Blur</td><td colspan=\"2\">Weather</td><td colspan=\"5\">Digital</td></tr><tr><td>Network</td><td>Clean</td><td>Gaussian Shot</td><td></td><td>Motion Zoom</td><td></td><td>Snow</td><td>Bright</td><td>TranslateRotate</td><td></td><td>TiltScale</td><td></td><td>mFR</td></tr><tr><td>Standard</td><td>23.9</td><td>57</td><td>55</td><td>62</td><td>65</td><td>66</td><td>65</td><td>43</td><td>53</td><td>57</td><td>49</td><td>57.2</td></tr><tr><td>Patch Uniform</td><td>24.5</td><td>32</td><td>25</td><td>50</td><td>52</td><td>54</td><td>57</td><td>40</td><td>48</td><td>49</td><td>46</td><td>45.3</td></tr><tr><td>AutoAugment* (AA)</td><td>22.8</td><td>50</td><td>45</td><td>57</td><td>68</td><td>63</td><td>53</td><td>40</td><td>44</td><td>50</td><td>46</td><td>51.7</td></tr><tr><td>Random AA*</td><td>23.6</td><td>53</td><td>46</td><td>53</td><td>63</td><td>59</td><td>57</td><td>42</td><td>48</td><td>54</td><td>47</td><td>52.2</td></tr><tr><td>SIN</td><td>27.2</td><td>53</td><td>50</td><td>57</td><td>72</td><td>51</td><td>62</td><td>43</td><td>53</td><td>57</td><td>53</td><td>55.0</td></tr><tr><td>MaxBlur pool</td><td>23.0</td><td>52</td><td>51</td><td>59</td><td>63</td><td>57</td><td>64</td><td>34</td><td>43</td><td>49</td><td>40</td><td>51.2</td></tr><tr><td>AUGMIX</td><td>22.4</td><td>46</td><td>41</td><td>30</td><td>47</td><td>38</td><td>46</td><td>25</td><td>32</td><td>35</td><td>33</td><td>37.4</td></tr><tr><td>AUGMIX+SIN</td><td>25.2</td><td>45</td><td>40</td><td>30</td><td>54</td><td>32</td><td>48</td><td>27</td><td>35</td><td>38</td><td>39</td><td>38.9</td></tr></table>",
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Table 3: ImageNet-P results. The mean flipping rate is the average of the flipping rates across all 10 perturbation types. AUGMIX improves perturbation stability by approximately $20 \\%$ . ",
+        "bbox": [
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+    },
+    {
+        "type": "image",
+        "img_path": "images/0f95f31726e708fda8050e5871180a33c4fc38dd8f9929d9ee99690701b9528e.jpg",
+        "image_caption": [
+            "Figure 7: Uncertainty results on ImageNet-C. Observe that under severe data shifts, the RMS calibration error with ensembles and AUGMIX is remarkably steady. Even though classification error increases, calibration is roughly preserved. Severity zero denotes clean data. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "randomly sampled augmentation chain decreases the error rate of Wide ResNet on CIFAR-10-C from $2 6 . 9 \\%$ to $1 7 . 0 \\%$ Table 4. Adding in the Jensen-Shannon divergence consistency loss drops error rate further to $1 4 . 7 \\%$ . Mixing random augmentations without the Jenson-Shannon divergence loss gives us an error rate of $1 3 . 1 \\%$ . Finally, re-introducing the Jensen-Shannon divergence gives us AUGMIX with an error rate of $1 1 . 2 \\%$ . Note that adding even more mixing is not necessarily beneficial. For instance, applying AUGMIX on top of Mixup increases the error rate to $1 3 . 3 \\%$ , possibly due to an increased chance of manifold intrusion (Guo et al., 2019). Hence AUGMIX’s careful combination of variety, consistency loss, and mixing explain its performance. ",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/6d78a7cf7fc043a62c153b7c8c7d700b063d933f9c36dd5cc7b63a6636f09b6d.jpg",
+        "table_caption": [
+            "Table 4: Ablating components of AUGMIX on CIFAR-10-C and CIFAR-100-C. Variety through randomness, the Jensen-Shannon divergence (JSD) loss, and augmentation mixing confer robustness. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>CIFAR-10-C Error Rate</td><td>CIFAR-100-C ErrorRate</td></tr><tr><td>Standard</td><td>26.9</td><td>53.3</td></tr><tr><td>AutoAugment*</td><td>23.9</td><td>49.6</td></tr><tr><td>Random AutoAugment*</td><td>17.0</td><td>43.6</td></tr><tr><td>Random AutoAugment* + JSDLoss</td><td>14.7</td><td>40.8</td></tr><tr><td>AugmentAndMix (No JSD Loss)</td><td>13.1</td><td>39.8</td></tr><tr><td>AUGMIX (Mixing + JSD Loss)</td><td>11.2</td><td>35.9</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "5 CONCLUSION ",
+        "text_level": 1,
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "AUGMIX is a data processing technique which mixes randomly generated augmentations and uses a Jensen-Shannon loss to enforce consistency. Our simple-to-implement technique obtains state-of-the-art performance on CIFAR-10/100-C, ImageNet-C, CIFAR-10/100-P, and ImageNet-P. AUGMIX models achieve state-of-the-art calibration and can maintain calibration even as the distribution shifts. We hope that AUGMIX will enable more reliable models, a necessity for models deployed in safety-critical environments. ",
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+    {
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+        "text": "Sangdoo Yun, Dongyoon Han, Seong Joon Oh, Sanghyuk Chun, Junsuk Choe, and Youngjoon Yoo. Cutmix: Regularization strategy to train strong classifiers with localizable features. ICCV, 2019. ",
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+        "type": "text",
+        "text": "Hongyi Zhang, Moustapha Cisse, Yann Dauphin, and David Lopez-Paz. mixup: Beyond empirical ´ risk minimization. ICLR, 2017. ",
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+    {
+        "type": "text",
+        "text": "Richard Zhang. Making convolutional networks shift-invariant again. In ICML, 2019. ",
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+    {
+        "type": "text",
+        "text": "Stephan Zheng, Yang Song, Thomas Leung, and Ian Goodfellow. Improving the robustness of deep neural networks via stability training. CVPR, 2016. ",
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+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Zhun Zhong, Liang Zheng, Guoliang Kang, Shaozi Li, and Yi Yang. Random erasing data augmentation. arXiv preprint arXiv:1708.04896, 2017. ",
+        "bbox": [
+            171,
+            165,
+            825,
+            194
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "A HYPERPARAMETER ABLATIONS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            102,
+            473,
+            117
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "In this section we demonstrate that AUGMIX’s hyperparameters are not highly sensitive, so that AUGMIX performs reliably without careful tuning. For this set of experiments, the baseline AUGMIX model trains for 90 epochs, has a mixing coefficient of $\\alpha = 0 . 5$ , has 3 examples per Jensen-Shannon Divergence (1 clean image, 2 augmented images), has a chain depth stochastically varying from 1 to 3, and has $k = 3$ augmentation chains. Figure 8 shows that the performance of various AUGMIX models with different hyperparameters. Under these hyperparameter changes, the mCE does not change substantially. ",
+        "bbox": [
+            173,
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+            229
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "image",
+        "img_path": "images/1cfcf05e745f24551323e62d6d3864d7681b43516d3591a80175e06aba0058eb.jpg",
+        "image_caption": [
+            "AugMix ImageNet-C Ablations "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            171,
+            247,
+            826,
+            404
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "image",
+        "img_path": "images/b2387776be0bcd6855c4139892a559b790e6134a8974823eeea4312a5b9f0b35.jpg",
+        "image_caption": [
+            "Figure 8: AUGMIX hyperparameter ablations on ImageNet-C. ImageNet-C classification performance is stable changes to AUGMIX’s hyperparameters. ",
+            "Figure 9: Fourier Sensitivity Heatmap of the baseline Wide ResNet, Cutout, and AUGMIX CIFAR-10 models. All Fourier basis perturbations are added to clean CIFAR-10 test images. AUGMIX maintains robustness at low frequencies and is far more robust to mid and high frequency modifications. Example perturbed images are shown above, with black pointer lines indicating the Fourier basis vector used to perturb the image. For each basis vector we compute the error rate of the model after perturbing the entire test set. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            186,
+            465,
+            823,
+            724
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "B FOURIER ANALYSIS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            838,
+            375,
+            853
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "A commonly mentioned hypothesis (Gilmer & Hendrycks, 2019) for the lack of robustness of deep neural networks is that they readily latch onto spurious high-frequency correlations that exist in the data. In order to better understand the reliance of models to such correlations, we measure model sensitivity to additive noise at differing frequencies. We create a $3 2 \\times 3 2$ sensitivity heatmap. That is, we add a total of $3 2 \\times 3 2$ Fourier basis vectors to the CIFAR-10 test set, one at a time, and record the resulting error rate after adding each Fourier basis vector. Each point in the heatmap shows the error rate on the CIFAR-10 test set after it has been perturbed by a single Fourier basis vector. Points corresponding to low frequency vectors are shown in the center of the heatmap, whereas high frequency vectors are farther from the center. For further details on Fourier sensitivity analysis, we refer the reader to Section 2 of Yin et al. (2019). In Figure 9 we observe that the baseline model is robust to low frequency perturbations but severely lacks robustness to high frequency perturbations, where error rates exceed $80 \\%$ . The model trained with Cutout shows a similar lack of robustness. In contrast, the model trained with AUGMIX maintains robustness to low frequency perturbations, and on the mid and high frequencies AUGMIX is conspicuously more robust. ",
+        "bbox": [
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+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "C AUGMENTATION OPERATIONS",
+        "text_level": 1,
+        "bbox": [
+            176,
+            258,
+            459,
+            275
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "The augmentation operations we use for AUGMIX are shown in Figure 10. ",
+        "bbox": [
+            174,
+            289,
+            661,
+            304
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "image",
+        "img_path": "images/7748e858401f577400d8e8329defa78203fec7a848cb47c79b85b290d10a48b5.jpg",
+        "image_caption": [
+            "Figure 10: Illustration of augmentation operations applied to the same image. Some operation severities have been increased to show detail. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            336,
+            319,
+            661,
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+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "We do not use augmentations such as contrast, color, brightness, sharpness, and Cutout as they may overlap with ImageNet-C test set corruptions. We should note that augmentation choice requires additional care. Guo et al. (2019) show that blithely applying augmentations can potentially cause augmented images to take different classes. Figure 11 shows how histogram color swapping augmentation may change a bird’s class, leading to a manifold intrusion. ",
+        "bbox": [
+            176,
+            627,
+            825,
+            696
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "image",
+        "img_path": "images/c459b1b2d285197ceac76a323861e94a9afd455ba855528c9f1baa820dd32885.jpg",
+        "image_caption": [
+            "Figure 11: An illustration of manifold intrusion (Guo et al., 2019), where histogram color augmentation can change the image’s class. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            336,
+            710,
+            661,
+            869
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "D ADDITIONAL RESULTS ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            102,
+            398,
+            117
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "We include various additional results for CIFAR-10, CIFAR-10-C and CIFAR-10-P below. Figure 12 reports accuracy for each corruption, Table 5 reports calibration results for various architectures and Table 6 reports clean error and mFR. We refer to Section 4.1 for details about the architecture and training setup. ",
+        "bbox": [
+            173,
+            132,
+            825,
+            189
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "image",
+        "img_path": "images/3ffcf7ca776f94b1bbae00d39894de3c48178b50545e4390eb343ce3213fe832.jpg",
+        "image_caption": [
+            "Figure 12: AUGMIX improves corruption robustness across all CIFAR-10-C noise, blur, weather, and digital corruptions, despite the model never having seen these corruptions during training. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            171,
+            208,
+            826,
+            388
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "table",
+        "img_path": "images/f08d61dd84fd8735141eb9c08f3d1b25cfed486430e2ea6ab45bb1cc9919a9ab.jpg",
+        "table_caption": [
+            "Table 5: RMS Calibration Error of various models and data augmentation methods across CIFAR-10 and CIFAR-10-C. All values are reported as percentages. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td></td><td>Standard Cutout</td><td>Mixup</td><td></td><td></td><td>CutMix AutoAugment* Adv Training AUGMIX</td><td></td><td></td></tr><tr><td rowspan=\"4\">CIFAR-10</td><td>AllConvNet</td><td>5.4</td><td>4.0</td><td>12.6</td><td>3.1</td><td>4.2</td><td>11.1</td><td>2.2</td></tr><tr><td>DenseNet</td><td>7.5</td><td>6.4</td><td>15.6</td><td>5.4</td><td>6.0</td><td>16.2</td><td>5.0</td></tr><tr><td>WideResNet</td><td>6.8</td><td>3.8</td><td>14.0</td><td>5.0</td><td>4.7</td><td>10.7</td><td>4.2</td></tr><tr><td>ResNeXt</td><td>3.0</td><td>4.4</td><td>13.5</td><td>3.5</td><td>3.3</td><td>5.8</td><td>3.0</td></tr><tr><td colspan=\"2\">Mean</td><td>5.7</td><td>4.7</td><td>13.9</td><td>4.2</td><td>4.6</td><td>11.0</td><td>3.6</td></tr><tr><td rowspan=\"4\">CIFAR-10-C</td><td>AllConvNet</td><td>21.2</td><td>21.3</td><td>9.7</td><td>15.4</td><td>16.2</td><td>10.4</td><td>5.2</td></tr><tr><td>DenseNet</td><td>26.7</td><td>27.8</td><td>12.9</td><td>25.6</td><td>21.1</td><td>15.0</td><td>11.7</td></tr><tr><td>WideResNet</td><td>27.6</td><td>19.6</td><td>11.1</td><td>17.8</td><td>17.1</td><td>10.6</td><td>8.7</td></tr><tr><td>ResNeXt</td><td>16.4</td><td>21.4</td><td>11.7</td><td>19.6</td><td>15.1</td><td>11.6</td><td>8.3</td></tr><tr><td colspan=\"2\">Mean</td><td>23.0</td><td>22.5</td><td>11.4</td><td>19.6</td><td>17.4</td><td>11.9</td><td>8.5</td></tr></table>",
+        "bbox": [
+            173,
+            460,
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+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "table",
+        "img_path": "images/59055bf704bcb6360d304ae76cdfd7b0a6a611bb829ce02374e8b90e50ce144e.jpg",
+        "table_caption": [
+            "Table 6: CIFAR-10 Clean Error and CIFAR-10-P mean Flip Probability. All values are percentages. While adversarial training performs well on CIFAR-10-P, it induces a substantial drop in accuracy (increase in error) on clean CIFAR-10 where AUGMIX does not. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td colspan=\"2\"></td><td colspan=\"7\">Standard Cutout Mixup CutMix AutoAugment* Adv Training AUGMIX</td></tr><tr><td rowspan=\"4\">CIFAR-10</td><td>AllConvNet</td><td>6.1</td><td>6.1</td><td>6.3</td><td>6.4</td><td>6.6</td><td>18.9</td><td>6.5</td></tr><tr><td>DenseNet</td><td>5.8</td><td>4.8</td><td>5.5</td><td>5.3</td><td>4.8</td><td>17.9</td><td>4.9</td></tr><tr><td>WideResNet</td><td>5.2</td><td>4.4</td><td>4.9</td><td>4.6</td><td>4.8</td><td>17.1</td><td>4.9</td></tr><tr><td>ResNeXt</td><td>4.3</td><td>4.4</td><td>4.2</td><td>3.9</td><td>3.8</td><td>15.4</td><td>4.2</td></tr><tr><td colspan=\"2\">Mean</td><td>5.4</td><td>4.9</td><td>5.2</td><td>5.0</td><td>5.0</td><td>17.3</td><td>5.1</td></tr><tr><td rowspan=\"4\">CIFAR-10-P</td><td>AllConvNet</td><td>4.2</td><td>5.0</td><td>3.9</td><td>4.5</td><td>4.0</td><td>2.0</td><td>1.5</td></tr><tr><td>DenseNet</td><td>5.0</td><td>5.7</td><td>3.9</td><td>6.3</td><td>4.8</td><td>2.1</td><td>1.8</td></tr><tr><td>WideResNet</td><td>4.2</td><td>4.3</td><td>3.4</td><td>4.6</td><td>4.2</td><td>2.2</td><td>1.6</td></tr><tr><td>ResNeXt</td><td>4.0</td><td>4.5</td><td>3.2</td><td>5.2</td><td>4.2</td><td>2.5</td><td>1.5</td></tr><tr><td colspan=\"2\">Mean</td><td>4.3</td><td>4.9</td><td>3.6</td><td>5.2</td><td>4.3</td><td>2.2</td><td>1.6</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "E CALIBRATION METRICS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            102,
+            408,
+            118
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "Due to the finite size of empirical test sets, the RMS Calibration Error must be estimated by partitioning all $n$ test set examples into $b$ contiguous bins $\\{ B _ { 1 } , B _ { 2 } , \\dots , B _ { b } \\}$ ordered by prediction confidence. In this work we use bins which contain 100 predictions, so that we adaptively partition confidence scores on the interval [0, 1] (Nguyen & O’Connor, 2015; Hendrycks et al., 2019b). Other works partition the interval $[ 0 , 1 ]$ with 15 bins of uniform length (Guo et al., 2017). With these $b$ bins, we estimate the RMS Calibration Error empirically with the formula ",
+        "bbox": [
+            173,
+            131,
+            826,
+            215
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "equation",
+        "img_path": "images/b8c6d83e1fb02a0a44e8936c6e32989c80cae12e2cccca3c86e85aa8098b1c36.jpg",
+        "text": "$$\n\\sqrt { \\sum _ { i = 1 } ^ { b } \\frac { | B _ { i } | } { n } \\biggl ( \\frac { 1 } { | B _ { i } | } \\sum _ { k \\in B _ { i } } \\mathbb { 1 } \\bigl ( y _ { k } = \\hat { y } _ { k } \\bigr ) - \\frac { 1 } { | B _ { i } | } \\sum _ { k \\in B _ { i } } c _ { k } \\biggr ) ^ { 2 ^ { \\top } } } .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            316,
+            219,
+            679,
+            268
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "This is separate from classification error because a random classifier with an approximately uniform posterior distribution is approximately calibrated. Also note that adding the “refinement” $\\mathbb { E } _ { C } [ ( \\mathbb { P } ( Y =$ $\\hat { Y } | C = c ) ( 1 - ( \\mathbb { P } ( Y = \\hat { Y } | C = c ) ) ]$ to the square of the RMS Calibration Error gives us the Brier Score (Nguyen & O’Connor, 2015). ",
+        "bbox": [
+            173,
+            270,
+            825,
+            330
+        ],
+        "page_idx": 14
+    }
+]

parse/train/hQGRD1Zael7/hQGRD1Zael7_content_list.json

@@ -0,0 +1,1085 @@
+[
+    {
+        "type": "text",
+        "text": "The Regularizing Effect of Different Output Layer Designs in Deep Neural Networks ",
+        "text_level": 1,
+        "bbox": [
+            194,
+            122,
+            805,
+            172
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Anonymous Author(s)   \nAffiliation   \nAddress   \nemail ",
+        "bbox": [
+            423,
+            226,
+            580,
+            281
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Abstract ",
+        "text_level": 1,
+        "bbox": [
+            462,
+            318,
+            535,
+            334
+        ],
+        "page_idx": 0
+    },
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+        "text": "1 Deep neural networks are prone to overfitting, especially on small datasets. Com  \n2 mon regularizers such as dropout or dropconnect reduce overfitting, but are complex   \n3 and prone to hyperparameter choices, thus prolonging development cycles in prac  \n4 tice. In this paper, we propose simple but effective design changes to the output   \n5 layer - namely randomization, sparsity, activation scaling, and ensembling - that   \n6 lead to improved regularization. These designs are motivated by experiments   \n7 showing that standard fully-connected output layers tend to rely on individual   \n8 input neurons, which in turn do not cover the variance of the data. We call these   \n9 two related phenomena neuron dependency and expressivity, propose different   \n10 ways to measure them, and optimize the presented output layers for them. In our   \n11 experiments, we compare these layer types for image classification and semantic   \n12 segmentation across architectures, datasets, and application settings. We report sig  \n13 nificantly and consistently improved performance of up to $10 \\%$ points in accuracy   \n14 over standard output layers while reducing the number of trainable parameters by   \n15 up to $90 \\%$ . It is demonstrated that neither training of output layers is required, nor   \n16 are output layers themselves crucial components of deep networks. ",
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+        "type": "text",
+        "text": "17 1 Introduction ",
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+        "text": "18 Neural networks are powerful feature extractors that have become the standard approach for a myriad   \n19 of tasks. New architectures are continuously introduced and set records on benchmark datasets   \n20 (e.g. [24, 15, 44]). These networks differ in layer composition, depth/width or use specific concepts   \n21 such as residual connections [15] or self-attention [34]. With growing capacity, their performance on   \n22 large datasets tends to increase [44]. However, model complexity is also associated with overfitting,   \n23 especially for small datasets where fine details of the training data are easily memorized [52, 2, 53].   \n24 Rather than defining another, possibly more complex architecture, we analyze what often remains   \n25 unconsidered: the output layer. In image classification, networks usually end with a fully-connected   \n26 (fc) layer that combines extracted features for the final output [43, 15, 17, 44]. As we will show, this   \n27 layer is prone to overfitting since high dependencies on individual, possibly memorized features can   \n28 arise. The same neurons are subsequently not able to generalize across examples. We call these two   \n29 related phenomena neuron dependency and expressivity and illustrate a simplified example in Fig. 2.   \n30 Both problems can be improved by simple but effective changes to the output layer that require only   \n31 few lines of code and achieve better generalization (i.e., better results on the test set [25], see e.g.   \n32 Fig. 1). Those changes rely on four principles: activation scaling, fixed randomization, sparsity and   \n33 in-layer ensembling (see Fig. 5). This work analyzes all layers in terms of their capability to reduce   \n34 dependencies and/or increase expressivity. Then, the connection to network performance is shown   \n35 through a comprehensive empirical study across datasets, architectures and application settings in   \n36 image classification and segmentation. Furthermore, we investigate how stronger regularization   \n37 can be induced by applying the identified principles to other parts of a network while reducing the   \n38 computational footprint. In contrast to common practice, we find neither training of output layers   \n39 to be necessary, nor that output layers are crucial components of deep networks. In summary, our   \n40 contributions are: ",
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+        "image_caption": [
+            "Figure 1: Effect of different output layer designs on cross-entropy loss (left) and accuracy (right) in a ResNet-50 for the STL-10 dataset. Best viewed in color. "
+        ],
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+            "Figure 2: Schematic of neuron dependency/expressivity in fc output layers. The left side of each subfigure represents penultimate layer activations (A1-2), the right shows output neurons for each class (O1-2). Filled/blank circles indicate high/low activation, up-/downward facing arrows signal positive/negative weights. Higher activations of O1 lead to correct predictions in this example. Model 1 depends on neuron A1 to be activated to give high prediction scores to O1. This is the case for a training instance in a). If Model 1 is applied to an unseen input pattern of same class in b), higher scores are erroneously given to O2 since A1 remains inactive and A2 slightly favors O2. Model 1 fails to generalize as it depends on A1, which is not expressive enough to cover the variance of the target class. Instead, Model 2 shown in c) exhibits neurons with low dependency and high expressivity, where A1 generalizes to unseen patterns, while the activation of A2 can be regarded as backup. Note that this example is simplified and educational. See Sect. 3.3 for measurements. "
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+        "text": "• Introducing neuron dependency and expressivity as two factors contributing to overfitting and proposing ways to measure these factors • Showing improved regularization of 5 different output layer designs up to $10 \\%$ in absolute accuracy compared to standard fc layers and other common regularizers • Empirical results showing that the proposed layers have improved dependency and expressivity, computational efficiency, wide applicability to both small and large datasets, extensibility to other parts of the network, and robustness in the choice of hyperparameters ",
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+    {
+        "type": "text",
+        "text": "48 2 Related Work ",
+        "text_level": 1,
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+        "text": "49 Regularization in deep learning is approached in various ways. Widely used methods are, e.g.,   \n50 normalization [19, 3], weight decay [32], data and adversarial augmentation [40, 1], early stopping [7],   \n51 boosting [38], multitask learning [6], dropout [42], dropconnect [50], and Gaussian noise layers [10].   \n52 To the best of our knowledge, this is the first work that evaluates regularization with respect to   \n53 different output layer designs. Similar to dropout/dropconnect, output layers can be categorized as   \n54 affecting the architecture according to the regularization taxonomy described in [25]. Unlike other   \n55 regularizers, our methods are either hyperparameter-free or robust to their choice and can be applied   \n56 to any deep net, including pre-trained ones that are less affected by overfitting (see Sect. 5.4 and 5.7).   \n57 Related to fixed randomization are the output layers used in [16, 39, 14], which show comparable   \n58 performance to trained layers. One can also preallocate output layer weights with a defined struc  \n59 ture [31, 16]. Besides output layers, weight fixing is for example applied to the first layer in the   \n60 Extreme Learning Machine [18], or to different weight dimensions in [36]. In contrast, we omit   \n61 hand-crafted weights, show improved regularization and relate to neuron dependencies. Further, we   \n62 show that fixing or scaling the last conv block next to the output layer has a strong regularizing effect.   \n63 Sparsity is common in deep learning, e.g. the ReLU activation [13] or a $L _ { 1 }$ penalty term in the loss   \n64 function [46]. Sparsity has also been applied to the channels of Convolutional Neural Networks   \n65 (CNNs) [8, 29]. Others induce sparsity by pruning connections before training under the lottery   \n66 ticket hypothesis [11, 30], with the goal of reducing the number of parameters while not sacrificing   \n67 performance [27, 45, 51]. Different to them, we show that (extreme) sparsity is not merely useful to   \n68 improve computational efficiency, but to improve performance when applied to the output layer.   \n69 The Network in Network (NIN) [28] and All-CNN [41] both use global average pooling (GAP)   \n70 followed by softmax, which replaces the fc output layer with an identify transform to simplify the   \n71 network. This is further analyzed in [33]. We show its connection to neuron dependency/expressivity   \n72 and achieve comparable or better performance on various datasets. Further, we observe that previous   \n73 works do not leverage the full capacity of the last layer in modern networks, which enables the   \n74 construction of computationally efficient in-layer ensembles that further boost performance in small   \n75 and large datasets. ",
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+    {
+        "type": "text",
+        "text": "76 3 Neuron dependency and expressivity ",
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+        "type": "text",
+        "text": "3.1 Setting and notation ",
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+        "text": "We consider neural networks consisting of an encoder $f _ { e n c } : \\pmb { \\mathsf { X } }  \\pmb { a }$ followed by an output layer $f _ { o u t } : \\pmb { a }  \\hat { \\pmb y }$ . In this paper, the encoder is a CNN, taking as input an image $\\pmb { \\chi } \\doteq \\mathbb { R } ^ { C \\times H ^ { \\star } W }$ with $C , W$ and $H$ being input channels, width and height, respectively; and transforming it to a feature vector $\\pmb { a } \\in \\mathbb { R } ^ { 1 \\times N }$ . Commonly in CNNs, 2D representations resulting from the final conv layer are aggregated by GAP [28] where $N$ corresponds to the number of pooled conv channels. The output layer transforms the embedding to output $\\hat { \\pmb y } \\in \\mathbb { R } ^ { K }$ holding the probabilities of $K$ classes. The output layer is parameterized by a weight matrix $\\pmb { W } \\in \\mathbb { R } ^ { N \\times K }$ , and is commonly initialized as $W ^ { r a n d o m } \\sim \\mathcal { U } ( - \\overset { \\cdot } { \\sqrt { 1 / N } } , \\overset { } { \\sqrt { 1 / N } } )$ [26]. Both $\\hat { y }$ and target $\\textbf {  { y } }$ are used to compute the cross-entropy loss $\\begin{array} { r } { \\ell = - \\sum _ { i } ^ { K } y _ { i } \\log ( \\hat { y } _ { i } ) } \\end{array}$ . We use the terms features/channels/nodes or neurons interchangeably meaning activations $\\textbf { \\em a }$ . When required, we refer to individual instances with a superscript, e.g. $( \\mathbf { X } ^ { ( i ) } , \\pmb { y } ^ { ( i ) } ) \\in \\mathcal { D }$ , with $\\mathcal { D }$ being a dataset. Corresponding subsets are denoted as $\\mathcal { D } _ { t r a i n }$ and $\\mathcal { D } _ { t e s t }$ . ",
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+        "type": "text",
+        "text": "3.2 Concepts ",
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+        "text": "During training, CNNs learn a set of visual patterns that are combined for a classification decision. However, if patterns remain undetected, e.g. due to noise in the image or inherent but unseen variance in the data, their activation values can become small and thus reduce the output values for the target class. When a network is overfitting, it learns malignant image-specific patterns by heart [52]. Such a network may depend on the activation of individual nodes, which in turn fail to generalize to patterns that are salient to a class. We call these two related phenomena neuron dependency and expressivity. ",
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+        "text": "97 Neuron dependency: How much does a model depend on a single neuron? In a network   \n98 with high neuron dependencies, output scores and thus performance drop significantly when certain   \n99 neurons remain inactive. In contrast, a network with low neuron dependencies distributes activations   \n00 across many neurons, so that a single inactive node does not have much influence on the classification.   \n101 Neuron expressivity: How much class-specific variance does a neuron cover? Neurons with low   \n02 expressivity focus on unimportant details that do not characterize the properties of a class. In contrast,   \n03 a neuron with high expressivity generalizes by activating to various patterns pertinent to a given class. ",
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+        "type": "text",
+        "text": "104 An example of neuron dependency/expressivity for a simplified fc output layer is illustrated in Fig. 2. ",
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+        "image_caption": [
+            "Figure 3: The effect of dataset size and activation scale on neuron dependency in a ResNet-50 trained on subsets of CIFAR-100, evaluated on the test set. Left: Small training sets lead to high neuron dependencies. Center: Scaling activations results in larger absolute logits. Right: Larger scales lead to higher dependencies. Best viewed in color. "
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+        "image_caption": [
+            "Figure 4: Neuron dependency (left) and expressivity (right) in a ResNet-50 with 2048 penultimate layer channels trained on CIFAR-100 for different output layer designs, showing the change in accuracy on the test set. Best viewed in color. "
+        ],
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+        "type": "text",
+        "text": "105 3.3 Measuring dependency and expressivity ",
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+        "text": "106 We introduce two ways of measuring dependency/expressivity: instance-based and class-based. The   \n107 former is used to determine the dependency on the most important node for the predicted class given an   \n108 instance. Importance scores for node $n$ and output class $\\hat { k }$ are computed with Gradient $\\odot .$ Activation [4],   \n109 a global attribution method where we leverage the partial derivative of the softmax values: ",
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+    {
+        "type": "equation",
+        "img_path": "images/f25e1698df05e5496b04f27bde4bc7d79793921697c42604073059c7433dffff.jpg",
+        "text": "$$\na _ { n } \\frac { \\partial \\hat { y } _ { \\hat { k } } } { \\partial a _ { n } } .\n$$",
+        "text_format": "latex",
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+        "text": "110 Instance-based dependency is then measured as avg. reduction in output probabilities when ablating   \n111 the most important feature w.r.t. the output class of any instance. This is illustrated for various   \n112 training set sizes of CIFAR-100 [23] in Fig. 3 (left). With less data, fc output layers tend to depend   \n113 more on single nodes. This is in contrast to class-based measures, which enable quantifying both   \n114 dependency/expressivity and use various features jointly. Importances are determined for each class   \n115 $k$ and over all test instances: ",
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+        "text": "$$\n\\sum _ { i = 1 } ^ { \\left| \\mathcal { D } _ { t e s t } \\right| } a _ { n } ^ { ( i ) } \\frac { \\partial \\hat { y } _ { k } ^ { ( i ) } } { \\partial a _ { n } ^ { ( i ) } } .\n$$",
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+        "text": "116 Class-based dependency is then measured as drop in accuracy when ablating a given number of most   \n117 important neurons per class. Measuring expressivity reverses this - the most important neurons per   \n118 class are retained, all others are ablated. This is illustrated for both dependency/expressivity in Fig. 4.   \n119 We see that standard (i.e. trained) fc output layers tend to depend on single channels to achieve high   \n120 performance, but these very channels hold only limited class information. ",
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+        "type": "text",
+        "text": "21 4 Output Layer Types ",
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+        "text": "122 We describe several simple output layer variants that require minimal changes to standard networks,   \n123 decrease neuron dependency and/or increase neuron expressivity. All types are illustrated in Fig. 5. ",
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+        "image_caption": [
+            "Figure 5: A visual comparison of various output layer types. Red/blue represent variable/fixed. "
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+        "type": "text",
+        "text": "124 4.1 Standard output layers ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "The ubiquitous approach to compute class scores is to learn the parameters of a weight matrix $W ^ { t r a i n e \\bar { d } }$ , s.t. $\\pmb { \\hat { y } } = \\sigma _ { S M } ( \\pmb { a } \\pmb { W } ^ { t r a i n e d } )$ with $\\sigma _ { S M } ( \\cdot )$ being softmax. Each feature is considered in the computation of each class score. As shown in Sect. 3, trained fc output layers can lead to high neuron dependencies, where the deletion of a single neuron might cause significant loss in performance, and low neuron expressivity, where multiple features are required for adequate predictions. ",
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+        "text": "4.2 Scaled output layers ",
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+    {
+        "type": "text",
+        "text": "The reduction of an activation, e.g. due to changing light conditions, has a large influence on the output scores. This is simulated in Fig. 3 (center) by multiplying features during training with a scalar $\\alpha > 0$ , so that $\\pmb { \\hat { y } } = \\sigma _ { S M } ( \\alpha \\pmb { a } \\pmb { W } ^ { s \\bar { c } a l e d } )$ . Note that the variances of the output logit distributions increase with $\\alpha$ , resulting in larger differences (or smaller entropies) after softmax normalization. This results in greater dependencies of the model on individual neurons, as shown in Fig. 3 (right). However, if $\\alpha$ is chosen small, the activations of individual neurons become insufficient for class discrimination with high confidence. The model is therefore forced to learn multiple class-specific features for each instance, which increases the expressivity of the neurons and also reduces their dependencies to some extent, as shown in Fig. 4. If not specified otherwise, we use $\\alpha = 0 . 1$ . ",
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+        "type": "text",
+        "text": "40 4.3 Random fixed layers ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "This setting uses $W ^ { r a n d o m }$ during training/inference, and its classification performance was first analyzed in [16]. The encoder learns to extract patterns that adjust to predetermined weights. Unlike activation scaling, the parameters are bounded and fixed to a small value range. For any class, the chosen uniform initialization is expected to assign similar weight values to multiple neurons, making them learn similar features. We suppose that the enforced similarity reduces dependency shown in Fig. 3 and 4 (both left), while small initialization values increase expressivity as in Sect. 4.2, shown in Fig. 4 (right). ",
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+    {
+        "type": "text",
+        "text": "8 4.4 Sparse fixed layers ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "In sparse output layers, class nodes use predetermined sets of channels, some of which might be shared across classes. First, a set of cutting indices $\\mathcal { T } _ { k }$ is randomly sampled for each class $k$ , where sparsity is determined by the proportion $q$ of class-specific connections to cut, so that $\\left| \\mathcal { T } _ { k } \\right| = \\left\\lfloor q \\bar { N } \\right\\rfloor$ with $0 < q < 1$ . Then, starting from a fixed random initialization as in Sect. 4.3, weights connecting to a given class are ablated so that: $W _ { i , k } ^ { s p a r s e } = 0 \\forall i \\in \\mathcal { T } _ { k }$ . Hyperparameter $q$ trades off dependency/expressivity. Larger values induce more sparsity, leading to greater dependencies to the remaining nodes, but forcing them to activate across instances, making them expressive. We set $q = 0 . 9$ in the experiments to show that high sparsity benefits generalization. ",
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+        "type": "text",
+        "text": "4.5 1-to-1 correspondence layers ",
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+        "type": "text",
+        "text": "158 The most extreme type of sparsity in an output layer is one with a single connection between a   \n159 feature and a class. If these connections correspond to an identity transform, the activations of the   \n160 penultimate layer are equivalent to the class logits - in practice, the output layer can hence be omitted.   \n161 This was analyzed in [33, 28] and showed comparable results to a standard output layer. Formally, we   \n162 have $\\pmb { \\hat { y } } = \\sigma _ { S M } \\big ( \\pmb { a } \\pmb { W } ^ { 1 t o 1 } \\big )$ with $\\pmb { a } \\in \\mathbb { R } ^ { 1 \\times K }$ and $W ^ { 1 t o 1 } \\in \\mathbb { R } ^ { K \\times K }$ , where ${ \\cal W } ^ { 1 t \\dot { o } 1 } = \\dot { d } i a g ( 1 , 1 , \\dot { \\bf \\Phi } , \\dot { \\bf \\Phi } , 1 )$   \n163 In this layer, both the model’s dependency on individual neurons as well as each neuron’s expressivity   \n164 are maximal. If a single neuron is ablated, the output logits for the class this neuron is connected to is   \n165 reduced to zero. However, individual neurons learn to cover the whole variance of a given class in the   \n166 training set, which is one conjecture for their performance. Note that as mentioned in [33], we have   \n167 the constraint $N = K$ , which might be restrictive for small networks and large numbers of classes. ",
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+    },
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+        "type": "text",
+        "text": "",
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+    },
+    {
+        "type": "text",
+        "text": "168 4.6 Ensemble layers ",
+        "text_level": 1,
+        "bbox": [
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+            155,
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+            170
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "169 Is there a way to optimize for both low neuron dependency and high expressivity? Of the approaches   \n170 discussed, 1-to-1 correspondence layers have the highest expressivity. Starting from this layer, a   \n171 simple approach to reduce neuron dependency is to use the capacity of the penultimate layer and   \n172 create multiple heads $h = 1 \\ldots H$ with $N = K H$ , each head being a 1-to-1 correspondence layer.   \n173 Each head’s output is effectively computed as $\\hat { \\pmb { y } } ^ { h } = \\sigma _ { S M } ( \\alpha \\pmb { a } ^ { h } )$ with $\\mathbf { \\Omega } _ { a } \\mathbf { \\Omega } _ { h } ^ { h }$ being the activation part of   \n174 head $h$ . As in Sect 4.2, we introduce a scalar $\\alpha$ , which controls the magnitude of feature activations.   \n175 176 For consisaveraged: $\\begin{array} { r } { \\frac { 1 } { H } \\dot { \\sum _ { h = 1 } ^ { H } } \\ell ( \\hat { \\pmb y } ^ { h } , \\pmb y ) } \\end{array}$ this approach as . Similarly, logit $W ^ { h e a d s }$ . The loss is computed for each head andraged over heads for inference. Due to the   \n177 induced redundancy, the performance only drops considerably after removing class-related neurons   \n178 from all heads. In our experiments, we set $H$ to its maximum given any setting (architecture/dataset).   \n179 Note that hyperparameter $\\alpha$ in ensemble layers is the only one which is tuned to individual settings. ",
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+    },
+    {
+        "type": "text",
+        "text": "180 5 Experiments ",
+        "text_level": 1,
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "181 We aim to show that the presented output layers from Sect. 4 outperform standard output layers and   \n182 common regularization methods in various settings. Details about training, compute resources, code,   \n183 datasets as well as additional experiments on dependency/expressivity are included in the appendix. ",
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+    {
+        "type": "text",
+        "text": "184 5.1 Small-scale and fine-grained classification ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "All layer types are first applied to small-scale and/or fine-grained classification, both of which are challenging and require regularization. Datasets include STL-10 (500 img/class) [9], CUB-200 ${ \\sim } 3 0$ img/class) [49], Cars-196 ${ \\sim } 4 0$ img/class) [22] and Food-101 (750 img/class) [5]. Table 1 shows results for the two popular backbones ResNet-50 [15] and DenseNet-169 [17], exchanging the output layer accordingly. In 53/56 settings, we see improved results over standard layers. Of these, 48 and 36 are significant with $p < 0 . 1$ and $p < 0 . 0 0 1$ , respectively. Although there is no clear best method, it is worth noting that sparse and ensemble layers as enhancements of both random and 1-to-1 layers are significantly better $\\mathit { p } < 0 . 0 0 1 )$ ) in 7/8 settings, respectively. As expected, smaller performance differences are exhibited in Food-101, which is a considerably larger dataset, thus requiring less regularization. Among the worse settings, only 1 is significant $( p < 0 . 1 )$ for Food-101 since it involves strong regularization to multiple layers. These regularizers are discussed seperately in Sect. 5.5. ",
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+    },
+    {
+        "type": "text",
+        "text": "197 5.2 Large-scale classification and transfer learning ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "198 Machine learning models are subject to the bias-variance tradeoff [12], in which induced biases of   \n199 the presented output layers might be too strong to fit the training data. We therefore want to shed   \n200 light on how these layers behave in large-scale and transfer learning settings, where overfitting is   \n201 less problematic. Datasets include CIFAR-100 (C100, 5000 img/class) [23], ImageNet (IN, ${ \\sim } 1 2 0 0$   \n202 img/class) from ILSVRC2012 [37] reported on the validation set, as well as CUB/Cars/Food with   \n203 models being pre-trained on IN. Table 2 shows the results for the ResNet-50 backbone. In C100,   \n204 we see consistent improvements with at least $p < 0 . 1$ . On the other datasets, results are mostly   \n205 comparable corroborating widespread applicability. It is worth mentioning that $W ^ { 1 t o 1 }$ and $W$ ensemble   \n206 perform consistently better, and $W ^ { e n s e m b l e }$ significantly $( p < 0 . 1 )$ in multiple cases. With growing   \n207 dataset sizes, both layers expose a strong constraint on the class neurons to fit an increasing number   \n208 of examples. We believe this to be responsible for progressively separating the signal from the noise,   \n209 leading to better generalization. On the other hand, neuron dependency is reduced in larger datasets   \n210 (see Fig. 3 left) diminishing the effect of $W ^ { s c a l e }$ and $W ^ { r a n d o \\bar { m } }$ . Moreover, $W ^ { r a n d o m }$ and $W ^ { s p a r s e }$   \n211 can be affected by predetermined feature-class weights that do not have to match features learned   \n212 during pre-training, which might require larger adjustments to the weights of the last conv layer. ",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/36831a8c6c68bfba50074f29516d98c815fa914dbb611859901e955e93bc994c.jpg",
+        "table_caption": [
+            "Table 1: Classification accuracy for different output layer designs in small-scale and fine-grained classification without pre-training. Exponent repeats describe probability values $( * { } ; \\ p \\ < \\ 0 . 1$ , $^ { * * }$ : $p < 0 . 0 1$ , $^ { \\ast \\ast \\ast }$ : $p \\ < \\ 0 . 0 0 1 $ indicating statistical significance based on a one-tailed normal approximation interval test comparing accuracy of the proposed layer designs to a baseline fc layer $( \\dot { W } ^ { t r a i n e d } )$ . Symbols $^ *$ and $\\dagger$ denote better/worse performance than baseline, respectively. Bold denotes best performance. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td colspan=\"2\"></td><td>STL-10</td><td>CUB-200</td><td>Cars-196</td><td>Food-101</td></tr><tr><td rowspan=\"7\">RrsSee50</td><td>Wtrained (baseline)</td><td>81.36</td><td>57.18</td><td>81.20</td><td>83.70</td></tr><tr><td>Wscaled</td><td>83.33*</td><td>63.46***</td><td>87.07***</td><td>85.46***</td></tr><tr><td>W scaled block</td><td>86.42***</td><td>66.74***</td><td>87.53***</td><td>85.03**</td></tr><tr><td>Wrandom</td><td>86.08***</td><td>60.91**</td><td>83.02*</td><td>84.20</td></tr><tr><td>Wrandom block</td><td>86.59***</td><td>67.21***</td><td>84.07***</td><td>84.04</td></tr><tr><td>Wsparse</td><td>87.23***</td><td>66.27***</td><td>85.47***</td><td>85.45***</td></tr><tr><td>W1to1</td><td>84.78***</td><td>58.56</td><td>80.51</td><td>84.41*</td></tr><tr><td rowspan=\"6\">Grr-nseese1g</td><td>Wensemble</td><td>87.94***</td><td>62.98***</td><td>85.76***</td><td>85.36***</td></tr><tr><td>Wtrained (baseline) W scaled</td><td>81.88 86.53***</td><td>55.33</td><td>80.82</td><td>84.31</td></tr><tr><td>W scaled block</td><td>85.89***</td><td>63.31*** 65.57***</td><td>85.85***</td><td>85.05*</td></tr><tr><td>Wrandom</td><td>86.11***</td><td>61.24***</td><td>85.35***</td><td>85.44**</td></tr><tr><td>Wrandom block</td><td>86.64***</td><td>65.99***</td><td>83.52**</td><td>84.90*</td></tr><tr><td>Wsparse</td><td></td><td></td><td>82.93*</td><td>83.25t</td></tr><tr><td>Wltol</td><td></td><td>86.58***</td><td>62.75***</td><td>85.79***</td><td>84.63</td></tr><tr><td>Wensemble</td><td></td><td>86.06***</td><td>55.37</td><td>83.75**</td><td>84.11</td></tr><tr><td></td><td></td><td>87.00***</td><td>64.15***</td><td>85.09***</td><td>84.91*</td></tr></table>",
+        "bbox": [
+            232,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/e20ac1e59597a5e5038176eea8b69eb3abf7b37ae4705bfdf847864dc1823386.jpg",
+        "table_caption": [
+            "Table 2: Classification results for different output layer designs in large-scale image recognition and transfer learning. $^ +$ denotes fine-tuning from ImageNet. See Table 1 for other symbols. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>C100</td><td>IN-top1</td><td>IN-top5</td><td>CUB-200+</td><td>Cars-196+</td><td>Food-101+</td></tr><tr><td>Wtrained</td><td>77.75</td><td>76.36</td><td>93.12</td><td>80.91</td><td>91.73</td><td>87.32</td></tr><tr><td>Wscaled</td><td>79.65*</td><td>76.08</td><td>92.84</td><td>78.68t</td><td>90.91t</td><td>87.21</td></tr><tr><td>Wrandom</td><td>78.91*</td><td>76.08</td><td>93.15</td><td>80.89</td><td>91.72</td><td>87.29</td></tr><tr><td>Wsparse</td><td>79.46*</td><td>75.32tt</td><td>92.36ttt</td><td>80.38</td><td>92.07</td><td>87.31</td></tr><tr><td>W1to1</td><td>79.07*</td><td>76.53</td><td>93.32</td><td>81.79</td><td>91.87</td><td>87.31</td></tr><tr><td>Wensemble</td><td>80.38***</td><td>76.62</td><td>93.46*</td><td>82.22*</td><td>92.77*</td><td>87.76</td></tr></table>",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "213 5.3 Use Case: Medical imaging ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Output layer design is critical in fields such as medical imaging, which presents special challenges to regularization: Datasets tend to be small, imbalanced, abnormalities might fill only a few pixels of the image, and appearances between classes are often similar. In addition, transfer learning with IN weights is either inaccessible due to architectural differences (e.g. image segmentation, 3D Magnetic Resonance Imaging) or less effective due to large domain differences. This is first illustrated on the APTOS Kaggle challenge dataset (3662 images, 193-1805 img/class) [20], with the goal of detecting diabetic retinopathy severities in retinal fundus images. We use the public training dataset to train a multi-class classifier and perform 5-fold cross-validation. Table 3 shows the results. We consistently get better performance with regularization and reduce the gap to a pre-trained network. Furthermore, an additional experiment in the appendix indicates that the standard output layer is biased towards the prevalent class, which is inherently remedied through randomization. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "225 We provide further evidence that the proposed layer designs positively affect tasks other than   \n226 classification. We learn a U-Net [35] for binary semantic slice-based segmentation of Computed   \n227 Tomography scans of livers comparing a standard 1x1 conv output layer with 64 parameters to both a   \n228 fixed randomized and an ensemble layer. Due to the limited number of parameters, we omit $W ^ { s c a l e }$   \n229 and $W ^ { s p a r s e }$ here. Different to classification, the output of a U-Net itself can be interpreted as a 1-to-1   \n230 layer. One can still build an ensemble by treating each output channel as a head. Both $W ^ { r a n d o m }$ and   \n231 W ensemble $H = 1 0$ ) are then applied to the CHAOS [21] and SLIVER [47] datasets. For CHAOS, ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/6e24e4fd1f52c2f93f88ac7dc28257b8bb8b6632248ec19d8dc5831115f0d98f.jpg",
+        "table_caption": [
+            "Table 3: Quadratic weighted kappa and accuracy (with significance) for different output layers in ResNet-50 for the APTOS dataset. $^ +$ denotes fine-tuning from IN. See Table 1 for other symbols. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>Kappa</td><td>Acc.</td></tr><tr><td>Wtrained</td><td>0.816</td><td>77.44</td></tr><tr><td>W scaled</td><td>0.818</td><td>78.38</td></tr><tr><td>Wrandom</td><td>0.848</td><td>79.32*</td></tr><tr><td>Wsparse</td><td>0.840</td><td>79.60*</td></tr><tr><td>Wltol</td><td>0.856</td><td>80.08*</td></tr><tr><td>Wensemble</td><td>0.866</td><td>80.78**</td></tr><tr><td>Wtrained+</td><td>0.909</td><td>85.02</td></tr><tr><td>W sparse+</td><td>0.910</td><td>85.17</td></tr><tr><td>Wensemble+</td><td>0.912</td><td>85.56</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/0b833a667fe5ec07eeabbbc6ea05f3ff97182307088fa791c8ded2ba404f0856.jpg",
+        "table_caption": [
+            "Table 4: Jaccard coefficients in segmentation "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>CHAOS</td><td>SLIVER</td></tr><tr><td>Wtrained</td><td>0.77</td><td>0.83</td></tr><tr><td>Wrandom</td><td>0.80</td><td>0.85</td></tr><tr><td>Wensemble</td><td>0.78</td><td>0.86</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/fe81b089d45e3d1993d9285f5dcef7b0d2f2b0b06193b02857defcc12b24812d.jpg",
+        "table_caption": [
+            "Table 5: Regularization comparison "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>STL</td><td>CUB</td><td>CUB+</td><td>Cars</td></tr><tr><td>Dropout [42]</td><td>82.73</td><td>63.20</td><td>80.26</td><td>83.98</td></tr><tr><td>Dropconn. [50]</td><td>86.15</td><td>61.48</td><td>80.41</td><td>85.06</td></tr><tr><td>Add. Noise [10]</td><td>82.51</td><td>52.74</td><td>80.91</td><td>76.77</td></tr><tr><td>Wtrained</td><td>81.36</td><td>57.18</td><td>80.91</td><td>81.20</td></tr><tr><td>Wsparse</td><td>87.23</td><td>66.27</td><td>80.38</td><td>85.47</td></tr><tr><td>Wensemble</td><td>87.94</td><td>62.98</td><td>82.22</td><td>85.76</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "we train on 15 randomly selected patients (2155 slices) and evaluate on the remaining 5 (719 slices). We then test for generalization by training on all 20 patients from CHAOS and evaluating on the external SLIVER dataset consisting of 20 patients (4159 slices). Table 4 shows improved results in both settings. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "5.4 Other regularization techniques ",
+        "text_level": 1,
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "Table 5 compares our most competitive methods to other popular regularizers when applied to a standard output layer. Nodes/connections in dropout/dropconnect are both removed with $p = 0 . 7$ , and the noise layer adds a Gaussian with $\\mu = 0$ and $\\sigma = 0 . 1$ before applying the fc layer. In all cases, our variants perform better. Whereas noise does not benefit training here, dropout/-connect is supporting regularization. However, both of the latter methods come with two main disadvantages. First, they add complexity by changing states in each iteration and having different behavior during training and inference. Second, hyperparameter tuning is necessary, while our layers are either hyperparameter-free or stable to them. See the ablation study in Sect. 5.7 for evidence. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "5.5 Beyond output layers - block scaling and randomization ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Activation scaling and randomization are techniques applicable to any layer and increase regularization further. This is demonstrated for ResNet-50 and DenseNet-169 in Table 1. Both architectures consist of multiple blocks, each holding groups of conv layer, batch normalization (BN) and activation function. For $W ^ { r a n d o m }$ block, all layers of the last block and the output layer are kept in their initialized state during training. Similarly, in $W ^ { s c a l e d }$ block, activations of all layer groups in the last block are scaled during training. In ResNet-50, block scaling outperforms output layer scaling in $3 / 4$ datasets by up to $3 \\%$ points, and block randomization increases performance in 3/4 datasets by up to $6 \\%$ points compared to output layer randomization. In DenseNet-169, block scaling outperforms output layer scaling in 2/4 datasets by up to $2 \\%$ points, and block randomization increases performance in 2/4 datasets by up to $4 \\%$ points compared to output layer randomization. Only in Food-101 and DenseNet, block randomization performs significantly worse than baseline because regularization is too strong leading to underfitting (tr $a i n l o s s = 0 . 4 7$ compared to 0.02 in $W ^ { r a n d o m }$ ). ",
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "5.6 Computational efficiency ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            790,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "The design of the head of deep CNNs has a great impact on computational efficiency. Standard output layers alone can contain a large amount of parameters, as CNNs typically hold more channels as they get deeper and the number of classes can become large. In ImageNet and a ResNet-50, for example, the output layer alone generates over 2 million parameters, which are saved in $W ^ { 1 t o 1 }$ and $W ^ { e n s e m b l e }$ . This problem compounds when using multiple fc layers. In a VGG-16, for instance, 3 fc layers are employed after the last conv layer. As Table 6 shows, omitting all fc layers saves up to $90 \\%$ in parameters, a considerable amount of memory, and time for a forward/backward pass while ",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/207951169f42b9b46861838692ebb93530d5aa4a96b4457463d196815c477319.jpg",
+        "table_caption": [
+            "Table 6: Computational efficiency comparison in CUB-200 highlighting that the number of trainable parameters can often be reduced while accuracy is improved. $^ +$ denotes fine-tuning from ImageNet. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Architecture</td><td>#Params in M.</td><td>Mem.[GB]</td><td>GFLOPS</td><td>Time [ms/it.]</td><td>Accuracy</td></tr><tr><td>VGG16 Wtrained+</td><td>135.1</td><td>7.5</td><td>31.1</td><td>114</td><td>78.68</td></tr><tr><td>VGG16 W1to1+</td><td>13.5</td><td>5.9</td><td>30.4</td><td>106</td><td>79.27</td></tr><tr><td>VGG16 Wensemble+</td><td>14.7</td><td>5.9</td><td>30.8</td><td>106</td><td>81.15**</td></tr><tr><td>Res50 Wtrained</td><td>23.9</td><td>5.1</td><td>8.2</td><td>71</td><td>57.18</td></tr><tr><td> Res50 Wrandom block</td><td>8.5</td><td>5.0</td><td>8.2</td><td>67</td><td>67.21***</td></tr></table>",
+        "bbox": [
+            174,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "image",
+        "img_path": "images/fe7727447bdb0dffda41c5653723499e8d22299b6bfed4abf9900ce522c38049.jpg",
+        "image_caption": [
+            "Figure 6: Ablation study showing stability and consistency of our output layer designs "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "266 increasing accuracy. If a ResNet-50 is used, randomization of the last conv block next to the output   \n267 layer yields savings of about $65 \\%$ in trainable parameters while increasing accuracy by $10 \\%$ points. ",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "268 5.7 Ablation study ",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "269 Note that $W ^ { r a n d o m }$ and $W ^ { 1 t o 1 }$ are hyperparameter-free compared to other regularizers such as   \n270 dropout/-connect, thus saving the cost of tuning them. Although other layer variants possess hyperpa  \n271 rameters, we show in Fig. 6 for the ResNet backbone that they are stable (no large jumps in vicinity)   \n272 and consistent (tend to monotonicity w.r.t. performance). In $W ^ { s p a r s e }$ , the maximum accuracy for   \n273 both datasets is at $q = 0 . 9 9$ (20 nodes per class) and drops only slightly for $q = 0 . 9 9 5$ . Similarly,   \n274 downscaling in $W ^ { s c a l e }$ improves performance at a small cost if the optimum is not hit. Also, more   \n275 heads in $W ^ { \\bar { e } n s e m b l e }$ tend to increase performance. What is the result of adding more heads than   \n276 given by the constraint $N = K H ?$ If $N < K H$ , which is the case for CUB-200 and $H > 1 0$ , we   \n277 add an additional 1x1 conv layer, BN and ReLU with $K H$ nodes to adjust for the missing channels.   \n278 Although this leads to a considerable increase in parameters ( $. N K H$ for the conv layer), it helps with   \n279 generalization, contradicting the common belief that overparameterization leads to overfitting [48].   \n280 In contrast, dropout is not stable or consistent. With a dropout rate of 0.9, the network fails to train   \n281 in both datasets. Furthermore, the optimum for CUB lies at 0.8, the same hyperparameter choice in   \n282 STL would result in worse performance than baseline. ",
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+    },
+    {
+        "type": "text",
+        "text": "283 6 Conclusion ",
+        "text_level": 1,
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "284 In this work, we introduced neuron dependency and expressivity as factors contributing to overfitting.   \n285 Then, different output layers were defined to optimize both and showed improved regularization in   \n286 various settings while being efficient and robust to hyperparameters. Although these layers are simple,   \n287 they have high practical relevance due to the importance of regularization and the ubiquity of output   \n288 layers in deep nets. In addition to their application, they may also be useful as primitives in future   \n289 (automatically created) architectures. Although improving regularization, we note that optimizing   \n290 for neuron dependencies/expressivity does not solve overfitting. For example, an unknown or noisy   \n291 instance may result in reduced activations in the majority of nodes in the penultimate layer. Finally,   \n292 we speculate that overfitting may not just be a function of the number of parameters in the encoder.   \n293 Instead, it might be more important how the extracted features are combined in the output layer. ",
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+        "type": "text",
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+        "text": "(a) Do the main claims made in the abstract and introduction accurately reflect the paper’s contributions and scope? [Yes] See Sect. 3, 5 and the appendix.   \n(b) Did you describe the limitations of your work? [Yes] See Sect. 4.5 $N = K$ constraint), Sect. 5.2 (some layers are not optimal for large-scale datasets and fine-tuning), Sect. 5.5 (strong regularization may lead to underfitting), and Sect. 6 (neuron dependency/expressivity are factors of overfitting, but this does not constitute all factors).   \n(c) Did you discuss any potential negative societal impacts of your work? [N/A] Focus is on architecture and technical, no particular application affecting society is targeted. Note that medical ML applications should be thoroughly evaluated, e.g., for bias and generalizability, before being used in practice.   \n(d) Have you read the ethics review guidelines and ensured that your paper conforms to them? [Yes] ",
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parse/train/r1lfF2NYvH/r1lfF2NYvH.md

@@ -0,0 +1,374 @@
+# INFOGRAPH: UNSUPERVISED AND SEMI-SUPERVISEDGRAPH-LEVEL REPRESENTATION LEARNING VIA MU-TUAL INFORMATION MAXIMIZATION
+
+Fan-Yun $\mathbf { S u n ^ { 1 , 2 } }$ , Jordan Hoffmann2,4, Vikas Verma $^ { 2 , 3 }$ , Jian Tang2,5,6
+
+1National Taiwan University,   
+2Mila-Quebec Institute for Learning Algorithms, Canada   
+3Aalto University, Finland   
+4Harvard University, USA   
+5HEC Montreal, Canada   
+6CIFAR AI Research Chair
+
+b04902045@ntu.edu.tw jhoffmann@g.harvard.edu vikas.verma@aalto.fi jian.tang@hec.ca
+
+# ABSTRACT
+
+This paper studies learning the representations of whole graphs in both unsupervised and semi-supervised scenarios. Graph-level representations are critical in a variety of real-world applications such as predicting the properties of molecules and community analysis in social networks. Traditional graph kernel based methods are simple, yet effective for obtaining fixed-length representations for graphs but they suffer from poor generalization due to hand-crafted designs. There are also some recent methods based on language models (e.g. graph2vec) but they tend to only consider certain substructures (e.g. subtrees) as graph representatives. Inspired by recent progress of unsupervised representation learning, in this paper we proposed a novel method called InfoGraph for learning graph-level representations. We maximize the mutual information between the graph-level representation and the representations of substructures of different scales (e.g., nodes, edges, triangles). By doing so, the graph-level representations encode aspects of the data that are shared across different scales of substructures. Furthermore, we further propose InfoGraph\*, an extension of InfoGraph for semi-supervised scenarios. InfoGraph\* maximizes the mutual information between unsupervised graph representations learned by InfoGraph and the representations learned by existing supervised methods. As a result, the supervised encoder learns from unlabeled data while preserving the latent semantic space favored by the current supervised task. Experimental results on the tasks of graph classification and molecular property prediction show that InfoGraph is superior to state-of-the-art baselines and InfoGraph\* can achieve performance competitive with state-of-the-art semi-supervised models.
+
+# 1 INTRODUCTION
+
+Graphs have proven to be an effective way to represent very diverse types of data including social networks Newman & Girvan (2004), biological reaction networksPavlopoulos et al. (2011), proteinprotein interactions Krogan et al. (2006), the quantum mechanical properties of individual molecules Xie & Grossman (2018); Jin et al. (2018), and many more. Graphs provide explicit information about the coupling between individual units in a larger part along with a well defined framework for assigning properties to the nodes and the edges connecting them. There has been a significant amount of previous work done studying many aspects of graphs including link prediction Gao et al. (2011); Wang et al. (2011) and node prediction Blei et al. (2003). Due to its flexibility, graph-like data structures can capture rich information which is critical in many applications.
+
+At the lowest level, much work has been done on learning node representations– low-dimensional vector embeddings of individual nodes Perozzi et al. (2014); Tang et al. (2015); Grover & Leskovec (2016). Another field that has attracted a large amount of attention recently is learning representations of entire graphs. Such a problem is critical in a variety of applications such as predicting the properties of molecular graphs in both drug discovery and material science Chen et al. (2019b;a). There has been some recent progress based on neural message passing algorithms Gilmer et al. (2017); Xie & Grossman (2018), which learn the representations of entire graphs in a supervised way. These methods have been shown achieving state-of-the-art results on a variety of different prediction tasks Kipf et al. (2018); Xie & Grossman (2018); Gilmer et al. (2017); Chen et al. (2019a).
+
+However, one of the most difficult obstacles for supervised learning on graphs is that it is often very costly or even impossible to collect annotated labels. For example, in the chemical domain labels are typically produced with a costly Density Functional Theory (DFT) calculation. One option is to use semi-supervised methods which combine a small handful of labels with a larger, unlabeled, dataset. In real-world applications, partially labeled datasets are common, making tools that are able to efficiently utilize the present labels particularly useful.
+
+Coming up with methods that are able to learn unsupervised representations of an entire graph, as opposed to nodes, is an important step in working with unlabeled or partially labeled graphs Narayanan et al. (2017); Hu et al. (2019); Nguyen et al. (2017). For example, there exists work that explores pre-training techniques for graphs to improve generalization Hu et al. (2019). Another common approach to unsupervised representation learning on graphs is through graph kernels Pržulj (2007); Kashima et al. (2003); Orsini et al. (2015). However, many of these methods do not provide explicit graph embeddings which many machine learning algorithms operate on. Furthermore, the handcrafted features of graph kernels lead to high dimensional, sparse or non-smooth representations and thus result in poor generalization performance, especially on large datasets Narayanan et al. (2017).
+
+Unsupervised learning of latent representations is also an important problem in other domains, such as image generation Kingma & Welling (2013); Kim & Mnih (2018) and natural language processing Mikolov et al. (2013a). A recent work introduced Deep Infomax, a method that maximizes the mutual information content between the input data and the learned representation Hjelm et al. (2018). This method outperforms other methods on many unsupervised learning tasks. Motivated by Deep InfoMax Hjelm et al. (2018), we aim to use mutual information maximization for unsupervised representation learning on the entire graph. Specifically, our objective is to maximize the mutual information between the representations of entire graphs and the representations of substructures of different granularity. We name our model InfoGraph.
+
+We also propose a semi-supervised learning model which we name InfoGraph\*. We employ a student-teacher framework similar to Mean-Teacher method Tarvainen & Valpola (2017). We maximize the mutual information between intermediate representations of the two models so that the student model learns from the teacher model. The student model is trained on the labeled data using a supervised objective function while the teacher model is trained on unlabeled data with InfoGraph. Using InfoGraph\*, we achieve performance competitive with state-of-the-art methods on molecular property prediction.
+
+We summarize our contributions as follows:
+
+• We propose InfoGraph, an unsupervised graph representation learning method based on Deep InfoMax (DIM) Hjelm et al. (2018). • We show that InfoGraph can be extended to semi-supervised prediction tasks on graphs. • We empirically show that InfoGraph surpasses state-of-the-art performance on graph classification tasks with unsupervised learning and obtains performance comparable with state-ofart methods on molecular property prediction tasks using semi-supervised learning.
+
+# 2 RELATED WORK
+
+Representation learning for graphs has mainly dealt with supervised learning tasks. Recently, however, researchers have proposed algorithms that learn graph-level representations in an unsupervised manner Narayanan et al. (2017); Adhikari et al. (2018).
+
+Concurrently to this work, information maximizing graph neural networks (IGNN) was introduced which uses mutual information maximization between edge states and transform parameters to achieve state-of-the-art predictions on a variety of supervised molecule property prediction tasks Chen et al. (2019b). In this work, our focus is on unsupervised and semi-supervised scenarios.
+
+Graph Kernels. Constructing graph kernels is a common unsupervised task in learning graph representations. These kernels are typically evaluated on node classification tasks. In graph kernels, a graph $G$ is decomposed into (possibly different) $\{ G _ { s } \}$ sub-structures. The graph kernel $K ( G _ { 1 } , G _ { 2 } )$ is defined based on the frequency of each sub-structure appearing in $G _ { 1 }$ and $G _ { 2 }$ respectively. Namely, $K ( G _ { 1 } , G _ { 2 } ) = \langle f _ { G _ { s _ { 1 } } } , f _ { G _ { s _ { 2 } } } \rangle$ , where $f _ { G _ { s } }$ is the vector containing frequencies of $\{ G _ { s } \}$ sub-structures, and $\langle , \rangle$ is an inner product in an appropriately normalized vector space. Much work has been devoted to deciding which sub-structures are more suitable than others (refer to appendix A.1). Instead of defining hand crafted similarity measures between substructures, InfoGraph adopts a more principled metric – mutual information.
+
+Contrastive methods. An important approach for unsupervised representation learning is to train an encoder to be contrastive between representations that capture statistical dependencies of interest and those that do not. For example, a contrastive approach may employ a scoring function, training the encoder to increase the score on “real” input (a.k.a, positive examples) and decrease the score on “fake” input (a.k.a., negative samples). For more detailed discussion, refer to appendix A.2.
+
+Deep Graph InfoMax (DGI) Velickovi ˇ c et al. (2018) also belongs to this category, which aims to train ´ a node encoder that maximizes mutual information between node representations and the pooled global graph representation. Although we built upon a similar methodology, our aim is different than theirs as our goal is to obtain embeddings at the whole graph level for unsupervised and semisupervised learning whereas DGI only evaluates node level embeddings. In order to differentiate our method with Deep Graph Infomax (Velickovi ˇ c et al. (2018)), we term our model InfoGraph. ´
+
+Semi-supervised Learning. A comprehensive overview of semi-supervised learning (SSL) methods is out of the scope of this paper. We refer readers to Appendix B for a short overview or Zhu et al. (2003); Chapelle et al. (2006); Oliver et al. (2018) for more comprehensive discussions. Here, we discuss a state-of-the-art method applicable for regression tasks – Mean Teacher Tarvainen & Valpola (2017).Mean Teacher adds a loss term which encourages the distance between the original network’s output and the teacher’s output to be small. The teacher’s predictions are made using an exponential moving average of parameters from previous training steps. Inspired by the “studentteacher” framework in Mean Teacher model, our semi-supervised model (InfoGraph\*) deploys two separate encoders but instead of explicitly encouraging the output of the student model to be similar to the teacher model’s output, we enable the student model to learn from the teacher model by maximizing mutual information between intermediate representations learned by two models.
+
+# 3 METHODOLOGY
+
+Most recent work on graphs focus on supervised learning tasks or learning node representations. However, many graph analytic tasks such as graph classification, regression, and clustering require representing entire graphs as fixed-length feature vectors. Though graph-level representations can be obtained through the node-level representations implicitly, explicitly extracting the graph can be more straightforward and optimal for graph-oriented tasks.
+
+Another scenario that is important, yet attracts comparatively less attention in the graph related literature is semi-supervised learning. One of the biggest challenges in prediction tasks in biology Yan et al. (2017); Yang et al. (2014) or molecular machine learning Duvenaud et al. (2015); Gilmer et al. (2017); Jia & Liang (2017) is the extreme scarcity of labeled data. Therefore, semi-supervised learning, in which a large number of unlabeled samples are incorporated with a small number of labeled samples to enhance accuracy of models, will play a key role in these areas.
+
+In this section, we first formulate an unsupervised whole graph representation learning problem and a semi-supervised prediction task on graphs. Then, we present our method to learn graph-level representations. Afterwards we present our proposed model for the semi-supervised learning scenario.
+
+![](images/0f719c9ab6ab5168fba6703ad60da52cc01175d671c92e304580b4030ebd633e.jpg)  
+Figure 1: Illustration of InfoGraph. N.A. denotes neighborhood aggregation. An input graph is encoded into a feature map by graph convolutions and jumping concatenation. The discriminator takes a (global representation, patch representation) pair as input and decides whether they are from the same graph. InfoGraph uses a batch-wise fashion to generate all possible positive and negative samples. For example, consider the toy example with 2 input graphs in the batch and 7 nodes (or patch representations) in total. For the global representation of the blue graph, there will be 7 input pairs to the discriminator and same for the red graph. Thus, the discriminator will take 14 (global representation, patch representation) pairs as input in this case.
+
+# 3.1 PROBLEM DEFINITION
+
+Unsupervised Graph Representation Learning. Given a set of graphs $\mathbb { G } = \{ G _ { 1 } , G _ { 2 } , . . . \}$ and a positive integer $\delta$ (the expected embedding size), our goal is to learn a $\delta$ -dimensional distributed representation of every graph $G _ { i } \in \mathbb { G }$ . We denote the number of nodes in $G _ { i }$ as $| G _ { i } |$ . We denote the matrix of representations of all graphs as Φ ∈ R|G|×δ.
+
+Semi-supervied Graph Prediction Tasks. Given a set of labeled graphs $\mathbb { G } ^ { L } = \{ G _ { 1 } , \cdot \cdot \cdot , G _ { | \mathbb { G } ^ { L } | } \}$ with corresponding output $\{ o _ { 1 } , \cdots , o _ { | \mathbb { G } ^ { L } | } \}$ , and a set of unlabeled samples $\begin{array} { r l } { \mathbb { G } ^ { U } } & { { } = } \end{array}$ $\{ G _ { | \mathbb { G } ^ { L } | + 1 } , \cdot \cdot \cdot , G _ { | \mathbb { G } ^ { L } | + | \mathbb { G } ^ { U } | } \}$ , our goal is to learn a model that can make predictions for unseen graphs. Note that in most cases $\left| \mathbb { G } ^ { U } \right| \gg \left| \mathbb { G } ^ { L } \right|$ .
+
+# 3.2 INFOGRAPH
+
+We focus on graph neural networks (GNNs)—a flexible class of embedding architectures which generate node representations by repeated aggregation over local node neighborhoods. The representations of nodes are learned by aggregating the features of their neighborhood nodes, so we refer to these as patch representations. GNNs utilize a READOUT function to summarize all the obtained patch representations into a fixed length graph-level representation.
+
+Formally, the $k$ -th layer of a GNN is
+
+$$
+h _ { v } ^ { ( k ) } = \mathrm { C O M B I N E } ^ { ( k ) } \left( h _ { v } ^ { ( k - 1 ) } , \mathrm { A G G R E G A T E } ^ { ( k ) } \left( \left\{ \left( h _ { v } ^ { ( k - 1 ) } , h _ { u } ^ { ( k - 1 ) } , e _ { u v } \right) : u \in \mathcal { N } ( v ) \right\} \right) \right) ,
+$$
+
+where $h _ { v } ^ { ( k ) }$ is the feature vector of node $v$ at the $k$ -th iteration/layer (or patch representation centered at node $i$ ), $e _ { u v }$ is the feature vector of the edge between $u$ and $v$ , and $\mathcal { N } ( v )$ are neighborhoods to node v. h(0)v is often initialized as node features. READOUT can be a simple permutation invariant function such as averaging or a more sophisticated graph-level pooling function Ying et al. (2018); Zhang et al. (2018).
+
+We seek to obtain graph representations by maximizing the mutual information between graph-level and patch-level representations. By doing so, the graph representations can learn to encode aspects of the data that are shared across all substructures. Assume that we are given a set of training samples $\mathbf { G } : = \{ G _ { j } \in \mathbb { G } \} _ { j = 1 } ^ { N }$ with empirical probability distribution $\mathbb { P }$ on the input space. Let $\phi$ denote the set of parameters of a $K$ -layer graph neural network. After the first $k$ layers of the graph neural network, the input graph will be encoded into a set of patch representations $\{ h _ { i } ^ { ( k ) } \} _ { i = 1 } ^ { N }$ . Next, we summarize feature vectors at all depths of the graph neural network into a single feature vector that captures patch information at different scales centered at every node. Inspired by $\mathrm { X u }$ et al. (2018b), we use
+
+concatenation. That is,
+
+$$
+\begin{array} { r } { h _ { \phi } ^ { i } = \mathrm { C O N C A T } ( \{ h _ { i } ^ { ( k ) } \} _ { k = 1 } ^ { K } ) } \\ { H _ { \phi } ( G ) = \mathrm { R E A D O U T } ( \{ h _ { \phi } ^ { i } \} _ { i = 1 } ^ { N } ) } \end{array}
+$$
+
+where $h _ { \phi } ^ { i }$ is the summarized patch representation centered at node $i$ and $H _ { \phi } ( G )$ is the global representation after applying READOUT. Note that here we slightly abuse the notation of $h$ .
+
+We define our mutual information (MI) estimator on global/local pairs, maximizing the estimated MI over the given dataset $\mathbf { G } : = \{ G _ { j } \in \mathbb { G } \} _ { j = 1 } ^ { N }$ :
+
+$$
+\hat { \phi } , \hat { \psi } = \underset { \phi , \psi } { \arg \operatorname* { m a x } } \sum _ { G \in \mathbf { G } } \frac { 1 } { | G | } \sum _ { u \in G } I _ { \phi , \psi } ( \vec { h } _ { \phi } ^ { u } ; H _ { \phi } ( G ) ) .
+$$
+
+$I _ { \phi , \psi }$ is the mutual information estimator modeled by discriminator $T _ { \psi }$ and parameterized by a neural network with parameters $\psi$ . We use the Jensen-Shannon MI estimator (following the formulation of Nowozin et al. (2016)),
+
+$$
+\begin{array} { r l } & { I _ { \phi , \psi } ( h _ { \phi } ^ { i } ( G ) ; H _ { \phi } ( G ) ) : = } \\ & { \quad \quad \quad \mathbb { E } _ { \mathbb { P } } [ - \mathrm { s p } ( - T _ { \phi , \psi } ( \vec { h } _ { \phi } ^ { i } ( x ) , H _ { \phi } ( x ) ) ) ] - \mathbb { E } _ { \mathbb { P } \times \mathbb { \tilde { P } } } [ \mathrm { s p } ( T _ { \phi , \psi } ( \vec { h } _ { \phi } ^ { i } ( x ^ { \prime } ) , H _ { \phi } ( x ) ) ) ] } \end{array}
+$$
+
+where $x$ is an input sample, $x ^ { \prime }$ (negative sample) is an input sampled from $\tilde { \mathbb { P } } = \mathbb { P }$ , a distribution identical to the empirical probability distribution of the input space, and $\operatorname { s p } ( z ) = \log ( 1 + e ^ { z } )$ is the softplus function. In practice, we generate negative samples using all possible combinations of global and local patch representations across all graph instances in a batch.
+
+Since $H _ { \phi } ( G )$ is encouraged to have high MI with patches that contain information at all scales, this favours encoding aspects of the data that are shared across patches and aspects that are shared across scales. The algorithm is illustrated in Fig. 1.
+
+It should be noted that our model is similar to Deep Graph Infomax (DGI) Velickovi ˇ c et al. (2018), a ´ model proposed for learning unsupervised node embeddings. However, there are important design differences due to the different problems that we are focusing on. First, in DGI they use random sampling to obtain negative samples due to the fact that they are mainly focusing on learning node embeddings on a graph. However, contrastive methods require a large number of negative samples to be competitive Hjelm et al. (2018), thus the use of batch-wise generation of negative samples is crucial as we are trying to learn graph embeddings given many graph instances. Second, the choice of graph convolution encoders is also crucial. We use GIN Xu et al. (2018a) while DGI uses GCN Kipf & Welling (2016) as GIN provides a better inductive bias for graph level applications. Graph neural network designs should be considered carefully so that graph representations can be discriminative towards other graph instances. For example, we use sum over mean for READOUT and that can provide important information regarding the size of the graph.
+
+# 3.3 SEMI-SUPERVISED INFOGRAPH
+
+Based on the previous unsupervised model, a straightforward way to do semi-supervised property prediction on graphs is to combine the purely supervised loss and the unsupervised objective function which acts as a regularization term. In doing so, the model is trained to predict properties for the labeled dataset while keeping a rich discriminative intermediate representation learned from both the labeled and the unlabeled dataset. That is, we try to minimize the following objective function:
+
+$$
+L _ { \mathrm { t o t a l } } = \sum _ { i = 1 } ^ { | \mathbb { G } ^ { L } | } L _ { \mathrm { s u p e r v i s e d } } ( y _ { \phi } ( G _ { i } ) , o _ { i } ) + \lambda \sum _ { j = 1 } ^ { | \mathbb { G } ^ { L } | + | \mathbb { G } ^ { U } | } L _ { \mathrm { u n s u p e r v i s e d } } ( h _ { \phi } ( G _ { j } ) ; H _ { \phi } ( G _ { j } ) )
+$$
+
+where ${ \cal L } _ { \mathrm { s u p e r v i s e d } } ( y _ { \phi } ( G _ { i } ) , o _ { i } )$ is defined as the loss function of graph $G _ { i }$ that measures the discrepancy between the classifier output $y _ { \phi } ( G _ { i } )$ and the true output $o _ { i }$ . $\bar { L } _ { \mathrm { u n s u p e r v i s e d } } ( h _ { \phi } ( G _ { j } ) ; H _ { \phi } ( G _ { j } )$ is the unsupervised InfoGraph loss term as defined in eq. equation 4 that can be optimized using both labeled and unlabeled data. The hyper-parameter $\lambda$ controls the relative weight between the purely supervised and the unsupervised loss. The intuition behind this is that the model will benefit from learning a good representation from the large amount of unlabeled data while learning to predict the corresponding supervised label.
+
+![](images/36b36de7af00fc7fc806574ea30f38fb525049f077cbc6028260c3888cee562c.jpg)  
+Figure 2: Illustration of the semi-supervised version of InfoGraph (InfoGraph\*). There are two separate encoders with the same architecture, one for the supervised task and the other trained using both labeled and unlabeled data with an unsupervised objective (eq. equation 4). We encourage the mutual information of the two representations learned by the two encoders to be high by deploying a discriminator that takes a pair of representation as input and determines whether they are from the same input graph.
+
+However, supervised tasks and unsupervised tasks may favor different information or a different semantic space. Simply combining the two loss functions using the same encoder may lead to “negative transfer” 1 (Pan & Yang, 2009; Rosenstein et al., 2005). We propose a simple way to alleviate this problem: we deploy two encoder models: the encoder on the labelled data (supervised encoder) and the encoder on the unlabelled data (unsupervised encoder). For transferring the learned representations from the unsupervised encoder to the supervised encoder, we define a loss term that encourages the representations learned by the two encoders to have high mutual information, at all levels of representations (third term of Eq. 8). Formally, let $\varphi$ denote the set of parameters of another $K$ -layered graph neural network, identical to the one parameterized by $\phi$ , and let $\lambda$ be a tunable hyper-parameter, $H _ { \phi } ^ { k } ( G )$ , $H _ { \varphi } ^ { k } ( G )$ be global encoder representations of the graph $G$ at encoder layer $k$ , then total loss function can be defined as follows:
+
+$$
+\begin{array} { r l } & { { \cal L } _ { \mathrm { t o t a l } } = \displaystyle \sum _ { i = 1 } ^ { | \mathbb { G } ^ { L } | } { \cal L } _ { \mathrm { s u p e r v i s e d } } ( y _ { \phi } ( G _ { i } ) , o _ { i } ) + \displaystyle \sum _ { j = 1 } ^ { | \mathbb { G } ^ { L } | + | \mathbb { G } ^ { U } | } { \cal L } _ { \mathrm { u n s u p e r v i s e d } } ( h _ { \varphi } ( G _ { j } ) ; H _ { \varphi } ( G _ { j } ) ) } \\ & { ~ - ~ \lambda ~ \displaystyle \sum _ { j = 1 } ^ { | \mathbb { G } ^ { L } | + | \mathbb { G } ^ { U } | } \frac { 1 } { | G _ { j } | } \displaystyle \sum _ { k = 1 } ^ { K } I ( H _ { \phi } ^ { k } ( G _ { j } ) ; H _ { \varphi } ^ { k } ( G _ { j } ) . } \end{array}
+$$
+
+Notice that this formulation can be seen as a special instance of the student-teacher framework. However, unlike the recent student-teacher methods for semi-supervised learning (Laine & Aila, 2016; Tarvainen & Valpola, 2017; Verma et al., 2019b), which enforce the predictions of the student model to be similar to the teacher model, we enforce the transfer of knowledge from the teacher model to the student model via mutual-information maximization at various levels of representations. In practice, to reduce the computation overhead introduced by the third term of $\operatorname { E q } 8$ , instead of enforcing the mutual-information maximization over all the layers of the encoders, at each training update, we enforce mutual-information maximization on a randomly chosen layer of the encoder (Verma et al., 2019a).
+
+In our semi-supervised experiments, we refer to the naive method using the objective function given in eq. equation 6 as InfoGraph. We refer to the method that uses two separate encoders and employ the objective function given in eq. equation 8 as InfoGraph\*. InfoGraph\* is fully summarized in Figure 3.
+
+# 4 EXPERIMENTS
+
+We evaluate the effectiveness of the graph-level representation learned by InfoGraph on downstream graph classification tasks and on semi-supervised molecular property prediction tasks.
+
+# 4.1 DATASETS
+
+For graph classification, we conduct experiments on 6 well-known benchmark datasets: MUTAG, PTC, REDDIT-BINARY, REDDIT-MULTI-5K, IMDB-BINARY, and IMDB-MULTI (Yanardag & Vishwanathan (2015)). For semi-supervised learning tasks, we use the publicly available QM9 dataset Ramakrishnan et al. (2014). Additional details of the datasets can be found in Appendix B.
+
+# 4.2 BASELINES
+
+For graph classification, we used 6 state-of-the-art graph kernels for comparison: Random Walk (RW) Gärtner et al. (2003), Shortest Path Kernel (SP) Borgwardt & Kriegel (2005), Graphlet Kernel (GK) Shervashidze et al. (2009), Weisfeiler-Lehman Sub-tree Kernel (WL) Shervashidze et al. (2011), Deep Graph Kernels (DGK) Yanardag & Vishwanathan (2015), and Multi-Scale Laplacian Kernel (MLG) Kondor & Pan (2016). Aside from graph kernels, we also compare with 3 unsupervised graph-level representation learning methods: node2vec Grover & Leskovec (2016), sub2vec Adhikari et al. (2018), and graph2vec Narayanan et al. (2017). Node2vec is a neural embedding framework that learns feature representations of individual nodes in graphs and we aggregate node embeddings to obtain graph embeddings.
+
+For semi-supervised tasks, aside from comparing the results with the fully supervised results, we also compare our results with a state-of-the-art semi-supervised method: Mean Teachers Tarvainen & Valpola (2017).
+
+# 4.3 EXPERIMENT CONFIGURATION
+
+For graph classification tasks, we adopt the same procedure of previous works Niepert et al. (2016); Verma & Zhang (2017); Yanardag & Vishwanathan (2015); Zhang et al. (2018) to make a fair comparison and used 10-fold cross validation accuracy to report the classification performance. Experiments are repeated 5 times. We report results from previous papers with the same experimental setup if available. If results are not previously reported, we implement them and conduct a hyperparameter search according to the original paper. For node2vec Grover & Leskovec (2016), we took the result from Narayanan et al. (2017) but we did not run it on all datasets as the implementation details are not clear in the paper. For Deep Graph Kernels, we report the best result out of Deep WL Kernels, Deep GK Kernels, and Deep RW Kernels. For sub2vec, we report the best result out of its two variants: sub2vec-N and sub2vec-S. For all methods, the embedding dimension is set to 512 and parameters of downstream classifiers are independently tuned using cross validation on training folds of data. The best average classification accuracy is reported for each method. The classification accuracies are computed using LIBSVM Chang & Lin (2011), and the $C$ parameter was selected from $\{ 1 0 ^ { - 3 } , 1 0 ^ { - 2 } , \dot { ~ } . ~ . ~ , 1 0 ^ { 2 } , \dot { 1 0 ^ { 3 } } \}$ .
+
+The QM9 dataset has 130462 molecules in it. We adopt similar experimental settings as traditional semi-supervised methods Tarvainen & Valpola (2017); Laine & Aila (2016); Miyato et al. (2018). We randomly chose 5000 samples as labeled samples for training and another 10000 as validation samples, 10000 samples for testing, and use the rest as unlabeled training samples. Note that we use the exact same split when running the supervised model and the semi-supervised model. We use the validation set to do model selection and we report scores on the test set. All targets were normalized
+
+Graph Kernels   
+
+<table><tr><td>Dataset</td><td>MUTAG</td><td>PTC-MR</td><td>RDT-B</td><td>RDT-M5K</td><td>IMDB-B</td><td>IMDB-M</td></tr><tr><td>(No.Graphs)</td><td>188</td><td>344</td><td>2000</td><td>4999</td><td>1000</td><td>1500</td></tr><tr><td>(No.classes)</td><td>2</td><td>2</td><td>2</td><td>5</td><td>2</td><td>3</td></tr><tr><td>(Avg. Graph Size)</td><td>17.93</td><td>14.29</td><td>429.63</td><td>508.52</td><td>19.77</td><td>13.00</td></tr></table>
+
+Other Unsupervised Methods   
+
+<table><tr><td rowspan=1 colspan=1>RW</td><td rowspan=1 colspan=1>83.72 ± 1.50</td><td rowspan=1 colspan=1>57.85±1.30</td><td rowspan=1 colspan=1>OMR</td><td rowspan=1 colspan=1>OMR</td><td rowspan=1 colspan=1>50.68±0.26</td><td rowspan=1 colspan=1>34.65± 0.19</td></tr><tr><td rowspan=1 colspan=1>SP</td><td rowspan=1 colspan=1>85.22± 2.43</td><td rowspan=1 colspan=1>58.24±2.44</td><td rowspan=1 colspan=1>64.11 ± 0.14</td><td rowspan=1 colspan=1>39.55± 0.22</td><td rowspan=1 colspan=1>55.60±0.22</td><td rowspan=1 colspan=1>37.99 ± 0.30</td></tr><tr><td rowspan=1 colspan=1>GK</td><td rowspan=1 colspan=1>81.66± 2.11</td><td rowspan=1 colspan=1>57.26 ± 1.41</td><td rowspan=1 colspan=1>77.34±0.18</td><td rowspan=1 colspan=1>41.01 ± 0.17</td><td rowspan=1 colspan=1>65.87±0.98</td><td rowspan=1 colspan=1>43.89±0.38</td></tr><tr><td rowspan=1 colspan=1>WL</td><td rowspan=1 colspan=1>80.72±3.00</td><td rowspan=1 colspan=1>57.97 ± 0.49</td><td rowspan=1 colspan=1>68.82 ±0.41</td><td rowspan=1 colspan=1>46.06±0.21</td><td rowspan=1 colspan=1>72.30 ± 3.44</td><td rowspan=1 colspan=1>46.95 ±0.46</td></tr><tr><td rowspan=1 colspan=1>DGK</td><td rowspan=1 colspan=1>87.44± 2.72</td><td rowspan=1 colspan=1>60.08± 2.55</td><td rowspan=1 colspan=1>78.04±0.39</td><td rowspan=1 colspan=1>41.27±0.18</td><td rowspan=1 colspan=1>66.96±0.56</td><td rowspan=1 colspan=1>44.55± 0.52</td></tr><tr><td rowspan=1 colspan=1>MLG</td><td rowspan=1 colspan=1>87.94 ± 1.61</td><td rowspan=1 colspan=1>63.26±1.48</td><td rowspan=1 colspan=1>&gt;1Day</td><td rowspan=1 colspan=1>&gt;1Day</td><td rowspan=1 colspan=1>66.55±0.25</td><td rowspan=1 colspan=1>41.17 ± 0.03</td></tr></table>
+
+<table><tr><td rowspan=1 colspan=1>node2vec</td><td rowspan=1 colspan=1>72.63±10.20</td><td rowspan=1 colspan=1>58.58±8.00</td><td rowspan=1 colspan=1>-</td><td rowspan=1 colspan=1>-</td><td rowspan=1 colspan=1>-</td><td rowspan=1 colspan=1>-</td></tr><tr><td rowspan=1 colspan=1>sub2vec</td><td rowspan=1 colspan=1>61.05± 15.80</td><td rowspan=1 colspan=1>59.99±6.38</td><td rowspan=1 colspan=1>71.48 ± 0.41</td><td rowspan=1 colspan=1>36.68± 0.42</td><td rowspan=1 colspan=1>55.26±1.54</td><td rowspan=1 colspan=1>36.67±0.83</td></tr><tr><td rowspan=1 colspan=1>graph2vec</td><td rowspan=1 colspan=1>83.15±9.25</td><td rowspan=1 colspan=1>60.17±6.86</td><td rowspan=1 colspan=1>75.78±1.03</td><td rowspan=1 colspan=1>47.86±0.26</td><td rowspan=1 colspan=1>71.1 ± 0.54</td><td rowspan=1 colspan=1>50.44±0.87</td></tr><tr><td rowspan=1 colspan=1>InfoGraph</td><td rowspan=1 colspan=1>89.01±1.13</td><td rowspan=1 colspan=1>61.65±1.43</td><td rowspan=1 colspan=1>82.50±1.42</td><td rowspan=1 colspan=1>53.46±1.03</td><td rowspan=1 colspan=1>73.03± 0.87</td><td rowspan=1 colspan=1>49.69±0.53</td></tr></table>
+
+Table 1: Classification accuracy on 6 datasets. The result in bold indicates the best reported classification accuracy. The top half of the table compares results with various graph kernel approaches while bottom half compares results with other state-of-the-art unsupervised graph representation learning methods. $ { \mathbf { \hat { \cdot } } } > 1$ day’ represents that the computation exceeds 24 hours. ‘OMR’ is out of memory error.
+
+<table><tr><td rowspan=1 colspan=1>Target</td><td rowspan=1 colspan=1>Mu (0)</td><td rowspan=1 colspan=1>Alpha（1）</td><td rowspan=1 colspan=1>HOMO(2)</td><td rowspan=1 colspan=1>LUMO(3)</td><td rowspan=1 colspan=1>Gap（4）</td><td rowspan=1 colspan=1>R2(5)</td><td rowspan=1 colspan=1>ZPVE（6）</td><td rowspan=1 colspan=1>U0（7</td><td rowspan=1 colspan=1>U(8)</td><td rowspan=1 colspan=1>H(9)</td><td rowspan=1 colspan=1>G(10)</td><td rowspan=1 colspan=1>Cv (11)</td></tr><tr><td rowspan=1 colspan=1>MAE</td><td rowspan=1 colspan=1>.3201</td><td rowspan=1 colspan=1>0.5792</td><td rowspan=1 colspan=1>0.0060</td><td rowspan=1 colspan=1>0.0062</td><td rowspan=1 colspan=1>0.0091</td><td rowspan=1 colspan=1>10.0469</td><td rowspan=1 colspan=1>0.0007</td><td rowspan=1 colspan=1>0.3204</td><td rowspan=1 colspan=1>0.2934</td><td rowspan=1 colspan=1>0.2722</td><td rowspan=1 colspan=1>0.2948</td><td rowspan=1 colspan=1>0.2368</td></tr></table>
+
+<table><tr><td rowspan=1 colspan=1>Semi-Supervised</td><td rowspan=1 colspan=12>Error Ratio</td></tr><tr><td rowspan=1 colspan=1>Mean-Teachers</td><td rowspan=1 colspan=1>1.09</td><td rowspan=1 colspan=1>1.00</td><td rowspan=1 colspan=1>0.99</td><td rowspan=1 colspan=1>1.00</td><td rowspan=1 colspan=1>0.97</td><td rowspan=1 colspan=1>0.52</td><td rowspan=1 colspan=1>0.77</td><td rowspan=1 colspan=1>1.16</td><td rowspan=1 colspan=1>0.93</td><td rowspan=1 colspan=1>0.79</td><td rowspan=1 colspan=1>0.86</td><td rowspan=1 colspan=1>0.86</td></tr><tr><td rowspan=1 colspan=1>InfoGraph</td><td rowspan=1 colspan=1>1.02</td><td rowspan=1 colspan=1>0.97</td><td rowspan=1 colspan=1>1.02</td><td rowspan=1 colspan=1>0.99</td><td rowspan=1 colspan=1>1.01</td><td rowspan=1 colspan=1>0.71</td><td rowspan=1 colspan=1>0.96</td><td rowspan=1 colspan=1>0.85</td><td rowspan=1 colspan=1>0.93</td><td rowspan=1 colspan=1>0.93</td><td rowspan=1 colspan=1>0.99</td><td rowspan=1 colspan=1>1.00</td></tr><tr><td rowspan=1 colspan=1>InfoGraph*</td><td rowspan=1 colspan=1>0.99</td><td rowspan=1 colspan=1>0.94</td><td rowspan=1 colspan=1>0.99</td><td rowspan=1 colspan=1>0.99</td><td rowspan=1 colspan=1>0.98</td><td rowspan=1 colspan=1>0.49</td><td rowspan=1 colspan=1>0.52</td><td rowspan=1 colspan=1>0.44</td><td rowspan=1 colspan=1>0.58</td><td rowspan=1 colspan=1>0.57</td><td rowspan=1 colspan=1>0.54</td><td rowspan=1 colspan=1>0.83</td></tr></table>
+
+Table 2: Results of semi-supervised experiments on QM9 dataset. The result in bold indicates the best performance. The top half of the table shows the mean absolute error (MAE) of the supervised model. The bottom half shows the error ratio (with respect to supervised result) of the semi-supervised models using the same underlying model. Lower scores are better and values less than 1.0 indicate better performance than the supervised baseline.
+
+to have mean 0 and variance 1. We minimize the mean squared error between the model output and the target, although we evaluate mean absolute error.
+
+# 4.4 MODEL CONFIGURATION
+
+For the unsupervised experiments, we use the Graph Isomorphism Network (GIN) Xu et al. (2018a). For the semi-supervised experiments, we adopt the same model as in Gilmer et al. (2017) (enn-s2s). As recommended in Oliver et al. (2018), we use the exact same underlying model architecture when comparing semi-supervised learning approaches as our goal is not to produce state-of-the-art results, but instead to provide a rigorous comparative analysis in a common framework. In both scenarios, models were trained using SGD with the Adam optimizer. We use Pytorch Paszke et al. (2017) and the Pytorch Geometric Fey & Lenssen (2019) libraries for all our experiments. For detailed hyper-parameter settings and architecture detail of the discriminator, see Appendix C.
+
+# 5 RESULTS
+
+The results of evaluating unsupervised graph level representations using downstream graph classification tasks are presented in Table 1. We show results from six methods including three state-of-the-art graph kernel methods: WL Shervashidze et al. (2011), DGK Yanardag & Vishwanathan (2015), and MLG Kondor & Pan (2016). While these kernel methods perform well on individual datasets, none of them are competitive across all of the datasets. Additionally, MLG suffers from a long run time and take more than 24 hours to run on the two larger benchmark datasets. We find that InfoGraph outperforms all of these baselines on 4 out of 6 of the datasets. In the other 2 datasets, InfoGraph still has very competitive performance.
+
+The results of the semi-supervised learning experiments on the molecular property prediction task are presented in Table 2. We observe that by simply combining the supervised objective with the unsupervised infomax objective (InfoGraph) obtains better performance compared to the purely supervised models on 7 out of 12 of the targets. However, in 1 out of 12 targets it does not obtain better performance and in 4 out of 12 targets, it results in poorer performance. This “negative transfer” effect may be caused by the fact that the supervised objective and the unsupervised objective favor different information or different latent semantic space. This effect is alleviated with InfoGraph\*, our modified version of InfoGraph for semi-supervised learning. InfoGraph\* improves over the supervised model in all the 12 targets. InfoGraph\* obtains the best result on 11 targets while the Mean Teacher method obtains the best results on 2 targets (with one overlap). However, the Mean Teacher model yields worse performance on 2 targets when compared to the supervised result.
+
+# 6 CONCLUSION AND FUTURE WORK
+
+In this paper, we propose InfoGraph to learn unsupervised graph-level representations and InfoGraph\* for semi-supervised learning. We conduct experiments on graph classification and molecular property prediction tasks to evaluate these two methods. Experimental results show that InfoGraph and InfoGraph\* are both very competitive with state-of-the-art methods. There are many research works on semi-supervised learning on image data, but few of them focus on semi-supervised learning for graph structured data. In the future, we aim to explore semi-supervised frameworks designed specifically for graphs.
+
+# ACKNOWLEDGMENTS
+
+We would like to thank Shengchao Liu and Weihua Hu for the extremely helpful discussions and comments.
+
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+
+# A RELATED WORK
+
+# A.1 GRAPH KERNELS
+
+Popular graph kernels are graphlets Pržulj (2007); Shervashidze et al. (2009), random walk and shortest path kernels Kashima et al. (2003); Borgwardt & Kriegel (2005), and the Weisfeiler-Lehman subtree kernel Shervashidze et al. (2011). Furthermore, deep graph kernels Yanardag & Vishwanathan (2015), graph invariant kernels Orsini et al. (2015), optimal assignment graph kernels Kriege et al. (2016) and multiscale Laplacian graph kernels Kondor & Pan (2016) have been proposed with the goal to redefine kernel functions to appropriately capture sub-structural similarity at different levels. Another line of research in this area focuses on efficiently computing these kernels either through exploiting certain structural dependencies, or via approximations/randomization Feragen et al. (2013); de Vries (2013); Neumann et al. (2012).
+
+# A.2 CONTRASTIVE METHODS
+
+Contrastive methods are central many popular word-embedding methods Collobert & Weston (2008); Mnih & Kavukcuoglu (2013); Mikolov et al. (2013b). Word2vec Mikolov et al. (2013a) is an unsupervised algorithm which obtains word representations by using the representations to predict context words (the words that surround it). Doc2vec Le & Mikolov (2014) is an extension of the continuous Skip-gram model that predicts representations of words from that of a document containing them. Researchers extended many of these unsupervised language models to learn representations of graph-structured input Adhikari et al. (2018); Narayanan et al. (2017). For example, graph2vec Narayanan et al. (2017) extends Doc2vec to arbitrary graphs. Intuitively, for graph2vec a graph and the rooted subgraphs in it correspond to a document and words in a paragraph vector, respectively. One of the technical contributions of the paper is using the Weisfeiler-Lehman relabelling algorithm Weisfeiler & Lehman (1968); Shervashidze et al. (2011) to enumerate all rooted subgraphs up to a specified depth. AWE (Anonymous Walk Embeddings) Ivanov & Burnaev (2018) is another method based on CBOW framework. instead of using rooted subgraphs as words like graph2vec, AWE considers anonymous walk embeddings for the same source node as co-occurring words. InfoGraph has the two advantages when compared with these methods. First, InfoGraph learns representations directly from data instead of utilizing hand-crafted procedures (i.e. Weisfeiler-Lehman relabelling algorithm in graph2vec and random walkw in AWE). Second, InfoGraph has a clear objective that can be easily combined with other objectives. For example, InfoGraph\*, the semi-supervised method that we proposed.
+
+# B SEMI-SUPERVISED LEARNING
+
+Here we discuss the most common class of SSL methods which involve adding an additional loss term to the training of a neural network as they are pragmatic and are currently the state-of-the-art on image classification datasets.
+
+Entropy Minimization (EntMin): EntMin Grandvalet & Bengio (2005) adds a loss term applied that encourages the network to make “confident” (low-entropy) predictions for all unlabeled examples, regardless of their class.
+
+Pseudo-Labeling: Pseudo-labeling Lee (2013) proceeds by producing “pseudo-labels” for unlabeled input data points using the prediction function itself over the course of training. Pseudo-labels which have a corresponding class probability that is larger than a predefined threshold are used as targets for a the standard supervised loss function.
+
+Π-Model: Neural networks can produce different outputs for the same input while common regularization techniques such as data augmentation, dropout, and adding noise are applied. Π-Model Laine & Aila (2016); Sajjadi et al. (2016) adds a loss term which encourages the distance between a network’s output for different passes of unlabeled data through the network to be small.
+
+Virtual Adversarial Training: Instead of relying on the built-in stochasticity as in Π-Model, Virtual Adversarial Training (VAT) Miyato et al. (2018) directly approximates a tiny perturbation to add to the input which would most significantly affect the output of the prediction function. This pertubation can be approximated with an extra back-propagation for each optimization step.
+
+Mean Teacher: A difficulty with the $\Pi$ -model approach is that it relies on a potentially unstable “target” prediction, namely the second stochastic network prediction which can rapidly change over the course of training. As a result, Tarvainen & Valpola (2017) proposed to obtain a more stable target output for unlabeled data by setting the target to predictions made using an exponential moving average of parameters from previous training steps.
+
+# C DATASETS
+
+# C.1 GRAPH CLASSIFICATION DATASETS
+
+MUTAG contains 188 mutagenic aromatic and heteroaromatic nitro compounds with 7 different discrete labels. PTC is a dataset of 344 different chemical compounds that have been tested for carcinogenicity in male and female rats. This dataset has 19 discrete labels. IMDB-BINARY and IMDB-MULTI are movie collaboration datasets. Each graph corresponds to an ego-network for each actor/actress, where nodes correspond to actors/actresses and an edge is drawn between two actors/actresses if they appear in the same movie. Each graph is derived from a pre-specified genre of movies, and the task is to classify the genre graph it is derived from. REDDIT-BINARY and REDDIT-MULTI5K are balanced datasets where each graph corresponds to an online discussion thread and nodes correspond to users. An edge was drawn between two nodes if at least one of them responded to another’s comment. The task is to classify each graph to the community or subreddit that it belongs to.
+
+# C.2 QM9
+
+All molecules in the dataset consist of Hydrogen (H), Carbon (C), Oxygen (O), Nitrogen $( \Nu )$ , and Flourine (F) atoms and contain up to 9 non-Hydrogen atoms. In all, this results in about 134,000 drug-like organic molecules that span a wide range of chemical compositions and properties. A total of 12 interesting and fundamental chemical properties are pre-computed for each molecule. For a detailed description of the properties in the QM9 dataset, see section 10.2 of Gilmer et al. (2017).
+
+# D MODEL CONFIGURATION
+
+For the unsupervised experiments, we use the Graph Isomorphism Network (GIN) Xu et al. (2018a). GNN layers are chosen from $\{ 4 , 8 , 1 2 \}$ . Initial learning rate is chosen from the set $\{ 1 0 ^ { - 2 } , 1 0 ^ { - 3 } , 1 0 ^ { - 4 } \}$ . The number of epochs are chosen from $\{ 1 0 , 2 0 , 1 0 0 \}$ . The batch size is set to 128.
+
+For the semi-supervised experiments, the number of set2set computations is set to 3. Model were trained with an initial learning rate 0.001 for 500 epochs with a batch size 20. For the supervised case, the weight decay is chosen from $\{ 0 , 1 0 ^ { - 3 } , 1 0 ^ { - \bar { 4 } } \}$ . For InfoGraph and InfoGraph\*, $\lambda$ is chosen from $\{ 1 0 ^ { - 3 } , \bar { 1 } 0 ^ { - 4 } , 1 \bar { 0 } ^ { - 5 } \}$ .
+
+The discriminator scores global-patch representation pairs by passing two representations to different non-linear transformations and then takes the dot product of the two transformed representations. Both non-linear transformations are parameterized by 3-layered feed-forward neural networks with jumping connections. Following each linear layer is a ReLU activation function.
+
+# E CONVERGENCE PLOT
+
+To prove that the objective Eq.8 with multiple loss terms can be optimized, we provide a convergence plot of InfoGraph\*. We can see that the three loss terms all converge after around 150 epochs of training.
+
+![](images/43a5109c64dac5e70124efbf666374231a359652e58fc08a6898f94f4a81d154.jpg)  
+Figure 3: Convergence plot of InfoGraph\* on QM9 target 7.