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+# THE PREDICTRON: END-TO-END LEARNING AND PLANNING
+
+David Silver\*, Hado van Hasselt\*, Matteo Hessel\*, Tom Schaul\*, Arthur Guez\*, Tim Harley, Gabriel Dulac-Arnold, David Reichert, Neil Rabinowitz, Andre Barreto, Thomas Degris DeepMind, London {davidsilver,hado,mtthss,schaul,aguez}@google.com
+
+# ABSTRACT
+
+One of the key challenges of artificial intelligence is to learn models that are effective in the context of planning. In this document we introduce the predictron architecture. The predictron consists of a fully abstract model, represented by a Markov reward process, that can be rolled forward multiple “imagined” planning steps. Each forward pass of the predictron accumulates internal rewards and values over multiple planning depths. The predictron is trained end-to-end so as to make these accumulated values accurately approximate the true value function. We applied the predictron to procedurally generated random mazes and a simulator for the game of pool. The predictron yielded significantly more accurate predictions than conventional deep neural network architectures.
+
+# 1 INTRODUCTION
+
+The central idea of model-based reinforcement learning is to decompose the RL problem into two subproblems: learning a model of the environment, and then planning with this model. The model is typically represented by a Markov reward process (MRP) or decision process (MDP). The planning component uses this model to evaluate and select among possible strategies. This is typically achieved by rolling forward the model to construct a value function that estimates cumulative reward. In prior work, the model is trained essentially independently of its use within the planner. As a result, the model is not well-matched with the overall objective of the agent. Prior deep reinforcement learning methods have successfully constructed models that can unroll near pixel-perfect reconstructions (Oh et al., 2015; Chiappa et al., 2016); but are yet to surpass state-of-the-art modelfree methods in challenging RL domains with raw inputs (e.g., Mnih et al., 2015; 2016; Lillicrap et al., 2016).
+
+In this paper we introduce a new architecture, which we call the predictron, that integrates learning and planning into one end-to-end training procedure. At every step, a model is applied to an internal state, to produce a next state, reward, discount, and value estimate. This model is completely abstract and its only goal is to facilitate accurate value prediction. For example, to plan effectively in a game, an agent must be able to predict the score. If our model makes accurate predictions, then an optimal plan with respect to our model will also be an optimal plan for the underlying game – even if that model uses a different state space (e.g., an abstract representation of enemy positions, ignoring their shapes and colours), action space (e.g., a high-level action to move away from an enemy), rewards (e.g., a single abstract step could have a higher value than any real reward), or even timestep (e.g., a single abstract step could “jump” the agent to the end of a corridor). All we require is that trajectories through the abstract model produce scores that are consistent with trajectories through the real environment. This is achieved by training the predictron end-to-end, so as to make its value estimates as accurate as possible.
+
+An ideal model could generalise to many different prediction tasks, rather than overfitting to a single task; and could learn from a rich variety of feedback signals, not just a single extrinsic reward. We therefore train the predictron to predict a host of different value functions for a variety of pseudoreward functions and discount factors. These pseudo-rewards can encode any event or aspect of the environment that the agent may care about, e.g., staying alive or reaching the next room.
+
+We focus upon the prediction task: estimating value functions in MRP environments with uncontrolled dynamics. In this case, the predictron can be implemented as a deep neural network with an
+
+MRP as a recurrent core. The predictron unrolls this core multiple steps and accumulates rewards into an overall estimate of value.
+
+We applied the predictron to procedurally generated random mazes, and a simulated pool domain, directly from pixel inputs. In both cases, the predictron significantly outperformed model-free algorithms with conventional deep network architectures; and was much more robust to architectural choices such as depth.
+
+# 2 BACKGROUND
+
+We consider environments defined by an MRP with states $s \in S$ . The MRP is defined by a function, $s ^ { \prime } , r , \gamma = p ( s , \alpha )$ , where $s ^ { \prime }$ is the next state, $r$ is the reward, and $\gamma$ is the discount factor, which can for instance represent the non-termination probability for this transition. The process may be stochastic, given IID noise $\alpha$ .
+
+The return of an MRP is the cumulative discounted reward over a single trajectory, $g _ { t } = r _ { t + 1 } +$ $\gamma _ { t + 1 } r _ { t + 2 } + \gamma _ { t + 1 } \gamma _ { t + 2 } r _ { t + 3 } + \ldots ,$ , where $\gamma _ { t }$ can vary per time-step. We consider a generalisation of the MRP setting that includes vector-valued rewards $\mathbf { r }$ , diagonal-matrix discounts $\gamma$ , and vector-valued returns $\mathbf { g }$ ; definitions are otherwise identical to the above. We use this bold font notation to closely match the more familiar scalar MRP case; the majority of the paper can be comfortably understood by reading all rewards as scalars, and all discount factors as scalar and constant, i.e., $\gamma _ { t } = \gamma$ .
+
+The value function of an MRP $p$ is the expected return from state $s$ , $v _ { p } ( s ) = \mathbb { E } _ { p } \left[ \mathbf { g } _ { t } \mid s _ { t } = s \right]$ . In the vector case, these are known as general value functions (Sutton et al., 2011). We will say that a (general) value function $v ( \cdot )$ is consistent with environment $p$ if and only if $v = v _ { p }$ which satisfies the following Bellman equation (Bellman, 1957),
+
+$$
+v _ { p } ( s ) = \mathbb { E } _ { p } \left[ \mathbf { r } + \gamma v _ { p } ( s ^ { \prime } ) \mid s \right] .
+$$
+
+In model-based reinforcement learning (Sutton and Barto, 1998), an approximation $m \approx p$ to the environment is learned. In the uncontrolled setting this model is normally an MRP $s ^ { \prime } , \mathbf { r } , \gamma = m ( s , \beta )$ that maps from state $s$ to subsequent state $s ^ { \prime }$ and additionally outputs rewards $\mathbf { r }$ and discounts $\gamma$ ; the model may be stochastic given an IID source of noise $\beta$ . A (general) value function $v _ { m } ( \cdot )$ is consistent with model $m$ (or valid, (Sutton, 1995)), if and only if it satisfies a Bellman equation $v _ { m } ( s ) = \mathbb { E } _ { m } \left[ \mathbf { r } + \gamma v _ { m } ( s ^ { \prime } ) \mid s \right]$ with respect to model $m$ . Conventionally, model-based RL methods focus on finding a value function $v$ that is consistent with a separately learned model $m$ .
+
+# 3 PREDICTRON ARCHITECTURE
+
+The predictron is composed of four main components. First, a state representation $\mathbf { s } = f ( s )$ that encodes raw input $s$ (this could be a history of observations, in the partially observed setting, for example when $f$ is a recurrent network) into an internal (abstract, hidden) state s. Second, a model $\mathbf { s } ^ { \prime } , \mathbf { r } , \gamma = m ( \mathbf { s } , \beta )$ that maps from internal state s to subsequent internal state $\mathbf { s } ^ { \prime }$ , internal rewards $\mathbf { r }$ , and internal discounts $\gamma$ . Third, a value function $v$ that outputs internal values $\mathbf { v } = v ( \mathbf { s } )$ representing the future, internal return from internal state s onwards. The predictron is applied by unrolling its model $m$ multiple “planning” steps to produce internal rewards, discounts and values. We use superscripts $\bullet ^ { k }$ to indicate internal steps of the model (which have no necessary connection to time steps $\bullet _ { t }$ of the environment). Finally, these internal rewards, discounts and values are combined together by an accumulator into an overall estimate of value g. The whole predictron, from input state $s$ to output g, may be viewed as a value function approximator for external targets (i.e. the returns in the real environment). We consider both $k$ -step and $\lambda$ -weighted accumulators.
+
+The $k$ -step predictron rolls its internal model forward $k$ steps. Specifically, the $k$ -step predictron return $\mathbf { g } ^ { k }$ (henceforth abbreviated as preturn) is the internal return obtained by accumulating $k$ model steps, plus a final value $\mathbf { v } ^ { k }$ from the $k$ th step,
+
+$$
+\mathbf { g } ^ { k } = \mathbf { r } ^ { 1 } + \gamma ^ { 1 } ( \mathbf { r } ^ { 2 } + \gamma ^ { 2 } ( \ldots ( \mathbf { r } ^ { k - 1 } + \gamma ^ { k - 1 } ( \mathbf { r } ^ { k } + \gamma ^ { k } \mathbf { v } ^ { k } ) ) \ldots ) ) .
+$$
+
+The 0-step preturn is simply the first value $\mathbf { g } ^ { 0 } = \mathbf { v } ^ { 0 }$ . The 1-step preturn is $\mathbf { g } ^ { 1 } = \mathbf { r } ^ { 1 } + \gamma ^ { 1 } \mathbf { v } ^ { 1 }$ , and so on (see Fig. 1a).
+
+The $\lambda$ -predictron combines together many $k$ -step preturns. Specifically, it computes a diagonal weight matrix $\lambda ^ { k }$ from each internal state $\boldsymbol { \bar { s } } ^ { k }$ . The accumulator uses weights $\lambda ^ { 0 } , . . . , \lambda ^ { K }$ to aggregate
+
+![](images/6f6c0ac1ea5dd3b78bbf370494686c721ff710971f39d404ac4fa8e2eec69c6a.jpg)  
+Figure 1: a) The $k$ -step predictron architecture. The first three columns illustrate 0, 1 and 2-step pathways through the predictron. The 0-step preturn reduces to standard model-free value function approximation; other preturns “imagine” additional steps with an internal model. Each pathway outputs a $k \mathrm { . }$ -step preturn $\mathbf { g } ^ { k }$ that accumulates discounted rewards along with a final value estimate. In practice all $k$ -step preturns are computed in a single forward pass. b) The $\lambda$ -predictron architecture. The $\lambda$ -parameters gate between the different preturns. The output is a $\lambda$ -preturn $\mathbf { g } ^ { \lambda }$ that is a mixture over the $k$ -step preturns. For example, if $\pmb { \lambda } ^ { 0 } = \mathbf { 1 } , \pmb { \lambda } ^ { 1 } = \mathbf { 1 } , \pmb { \lambda } ^ { 2 } = \mathbf { 0 }$ then we recover the 2-step preturn, $\mathbf { g } ^ { \lambda } = \mathbf { g } ^ { 2 }$ . Discount factors $\gamma ^ { k }$ and $\lambda$ -parameters $\lambda ^ { k }$ are dependent on state $\mathbf { s } ^ { k }$ ; this dependence is not shown in the figure.
+
+over $k$ -step preturns $\mathbf { g } ^ { 0 } , . . . , \mathbf { g } ^ { K }$ and output a combined value that we call the $\lambda$ -preturn $\mathbf { g } ^ { \lambda }$ ,
+
+$$
+\mathbf { g } ^ { \lambda } = \sum _ { k = 0 } ^ { K } w ^ { k } \mathbf { g } ^ { k } \qquad \mathrm { w h e r e } \qquad w ^ { k } = \left\{ \begin{array} { l l } { ( 1 - \lambda ^ { k } ) \prod _ { j = 0 } ^ { k - 1 } \lambda ^ { j } } & { \mathrm { i f ~ } k < K } \\ { \qquad } \\ { \prod _ { j = 0 } ^ { K - 1 } \lambda ^ { j } } & { \mathrm { o t h e r w i s e . } } \end{array} \right.
+$$
+
+where 1 is the identity matrix. This $\lambda$ -preturn is analogous to the $\lambda$ -return in the forward-view $\mathrm { T D } ( \lambda )$ algorithm (Sutton, 1988; Sutton and Barto, 1998). It may also be computed by a backward accumulation through intermediate steps $\mathbf { g } ^ { k , \lambda }$ ,
+
+$$
+\mathbf { g } ^ { k , \lambda } = ( \mathbf { 1 } - \lambda ^ { k } ) \mathbf { v } ^ { k } + \lambda ^ { k } \left( \mathbf { r } ^ { k + 1 } + \gamma ^ { k + 1 } \mathbf { g } ^ { k + 1 , \lambda } \right) ,
+$$
+
+where $\mathbf { g } ^ { K , \lambda } = \mathbf { v } ^ { K }$ , and then using $\mathbf { g } ^ { \lambda } = \mathbf { g } ^ { 0 , \lambda }$ . Computation in the $\lambda$ -predictron operates in a sweep, iterating first through the model from $k = 0 \ldots K$ and then back through the accumulator from $k = K \ldots 0$ in a single “forward” pass of the network (see Figure 1b). Each $\lambda ^ { k }$ weight acts as a gate on the computation of the $\lambda$ -preturn: a value of $\lambda ^ { k } = 0$ will truncate the $\lambda$ -preturn at layer $k$ , while a value of $\mathbf { \hat { \lambda } } \mathbf { \lambda } ^ { k } = \mathbf { 1 }$ will utilise deeper layers based on additional steps of the model $m$ ; the final weight is always $\pmb { \lambda } ^ { K } = \mathbf { 0 }$ . The individual $\dot { \lambda } ^ { k }$ weights may depend on the corresponding abstract state $\mathbf { s } ^ { k }$ and can differ per prediction. This enables the predictron to compute to an adaptive depth (Graves, 2016) depending on the internal state and learning dynamics of the network.
+
+# 4 PREDICTRON LEARNING UPDATES
+
+We first consider updates that optimise the joint parameters $\pmb { \theta }$ of the state representation, model, and value function. We begin with the $k$ -step predictron. We update the $k$ -step predictron $\mathbf { g } ^ { k }$ towards a target outcome $\mathbf { g }$ , such as the Monte-Carlo return from the real environment, by minimising a mean-squared error loss,
+
+$$
+L ^ { k } = { \frac { 1 } { 2 } } \left\| \mathbb { E } _ { p } \left[ \mathbf { g } \mid s \right] - \mathbb { E } _ { m } \left[ \mathbf { g } ^ { k } \mid s \right] \right\| ^ { 2 } . \qquad { \frac { \partial l ^ { k } } { \partial \theta } } = \left( \mathbf { g } - \mathbf { g } ^ { k } \right) { \frac { \partial \mathbf { g } ^ { k } } { \partial \theta } } .
+$$
+
+where $l ^ { k } = \textstyle { \frac { 1 } { 2 } } \left\| \mathbf { g } - \mathbf { g } ^ { k } \right\| ^ { 2 }$ is the sample loss. We can use the gradient of the sample loss to update parameters, e.g. by stochastic gradient descent. For stochastic models, two independent samples are required for $\mathbf { g } ^ { k }$ and ∂ g k to get unbiased samples for the gradient of $L ^ { k }$ .
+
+The $\lambda$ -predictron combines together many $k$ -step preturns. To update the joint parameters $\pmb \theta$ , we can uniformly average the losses on the individual preturns $\mathbf { g } ^ { k }$ ,
+
+$$
+L ^ { 0 : K } = \frac { 1 } { 2 K } \sum _ { k = 0 } ^ { K } \left\| \mathbb { E } _ { p } \left[ \mathbf { g } \mid s \right] - \mathbb { E } _ { m } \left[ \mathbf { g } ^ { k } \mid s \right] \right\| ^ { 2 } , \qquad \frac { \partial l ^ { 0 : K } } { \partial \theta } = \frac { 1 } { K } \sum _ { k = 0 } ^ { K } \left( \mathbf { g } - \mathbf { g } ^ { k } \right) \frac { \partial \mathbf { g } ^ { k } } { \partial \theta } .
+$$
+
+Alternative, we could weight each loss by the usage $\boldsymbol { w } ^ { k }$ of the corresponding preturn, such that the gradient is $\begin{array} { r } { \sum _ { k = 0 } ^ { K } \pmb { w } ^ { k } \left( \mathbf { g } - \mathbf { g } ^ { k } \right) \frac { \partial \mathbf { g } ^ { k } } { \partial \pmb { \theta } } } \end{array}$ 
 ∂ g k∂ θ .
+
+The $\lambda$ -predictron uses an accumulator with additional parameters $\eta$ that determine the relative weighting of the $k$ -step preturns. These weights are also updated so as to minimise a mean-squared error loss $L ^ { \lambda }$ ,
+
+$$
+L ^ { \lambda } = \frac { 1 } { 2 } \left\| \mathbb { E } _ { p } \left[ \mathbf { g } \mid s \right] - \mathbb { E } _ { m } \left[ \mathbf { g } ^ { \lambda } \mid s \right] \right\| ^ { 2 } , \qquad \frac { \partial l ^ { \lambda } } { \partial \eta } = \left( \mathbf { g } - \mathbf { g } ^ { \lambda } \right) \frac { \partial \mathbf { g } ^ { \lambda } } { \partial \eta } .
+$$
+
+In summary, the joint parameters $\pmb \theta$ of the state representation $f$ , the model $m$ , and the value function $v$ are updated to make each of the $k$ -step preturns $\mathbf { g } ^ { k }$ more similar to the target $\mathbf { g }$ , and the parameters $\eta$ of the $\lambda$ -accumulator are updated to make the aggregate $\lambda$ -preturn $\mathbf { g } ^ { \lambda }$ more similar to the target g.
+
+# 4.1 CONSISTENCY (SEMI-SUPERVISED) LEARNING WITH THE $\lambda$ -PREDICTRON
+
+Ideally, the predictron $( f , m , v )$ learns preturns that are all equal in expectation to the true value function of the environment, $\mathbb { E } _ { m } \left[ \mathbf { g } ^ { k } \mid s \right] = \mathbb { E } _ { p } \left[ \mathbf { g } _ { t } \mid s \right] = v _ { p } ( s )$ , in which case the preturns must be equal in expectation, $\mathbb { E } _ { m } \left[ \mathbf { g } ^ { 0 } \mid s \right] = \mathbb { E } _ { m } \left[ \mathbf { g } ^ { 1 } \mid s \right] = \ldots = \mathbb { E } _ { m } \left[ \mathbf { g } ^ { K } \mid s \right]$ . In addition, each $k$ -step preturn must then be equal in expectation to th $: \lambda - p$ return, $\mathbb { E } _ { m } \left[ \mathbf { \bar { g } } ^ { k } \mid s \right] \mathbf { \bar { \Lambda } } = \mathbb { E } _ { m } \left[ \mathbf { g } ^ { \lambda } \mid s \right]$ , for any $\lambda$ parameters. All these consistency relations between preturns give rise to additional constraints upon the predictron. Specifically, we may adjust the parameters of the predictron to lead to consistent preturns, even in the absence of labelled targets.
+
+Concretely, we can adjust each preturn $\mathbf { g } ^ { k }$ towards the $\lambda$ -preturn $\mathbf { g } ^ { \lambda }$ ; in other words, we can update each individual value estimate towards the best aggregated estimate by minimizing
+
+$$
+L = \frac { 1 } { 2 } \sum _ { k = 0 } ^ { K } \left\| \mathbb { E } _ { m } \left[ \mathbf { g } ^ { \lambda } \mid s \right] - \mathbb { E } _ { m } \left[ \mathbf { g } ^ { k } \mid s \right] \right\| ^ { 2 } , \qquad \quad \quad \frac { \partial l } { \partial \theta } = \sum _ { k = 0 } ^ { K } \left( \mathbf { g } ^ { \lambda } - \mathbf { g } ^ { k } \right) \frac { \partial \mathbf { g } ^ { k } } { \partial \theta } .
+$$
+
+Here $\mathbf { g } ^ { \lambda }$ is considered fixed; the parameters $\pmb \theta$ are only updated to make $\mathbf { g } ^ { k }$ more similar to $\mathbf { g } ^ { \lambda }$ , not vice versa. This consistency update does not require any labels $\mathbf { g }$ or samples from the environment. As a result, it can be applied to (potentially hypothetical) states that have no associated ‘real’ (e.g. Monte-Carlo) outcome: we update the value estimates to be self-consistent with each other. Note the similarity with the semi-supervised setting, where we may have unlabelled inputs.
+
+# 5 EXPERIMENTS
+
+We conducted experiments on two domains. The first domain consists of randomly generated $2 0 \times 2 0$ mazes in which each location either is empty or contains a wall. Two locations in a maze are considered connected if they are both empty and we can reach one from the other by moving horizontally or vertically through adjacent empty cells. The goal is to predict, for each of the locations on the diagonal from top-left to bottom-right of the maze, whether the bottom-right corner is connected to that location, given the entire maze as an input image. Some of these predictions will be straightforward, for instance for locations on the diagonal that contain a wall themselves and for locations close to the bottom right. Many other predictive questions seem to require a simple algorithm, such as some form of a flood fill or search; our hypothesis is that an internal model can learn to emulate such algorithms, where naive approximation may struggle. A few example mazes are shown in Figure 2.
+
+Our second domain is a simulation of the game of pool, using four balls and four pockets. The simulator is implemented in the physics engine Mujoco (Todorov et al., 2012). We generate sequences of RGB frames starting from a random arrangement of balls on the table. The goal is to simultaneously learn to predict future events for each of the four balls, given 5 RGB frames as input. These events include: collision with any other ball, collision with any boundary of the table, entering a quadrant $\times 4$ , for each quadrant), being located in a quadrant $\times 4$ , for each quadrant), and entering a pocket $( \times 4$ , for each pocket). Each of these $1 4 \times 4$ events provides a binary pseudo-reward that we combine with 5 different discount factors $\{ 0 , 0 . 5 , 0 . 9 , 0 . 9 8 , 1 \}$ and predict their cumulative discounted sum over various time spans. This yields a total of 280 general value functions. An example trajectory is shown in Figure 2. In both domains, inputs are presented as minibatches of i.i.d. samples with their regression targets. Additional domain details are provided in Appendix E.
+
+![](images/8a31c76eabf685b5e20aa0765cb76bf5f66494f925957476c5705091f578ef29.jpg)  
+Figure 2: Left: Two sample mazes from the random-maze domain. Light blue cells are empty, darker blue cells contain a wall. One maze is connected from top-left to bottom-right (indicated in black), the other is not. Right: An example trajectory in the pool domain (before downsampling). It was selected by maximising the prediction of pocketing balls, using the predictron.
+
+![](images/e602264f049e19e6be76364d251d62f7e9f44ac88523eb8c4214db23eff3de07.jpg)  
+Figure 3: Exploring predictron variants. Aggregated prediction errors over all predictions (20 for mazes, 280 for pool) for the eight predictron variants corresponding to the cube on the left (as described in the main text), for both random mazes (top) and pool (bottom). Each line is the median of RMSE over five seeds; shaded regions encompass all seeds. The full $( r , \gamma , \lambda )$ -prediction (red) consistently performed best.
+
+# 5.1 EXPLORING THE PREDICTRON ARCHITECTURE
+
+Our first set of experiments examines three binary dimensions that differentiate the predictron from standard deep networks. We compare eight predictron variants corresponding to the corners of the cube on the left in Figure 3.
+
+The first dimension corresponds to whether or not the predictron architecture utilises the structure of an MRP model. In the MRP case, labelled $r , \gamma$ , internal rewards and discounts are both learned. In the non- $r$ , $\gamma$ case, which corresponds to a vanilla hidden-to-hidden neural network module, internal rewards and discounts are ignored by fixing their values to $\mathbf { r } ^ { k } = \mathbf { 0 }$ and $\gamma ^ { k } = \mathbf { 1 }$ .
+
+The second dimension is whether a $K$ -step accumulator or $\lambda$ -accumulator is used to aggregate over preturns. When a $\lambda$ -accumulator is used, a $\lambda$ -preturn is computed as described in Section 3. Otherwise, intermediate preturns are ignored by fixing their values to $\lambda ^ { k } = 1$ for $k < K$ . In this case, the overall output of the predictron is simply the maximum-depth preturn $\mathbf { g } ^ { K }$ .
+
+The third dimension, labelled usage weighting, defines the loss that is used to update the parameters $\pmb \theta$ . On this dimension, we consider two options: the preturn losses can either be weighted uniformly (see Equation 6), or the update for each preturn $\mathbf { g } ^ { k }$ can be weighted according to the weight $\boldsymbol { w } ^ { k }$ that determines how much it is used in the $\lambda$ -predictron’s overall output. We call the latter loss ‘usage weighted‘. Note that for architectures without a $\lambda$ -accumulator, $\bar { \boldsymbol { w } } ^ { k } = 0$ for $k < K$ , and $\mathbf { \Delta } w ^ { K } = \mathbf { \bar { \mu } }$ , thus usage weighting then implies backpropagating only the loss on the final preturn $\mathbf { g } ^ { K }$ .
+
+All variants utilise a convolutional core with 2 intermediate hidden layers (see Appendix A); parameters were updated by supervised learning (see Appendix $\mathbf { B }$ for more details). Root mean squared prediction errors for each architecture, aggregated over all predictions, are shown in Figure 3. The top row corresponds to the random mazes and the bottom row to the pool domain. The main conclusion is that learning an MRP model improved performance greatly. The inclusion of $\lambda$ weights helped as well, especially on pool. Usage weighting further improved performance.
+
+![](images/dba61ef00d493777d067bc381985a11c743383fcb9df81dc1d0a496239d6428e.jpg)  
+Figure 4: Comparing predictron to baselines. Aggregated prediction errors on random mazes (top) and pool (bottom) over all predictions for the eight architectures corresponding to the cube on the left. Each line is the median of RMSE over five seeds; shaded regions encompass all seeds. The full $( r , \gamma , \lambda )$ -predictron (red), consistently outperformed conventional deep network architectures (black), with and without skips and with and without weight sharing.
+
+# 5.2 COMPARING THE PREDICTRON TO OTHER DEEP NETWORKS
+
+Our second set of experiments compares the predictron to feedforward and recurrent deep learning architectures, with and without skip connections. We compare the corners of a new cube, as depicted on the left in Figure 4, based on three different binary dimensions.
+
+The first dimension of this second cube is whether we use a predictron, or a (non- $\boldsymbol { \cdot } \lambda$ , non- $\cdot r , \gamma$ ) deep network that does not have an internal model and does not output or learn from intermediate predictions. We use the most effective predictron from the previous section, i.e., the $( r , \gamma , \lambda )$ -predictron with usage weighting.
+
+The second dimension is whether weights are shared between all cores (as in a recurrent network), or whether each core uses separate weights (as in a feedforward network). We note that the non$\lambda$ , non- $\cdot r , \gamma$ variants of the predictron then correspond to standard (convolutional) feedforward and (unrolled) recurrent neural networks respectively.
+
+The third dimension is whether we include skip connections. This is equivalent to defining the model step to output a change to the current state, $\Delta \mathbf { s } .$ , and then defining $\mathbf { s } ^ { \hat { k } + 1 } = h ( \mathbf { s } ^ { k } + \Delta \mathbf { s } ^ { \tilde { k } } )$ , where $h$ is the non-linear function—in our case a ReLU, $h ( x ) = \operatorname* { m a x } ( \bar { 0 , x } )$ . The deep network with skip connections is a variant of ResNet (He et al., 2015).
+
+Root mean squared prediction errors for each architecture are shown in Figure 4. All $( r , \gamma , \lambda )$ - predictrons (red lines) outperformed the corresponding feedforward or recurrent neural network baselines (black lines) both in the random mazes and in pool. We also investigated the effect of changing the depth of the networks (see Appendix C). The predictron outperformed the corresponding feedforward or recurrent baselines for all depths, with and without skip connections.
+
+# 5.3 SEMI-SUPERVISED LEARNING BY CONSISTENCY
+
+We now consider how to use the predictron for semi-supervised learning, training the model on a combination of labelled and unlabelled random mazes. Semi-supervised learning is important because a common bottleneck in applying machine learning in the real world is the difficulty of collecting labelled data, whereas often large quantities of unlabelled data exist.
+
+We trained a full $( r , \gamma , \lambda )$ -predictron by alternating standard supervised updates with consistency updates, obtained by stochastically minimizing the consistency loss (8), on the unlabelled samples. For each supervised update we apply either 0, 1, or 9 consistency updates. Figure 5 shows that the performance improved monotonically with the number of consistency updates, measured as a function of the number of labelled samples consumed.
+
+![](images/a6a297ad344d3d9b89961b40f0a239cf9bf15e8964e2525c883b866251e3e396.jpg)  
+Figure 5: Semi-supervised learning. Prediction errors of the $( r , \gamma , \lambda )$ -predictrons (shared core, no skips) using 0, 1, or 9 consistency updates for every update with labelled data, plotted as function of the number of labels consumed. Learning performance improves with more consistency updates.
+
+# 5.4 ANALYSIS OF ADAPTIVE DEPTH
+
+In principle, the predictron can adapt its depth to ‘think more’ about some predictions than others, perhaps depending on the complexity of the underlying target. We investigate this by looking at qualitatively different prediction types in pool: ball collisions, rail collisions, pocketing balls, and entering or staying in quadrants. For each prediction type we consider several different time-spans (determined by the real-world discount factors associated with each pseudo-reward). Figure 6 shows distributions of depth for each type of prediction. The ‘depth’ of a predictron is here defined as the effective number of model steps. If the predictron relies fully on the very first value (i.e., $\lambda ^ { 0 } = 0$ ), this counts as 0 steps. If, instead, it learns to place equal weight on all rewards and on the final value, this counts as 16 steps. Concretely, the depth $^ d$ can be defined recursively as $\pmb { d } = \pmb { d } ^ { 0 }$ where $\pmb { d } ^ { k } = \lambda ^ { k } ( 1 + \gamma ^ { k } \pmb { d } ^ { k + 1 } )$ and $\mathbf { { \mathbf { { \mathbf { { \mathbf { { \mathbf { \alpha } } } } } } } } } \mathbf { { \mathbf { { \mathbf { { d } } } } } } ^ { K } = \mathbf { { \mathbf { 0 } } }$ . Note that even for the same input state, each prediction has a separate depth.
+
+The depth distributions exhibit three properties. First, different types of predictions used different depths. Second, depth was correlated with the real-world discount for the first four prediction types. Third, the distributions are not strongly peaked, which implies that the depth can differ per input even for a single real-world discount and prediction type. In a control experiment (not shown) we used a scalar $\lambda$ shared among all predictions, which reduced performance in all scenarios, indicating that the heterogeneous depth is a valuable form of flexibility.
+
+# 5.5 VISUALIZING THE PREDICTIONS IN THE POOL DOMAIN
+
+We test the quality of the predictions in the pool domain to evaluate whether they are well-suited to making decisions. For each sampled pool position, we consider a set $I$ of different initial conditions (different angles and velocity of the white ball), and ask which is more likely to lead to pocketing coloured balls. For each initial condition $s \in I$ , we apply the $( r , \gamma , \lambda )$ -predictron (shared cores, 16 model steps, no skip connections) to obtain predictions $\mathbf { g } ^ { \lambda }$ . We sum the predictions that correspond to pocketing any ball except the white ball, and to real-world discounts $\gamma = 0 . 9 8$ and $\gamma = 1$ . We select the condition $s ^ { * }$ that maximises this sum.
+
+![](images/9e5eda1ba0817010e3a899cfcd39b4555fece7632765839f1302bb06efcfea60.jpg)  
+Figure 6: Thinking depth. Distributions of thinking depth on pool for different types of predictions and for different real-world discounts.
+
+We then roll forward the pool simulator from $s ^ { * }$ and log the number of pocketing events. Figure 2 shows a sampled rollout, using the predictron to pick $s ^ { * }$ . When providing the choice of 128 angles and two velocities for initial conditions $\left. \vert I \right. = 2 5 6 )$ , this procedure resulted in pocketing 27 coloured balls in 50 episodes. Using the same procedure with an equally deep convolutional network only resulted in 10 pocketing events. These results suggest that the lower loss of the learned $( r , \gamma , \lambda )$ -predictron translated into meaningful improvements when informing decisions. A video of the rollouts selected by the predictron is available here: https://youtu.be/BeaLdaN2C3Q.
+
+# 6 RELATED WORK
+
+Lee et al. (2015) introduced a neural network architecture where classifications branch off intermediate hidden layers. An important difference with respect to the $\lambda$ -predictron, is that the weights are hand-tuned as hyper-parameters, whereas in the predictron the $\lambda$ weights are learnt and, more importantly, conditional on the input. Another difference is that the loss on the auxiliary classifications is used to speed up learning, but the classifications themselves are not combined into an aggregate prediction; the output of the model itself is the deepest prediction.
+
+Graves (2016) introduced an architecture with adaptive computation time (ACT), with a discrete (but differentiable) decision on when to halt, and aggregating over the outputs at each pondering step. This is related to our $\lambda$ weights, but obtains depth in a different way; one notable difference is that the $\lambda$ -predictron can choose different pondering depths for each of its predictions.
+
+Value iteration networks (VINs) (Tamar et al., 2016) also learn value functions end-to-end using an internal model, similar to the (non- $\lambda$ ) predictron. However, VINs plan via convolutional operations over the full input state space; whereas the predictron plans via imagined trajectories through an abstract state space. This may allow the predictron architecture to scale much more effectively in domains that do not have a natural two-dimensional encoding of the state space.
+
+The notion of learning about many predictions of the future relates to work on predictive state representations (PSRs; Littman et al., 2001), general value functions (GVFs; Sutton et al., 2011), and nexting (Modayil et al., 2012). Such predictions have been shown to be useful as representations (Schaul and Ring, 2013) and for transfer (Schaul et al., 2015). So far, however, none of these have been considered for learning abstract models.
+
+Schmidhuber (2015) discusses learning abstract models, but maintains separate losses for the model and a controller, and suggests training the model unsupervised to compactly encode the entire history of observations, through predictive coding. The predictron’s abstract model is instead trained endto-end to obtain accurate values.
+
+# 7 CONCLUSION
+
+The predictron is a single differentiable architecture that rolls forward an internal model to estimate external values. This internal model may be given both the structure and the semantics of traditional reinforcement learning models. But unlike most approaches to model-based reinforcement learning, the model is fully abstract: it need not correspond to the real environment in any human understandable fashion, so long as its rolled-forward “plans” accurately predict outcomes in the true environment.
+
+The predictron may be viewed as a novel network architecture that incorporates several separable ideas. First, the predictron outputs a value by accumulating rewards over a series of internal planning steps. Second, each forward pass of the predictron outputs values at multiple planning depths. Third, these values may be combined together, also within a single forward pass, to output an overall ensemble value. Finally, the different values output by the predictron may be encouraged to be self-consistent with each other, to provide an additional signal during learning. Our experiments demonstrate that these differences result in more accurate predictions of value, in reinforcement learning environments, than more conventional network architectures.
+
+We have focused on value prediction tasks in uncontrolled environments. However, these ideas may transfer to the control setting, for example by using the predictron as a Q-network (Mnih et al., 2015). Even more intriguing is the possibility of learning an internal MDP with abstract internal actions, rather than the MRP considered in this paper. We aim to explore these ideas in future work.
+
+# REFERENCES
+
+R. Bellman. Dynamic programming. Princeton University Press, 1957.
+
+S. Chiappa, S. Racaniere, D. Wierstra, and S. Mohamed. Recurrent environment simulators. 2016.
+
+X. Glorot, A. Bordes, and Y. Bengio. Deep sparse rectifier neural networks. In Aistats, volume 15, page 275, 2011.
+
+A. Graves. Adaptive computation time for recurrent neural networks. CoRR, abs/1603.08983, 2016. URL http://arxiv.org/abs/1603.08983.
+
+K. He, X. Zhang, S. Ren, and J. Sun. Deep residual learning for image recognition. arXiv preprint arXiv:1512.03385, 2015.
+
+S. Ioffe and C. Szegedy. Batch normalization: Accelerating deep network training by reducing internal covariate shift. arXiv preprint arXiv:1502.03167, 2015.
+
+D. P. Kingma and J. Ba. A method for stochastic optimization. In International Conference on Learning Representation, 2015.
+
+Y. LeCun, L. Bottou, Y. Bengio, and P. Haffner. Gradient-based learning applied to document recognition. Proceedings of the IEEE, 86(11):2278–2324, 1998.
+
+C.-Y. Lee, S. Xie, P. Gallagher, Z. Zhang, and Z. Tu. Deeply-supervised nets. In AISTATS, volume 2, page 6, 2015.
+
+T. Lillicrap, J. Hunt, A. Pritzel, N. Heess, T. Erez, Y. Tassa, D. Silver, and D. Wierstra. Continuous control with deep reinforcement learning. In ICLR, 2016.
+
+M. L. Littman, R. S. Sutton, and S. P. Singh. Predictive representations of state. In NIPS, volume 14, pages 1555–1561, 2001.
+
+V. Mnih, K. Kavukcuoglu, D. Silver, A. A. Rusu, J. Veness, M. G. Bellemare, A. Graves, M. Riedmiller, A. K. Fidjeland, G. Ostrovski, S. Petersen, C. Beattie, A. Sadik, I. Antonoglou, H. King, D. Kumaran, D. Wierstra, S. Legg, and D. Hassabis. Human-level control through deep reinforcement learning. Nature, 518(7540):529–533, 2015.
+
+V. Mnih, A. P. Badia, M. Mirza, A. Graves, T. Lillicrap, T. Harley, D. Silver, and K. Kavukcuoglu. Asynchronous methods for deep reinforcement learning. In International Conference on Machine Learning, 2016.
+
+J. Modayil, A. White, and R. S. Sutton. Multi-timescale nexting in a reinforcement learning robot. In International Conference on Simulation of Adaptive Behavior, pages 299–309. Springer, 2012.
+
+J. Oh, X. Guo, H. Lee, R. L. Lewis, and S. Singh. Action-conditional video prediction using deep networks in atari games. In Advances in Neural Information Processing Systems, pages 2863– 2871, 2015.
+
+T. Schaul and M. B. Ring. Better Generalization with Forecasts. In Proceedings of the International Joint Conference on Artificial Intelligence (IJCAI), Beijing, China, 2013.
+
+T. Schaul, D. Horgan, K. Gregor, and D. Silver. Universal Value Function Approximators. In International Conference on Machine Learning (ICML), 2015.
+
+J. Schmidhuber. On learning to think: Algorithmic information theory for novel combinations of reinforcement learning controllers and recurrent neural world models. arXiv preprint arXiv:1511.09249, 2015.
+
+R. S. Sutton. Learning to predict by the methods of temporal differences. Machine Learning, 3: 9–44, 1988.
+
+R. S. Sutton. TD models: Modeling the world at a mixture of time scales. In Proceedings of the Twelfth International Conference on Machine Learning, pages 531–539, 1995.
+
+R. S. Sutton and A. G. Barto. Reinforcement Learning: An Introduction. The MIT press, Cambridge MA, 1998.
+
+R. S. Sutton, J. Modayil, M. Delp, T. Degris, P. M. Pilarski, A. White, and D. Precup. Horde: A scalable real-time architecture for learning knowledge from unsupervised sensorimotor interaction. In The 10th International Conference on Autonomous Agents and Multiagent Systems-Volume 2, pages 761–768. International Foundation for Autonomous Agents and Multiagent Systems, 2011.
+
+A. Tamar, Y. Wu, G. Thomas, S. Levine, and P. Abbeel. Value iteration networks. In Neural Information Processing Systems (NIPS), 2016.
+
+E. Todorov, T. Erez, and Y. Tassa. Mujoco: A physics engine for model-based control. In 2012 IEEE/RSJ International Conference on Intelligent Robots and Systems, pages 5026–5033. IEEE, 2012.
+
+![](images/470c195ad3d74763aaa60fca5f7047608345478b942bb4154c2bfe8bc163ff2a.jpg)  
+Figure 7: The predictron core used in our experiments.
+
+# A ARCHITECTURE
+
+The state representation $f$ is a two-layer convolutional neural network (LeCun et al., 1998). There is a core $c$ , again based on convolutions, that combines both MRP model and $\lambda$ -network into a single repeatable module, such that $\mathbf { s } ^ { k + 1 } , \mathbf { r } ^ { k + 1 } , \gamma ^ { k + 1 } , \lambda ^ { k } = c ( \mathbf { s } ^ { k } )$ . This core is deterministic, and is duplicated $K$ times in the predictron with shared weights. (The predictron with unshared weights has $K$ distinct cores.) Finally, the value network $v$ is a fully connected neural network that computes $\mathbf { v } ^ { k } = v ( \mathbf { s } ^ { k } )$ .
+
+Concretely, the core (Figure 7) consists first of a convolutional layer that maps into an intermediate (hidden) layer. From this layer, another two convolutions compute the next abstract state of the predictron. Additionally, this same hidden layer is flattened and fed into three separate networks, with two fully connected layers each. The outputs of these three networks represent the internal rewards, discounts, and lambdas. A similar small network also hangs off the internal states, in addition to the core, and computes the values. All convolutions use $3 \times 3$ filters and a stride of one, and use padding to retain the size of the feature maps. All feature maps have 32 channels. The hidden layers within the MLPs have 32 hidden units.
+
+In Figure 7 the convolutional layers are schematically drawn with three channels, flattening is represented by curly brakets, while the arrows represent the small multi-layer perceptrons which compute values, rewards, discounts and lambdas.
+
+We allow up to 16 model steps in our experiments, resulting in 52-layer deep networks—two convolutional layers for the state representations, $3 \times 1 6 = 4 8$ convolutional layers for the core steps, and two fully-connected layers for the values on top of the final state. Between each two layers we apply batch normalization (Ioffe and Szegedy, 2015) followed by a ReLU non-linearity (Glorot et al., 2011). The value and reward networks end with a linear layer, whereas the discount and $\lambda$ -networks additionally add a sigmoid non-linearity to ensure that these quantities are in $[ 0 , 1 ]$ .
+
+# B TRAINING
+
+All experiments used the supervised (Monte-Carlo) update described in Section 4 except for the semi-supervised experiment which used the consistency update described in Section 4.1. We update all parameters by applying the Adam optimiser (Kingma and Ba, 2015) to stochastic gradients of the corresponding loss functions. Each return is normalised by dividing it by its standard deviation (as measured, prior to the experiment, on a set of 20,000 episodes). In all experiments, the learning rate was 0.001, and the other parameters of the Adam optimiser were $\beta _ { 1 } = 0 . 9$ , $\beta _ { 2 } = 0 . 9 9 9$ , and $\epsilon = 1 0 ^ { - 8 }$ . We used mini-batches of 100 samples.
+
+# C COMPARING ARCHITECTURES OF DIFFERENT DEPTHS
+
+We investigated the effect of changing the depth of the networks, with and without skip connections. Figure 8 in shows that skip connections (dashed lines) make the conventional architectures
+
+![](images/b6658dee23cb96957d5c8447b1e18b5490b5e092b78dedcaac61ba8d741f03c4.jpg)  
+Figure 8: Comparing depths. Comparing the $( r , \gamma , \lambda )$ -predictron (red) against more conventional deep networks (black) for various depths (2, 4, 8, or 16 model steps, corresponding to 10, 16, 28, or 52 total layers of depth). Lighter colours correspond to shallower networks. Dashed lines correspond to networks with skip connections.
+
+(black/grey lines) more robust to the depth (i.e., the black/grey dashed lines almost overlap, especially on pool), and that the predictron outperforms the corresponding feedforward or recurrent baselines for all depths, with and without skips.
+
+# D CAPACITY COMPARISONS
+
+In this section, we present some additional experiments comparing the predictron to more conventional deep networks. The purposes of these experiments are 1) to show that the conclusions obtained above do not depend on the precise architecture used, and 2) to show that the structure of the network—whether we use a predictron or not—is more important than the raw number of parameters.
+
+Specifically, we again consider the same 20 by 20 random mazes, and the pool task described in the main text. As described in Section A, for the results in the paper we used an encoder that preserved the size of the input plans, $2 0 \times 2 0$ for the mazes and $2 8 \times 2 8$ for pool. Each convolution had 32 channels and therefore the abstract states were $2 0 \times 2 0 \times 3 2$ for the mazes and $2 8 \times 2 8 \times 3 2$ for pool.
+
+We now consider a different architecture, where we no longer pad the convolutions used in the encoder. For the mazes, we still use two layers of $3 \times 3$ stride-1 convolutions, which means the planes reduce in size to $1 6 \times 1 6$ . This means that the abstract states are about one third smaller. For pool, we use three $5 \times 5$ stride-1 convolutions, which bring us from $2 8 \times 2 8$ down to $1 6 \times 1 6$ as well. So, the abstract states are now of equal size for both experiments. For pool, this is approximately a two-thirds reduction, which helps reduce the compute needed to run the model.
+
+Most of the parameters in the predictron are in the fully connected layers. Previously, the first fully connected layer for each of the internal values, rewards, discounts, and $\lambda$ -parameters would take a flattened abstract state, and then go into 32 hidden nodes. This means the number of parameters in this layer were $2 0 \times 2 0 \times 3 2 \times 3 2 = 4 0 9 , 6$ 00 for the mazes and $2 8 \times 2 8 \times 3 2 \times 3 2 = 8 0 2 , 8 1$ 6 for pool. The predictron with shared core would have four of these layers, one for each of the internal values, rewards, discounts, and $\lambda s$ , compared to one for the deep network which only has values. We change this in two ways. First, we add a $1 \times 1$ convolution with a stride of 1 and 8 channels before the first fully connected layer for each of these outputs. This reduces the number of channels, and therefore the number of parameters in the subsequent fully-connected layer, by one fourth. Second, we tested three different numbers of hidden nodes: 32, 128, or 512.
+
+![](images/93fd02c8270d80a1af3e7ef67faee6943d3152147776544fec0ca60f183fb98d.jpg)  
+Figure 9: Comparing depths. Comparing the $( r , \gamma , \lambda )$ -predictron (red) against more conventional deep networks (blue) for different numbers hidden nodes in the fully connected layers, and therefore different total numbers of parameters. The deep networks with 32, 128, and 512 nodes respectively have 381,416, 1,275,752, and 4,853,096 parameters in total. The predictrons with 32 and 128 nodes respectively have 1,275,752, and 4,853,096 parameters in total. Note that the number of parameters for the 32 and 128 node predictrons are exactly equal to the number of parameters for the 128 and 512 node deep networks.
+
+The deep network with 128 hidden nodes for its values has the exact same number of parameters as the $( r , \gamma , \lambda )$ -predictron with 32 hidden nodes for each of its outputs. Before, the deep network had fewer parameters, because we kept this number fixed at 32 across experiments. This opens the question of whether the improved performance of the predictron was not just an artifact of having more parameters. We tested this hypothesis, and the results are shown in Figure 9.
+
+Figure 9 shows that in each setting—on the mazes and pool, and with or without shared cores— both. The predictrons always performed better than all the deep networks. This includes the 32 node predictron (darkest red) compared to the 512 node deep network (lightest blue), even though the latter has approximately 4 times as many parameters (1.27M vs 4.85M). This means that the number of parameters mattered less than whether or not we use a predictron.
+
+# E ADDITIONAL DOMAIN DETAILS
+
+We now provide some additional details of domains.
+
+# E.1 POOL
+
+To generate sequences in the Pool domain, the initial locations of 4 balls of different colours are sampled at random. The white ball is the only one moving initially. Its velocity has a norm sampled uniformly between 7 and 14. The initial angle is sampled uniformly in the range $( 0 , 2 \pi )$ . From the initial condition, the Mujoco simulation is run forward until all balls have stopped moving; sequences that last more than 151 frames are rejected, and a new one is generated as replacement. Each frame is rendered by Mujoco as a $2 8 0 \mathbf { x } 2 8 0$ RGB image, and subsequently downsampled through bilinear interpolation to a 28x28 RGB input (see Figure 10 for an example). Since the 280 signals described in Section 6.1 as targets for the Pool experiments have very different levels of sparsity, resulting in values with very different scales, we have normalised the pseudo returns. The normalization procedure consisted in dividing all targets by their standard deviation, as empirically measured across an initial set of 20,000 sequences.
+
+![](images/5d383c73a965d3d3933c82e67191cd7d3082ff03872892bee902b7940be8a77b.jpg)  
+Figure 10: Pool input frame. An example of a $2 8 \mathbf { x } 2 8$ RGB input frame in the pool domain.
+
+# E.2 RANDOM MAZES
+
+To generate mazes we first determine, with a stochastic line search, a number of walls so that the topleft corner is connected to the bottom-right corner (both always forced to be empty) in approximately $50 \%$ of the mazes. We then shuffle the walls uniformly randomly. For 20 by 20 mazes this means $70 \%$ of locations are empty and $30 \%$ contain walls. More than a googol different such 20-by-20 mazes exist (as $\mathrm { \binom { 3 9 8 } { 1 2 0 } } > \mathrm { \bar { 1 0 } ^ { \bar { 1 } 0 0 } } ,$ ).

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+        "text": "THE PREDICTRON: END-TO-END LEARNING AND PLANNING ",
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+        "text": "David Silver\\*, Hado van Hasselt\\*, Matteo Hessel\\*, Tom Schaul\\*, Arthur Guez\\*, Tim Harley, Gabriel Dulac-Arnold, David Reichert, Neil Rabinowitz, Andre Barreto, Thomas Degris DeepMind, London {davidsilver,hado,mtthss,schaul,aguez}@google.com ",
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+        "type": "text",
+        "text": "ABSTRACT ",
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+    },
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+        "text": "One of the key challenges of artificial intelligence is to learn models that are effective in the context of planning. In this document we introduce the predictron architecture. The predictron consists of a fully abstract model, represented by a Markov reward process, that can be rolled forward multiple “imagined” planning steps. Each forward pass of the predictron accumulates internal rewards and values over multiple planning depths. The predictron is trained end-to-end so as to make these accumulated values accurately approximate the true value function. We applied the predictron to procedurally generated random mazes and a simulator for the game of pool. The predictron yielded significantly more accurate predictions than conventional deep neural network architectures. ",
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+        "text": "1 INTRODUCTION ",
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+        "text": "The central idea of model-based reinforcement learning is to decompose the RL problem into two subproblems: learning a model of the environment, and then planning with this model. The model is typically represented by a Markov reward process (MRP) or decision process (MDP). The planning component uses this model to evaluate and select among possible strategies. This is typically achieved by rolling forward the model to construct a value function that estimates cumulative reward. In prior work, the model is trained essentially independently of its use within the planner. As a result, the model is not well-matched with the overall objective of the agent. Prior deep reinforcement learning methods have successfully constructed models that can unroll near pixel-perfect reconstructions (Oh et al., 2015; Chiappa et al., 2016); but are yet to surpass state-of-the-art modelfree methods in challenging RL domains with raw inputs (e.g., Mnih et al., 2015; 2016; Lillicrap et al., 2016). ",
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+        "text": "In this paper we introduce a new architecture, which we call the predictron, that integrates learning and planning into one end-to-end training procedure. At every step, a model is applied to an internal state, to produce a next state, reward, discount, and value estimate. This model is completely abstract and its only goal is to facilitate accurate value prediction. For example, to plan effectively in a game, an agent must be able to predict the score. If our model makes accurate predictions, then an optimal plan with respect to our model will also be an optimal plan for the underlying game – even if that model uses a different state space (e.g., an abstract representation of enemy positions, ignoring their shapes and colours), action space (e.g., a high-level action to move away from an enemy), rewards (e.g., a single abstract step could have a higher value than any real reward), or even timestep (e.g., a single abstract step could “jump” the agent to the end of a corridor). All we require is that trajectories through the abstract model produce scores that are consistent with trajectories through the real environment. This is achieved by training the predictron end-to-end, so as to make its value estimates as accurate as possible. ",
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+        "text": "An ideal model could generalise to many different prediction tasks, rather than overfitting to a single task; and could learn from a rich variety of feedback signals, not just a single extrinsic reward. We therefore train the predictron to predict a host of different value functions for a variety of pseudoreward functions and discount factors. These pseudo-rewards can encode any event or aspect of the environment that the agent may care about, e.g., staying alive or reaching the next room. ",
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+        "text": "We focus upon the prediction task: estimating value functions in MRP environments with uncontrolled dynamics. In this case, the predictron can be implemented as a deep neural network with an ",
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+        "type": "text",
+        "text": "MRP as a recurrent core. The predictron unrolls this core multiple steps and accumulates rewards into an overall estimate of value. ",
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+        "text": "We applied the predictron to procedurally generated random mazes, and a simulated pool domain, directly from pixel inputs. In both cases, the predictron significantly outperformed model-free algorithms with conventional deep network architectures; and was much more robust to architectural choices such as depth. ",
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+        "type": "text",
+        "text": "2 BACKGROUND ",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "We consider environments defined by an MRP with states $s \\in S$ . The MRP is defined by a function, $s ^ { \\prime } , r , \\gamma = p ( s , \\alpha )$ , where $s ^ { \\prime }$ is the next state, $r$ is the reward, and $\\gamma$ is the discount factor, which can for instance represent the non-termination probability for this transition. The process may be stochastic, given IID noise $\\alpha$ . ",
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+        "text": "The return of an MRP is the cumulative discounted reward over a single trajectory, $g _ { t } = r _ { t + 1 } +$ $\\gamma _ { t + 1 } r _ { t + 2 } + \\gamma _ { t + 1 } \\gamma _ { t + 2 } r _ { t + 3 } + \\ldots ,$ , where $\\gamma _ { t }$ can vary per time-step. We consider a generalisation of the MRP setting that includes vector-valued rewards $\\mathbf { r }$ , diagonal-matrix discounts $\\gamma$ , and vector-valued returns $\\mathbf { g }$ ; definitions are otherwise identical to the above. We use this bold font notation to closely match the more familiar scalar MRP case; the majority of the paper can be comfortably understood by reading all rewards as scalars, and all discount factors as scalar and constant, i.e., $\\gamma _ { t } = \\gamma$ . ",
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+        "text": "The value function of an MRP $p$ is the expected return from state $s$ , $v _ { p } ( s ) = \\mathbb { E } _ { p } \\left[ \\mathbf { g } _ { t } \\mid s _ { t } = s \\right]$ . In the vector case, these are known as general value functions (Sutton et al., 2011). We will say that a (general) value function $v ( \\cdot )$ is consistent with environment $p$ if and only if $v = v _ { p }$ which satisfies the following Bellman equation (Bellman, 1957), ",
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+    {
+        "type": "equation",
+        "img_path": "images/592d1d3e31a4ecdf1a1e4f2bf7665fd4a0cd742f9ccc0a118110105edca09678.jpg",
+        "text": "$$\nv _ { p } ( s ) = \\mathbb { E } _ { p } \\left[ \\mathbf { r } + \\gamma v _ { p } ( s ^ { \\prime } ) \\mid s \\right] .\n$$",
+        "text_format": "latex",
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+    },
+    {
+        "type": "text",
+        "text": "In model-based reinforcement learning (Sutton and Barto, 1998), an approximation $m \\approx p$ to the environment is learned. In the uncontrolled setting this model is normally an MRP $s ^ { \\prime } , \\mathbf { r } , \\gamma = m ( s , \\beta )$ that maps from state $s$ to subsequent state $s ^ { \\prime }$ and additionally outputs rewards $\\mathbf { r }$ and discounts $\\gamma$ ; the model may be stochastic given an IID source of noise $\\beta$ . A (general) value function $v _ { m } ( \\cdot )$ is consistent with model $m$ (or valid, (Sutton, 1995)), if and only if it satisfies a Bellman equation $v _ { m } ( s ) = \\mathbb { E } _ { m } \\left[ \\mathbf { r } + \\gamma v _ { m } ( s ^ { \\prime } ) \\mid s \\right]$ with respect to model $m$ . Conventionally, model-based RL methods focus on finding a value function $v$ that is consistent with a separately learned model $m$ . ",
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+    {
+        "type": "text",
+        "text": "3 PREDICTRON ARCHITECTURE ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The predictron is composed of four main components. First, a state representation $\\mathbf { s } = f ( s )$ that encodes raw input $s$ (this could be a history of observations, in the partially observed setting, for example when $f$ is a recurrent network) into an internal (abstract, hidden) state s. Second, a model $\\mathbf { s } ^ { \\prime } , \\mathbf { r } , \\gamma = m ( \\mathbf { s } , \\beta )$ that maps from internal state s to subsequent internal state $\\mathbf { s } ^ { \\prime }$ , internal rewards $\\mathbf { r }$ , and internal discounts $\\gamma$ . Third, a value function $v$ that outputs internal values $\\mathbf { v } = v ( \\mathbf { s } )$ representing the future, internal return from internal state s onwards. The predictron is applied by unrolling its model $m$ multiple “planning” steps to produce internal rewards, discounts and values. We use superscripts $\\bullet ^ { k }$ to indicate internal steps of the model (which have no necessary connection to time steps $\\bullet _ { t }$ of the environment). Finally, these internal rewards, discounts and values are combined together by an accumulator into an overall estimate of value g. The whole predictron, from input state $s$ to output g, may be viewed as a value function approximator for external targets (i.e. the returns in the real environment). We consider both $k$ -step and $\\lambda$ -weighted accumulators. ",
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+    {
+        "type": "text",
+        "text": "The $k$ -step predictron rolls its internal model forward $k$ steps. Specifically, the $k$ -step predictron return $\\mathbf { g } ^ { k }$ (henceforth abbreviated as preturn) is the internal return obtained by accumulating $k$ model steps, plus a final value $\\mathbf { v } ^ { k }$ from the $k$ th step, ",
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+        "type": "equation",
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+        "text": "$$\n\\mathbf { g } ^ { k } = \\mathbf { r } ^ { 1 } + \\gamma ^ { 1 } ( \\mathbf { r } ^ { 2 } + \\gamma ^ { 2 } ( \\ldots ( \\mathbf { r } ^ { k - 1 } + \\gamma ^ { k - 1 } ( \\mathbf { r } ^ { k } + \\gamma ^ { k } \\mathbf { v } ^ { k } ) ) \\ldots ) ) .\n$$",
+        "text_format": "latex",
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+        "type": "text",
+        "text": "The 0-step preturn is simply the first value $\\mathbf { g } ^ { 0 } = \\mathbf { v } ^ { 0 }$ . The 1-step preturn is $\\mathbf { g } ^ { 1 } = \\mathbf { r } ^ { 1 } + \\gamma ^ { 1 } \\mathbf { v } ^ { 1 }$ , and so on (see Fig. 1a). ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "The $\\lambda$ -predictron combines together many $k$ -step preturns. Specifically, it computes a diagonal weight matrix $\\lambda ^ { k }$ from each internal state $\\boldsymbol { \\bar { s } } ^ { k }$ . The accumulator uses weights $\\lambda ^ { 0 } , . . . , \\lambda ^ { K }$ to aggregate ",
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+    {
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+        "image_caption": [
+            "Figure 1: a) The $k$ -step predictron architecture. The first three columns illustrate 0, 1 and 2-step pathways through the predictron. The 0-step preturn reduces to standard model-free value function approximation; other preturns “imagine” additional steps with an internal model. Each pathway outputs a $k \\mathrm { . }$ -step preturn $\\mathbf { g } ^ { k }$ that accumulates discounted rewards along with a final value estimate. In practice all $k$ -step preturns are computed in a single forward pass. b) The $\\lambda$ -predictron architecture. The $\\lambda$ -parameters gate between the different preturns. The output is a $\\lambda$ -preturn $\\mathbf { g } ^ { \\lambda }$ that is a mixture over the $k$ -step preturns. For example, if $\\pmb { \\lambda } ^ { 0 } = \\mathbf { 1 } , \\pmb { \\lambda } ^ { 1 } = \\mathbf { 1 } , \\pmb { \\lambda } ^ { 2 } = \\mathbf { 0 }$ then we recover the 2-step preturn, $\\mathbf { g } ^ { \\lambda } = \\mathbf { g } ^ { 2 }$ . Discount factors $\\gamma ^ { k }$ and $\\lambda$ -parameters $\\lambda ^ { k }$ are dependent on state $\\mathbf { s } ^ { k }$ ; this dependence is not shown in the figure. "
+        ],
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+    {
+        "type": "text",
+        "text": "over $k$ -step preturns $\\mathbf { g } ^ { 0 } , . . . , \\mathbf { g } ^ { K }$ and output a combined value that we call the $\\lambda$ -preturn $\\mathbf { g } ^ { \\lambda }$ , ",
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+        "img_path": "images/349f1e8d5535c720c97c4daf1653bc4cef214c958e36bf810ab5162246522f2f.jpg",
+        "text": "$$\n\\mathbf { g } ^ { \\lambda } = \\sum _ { k = 0 } ^ { K } w ^ { k } \\mathbf { g } ^ { k } \\qquad \\mathrm { w h e r e } \\qquad w ^ { k } = \\left\\{ \\begin{array} { l l } { ( 1 - \\lambda ^ { k } ) \\prod _ { j = 0 } ^ { k - 1 } \\lambda ^ { j } } & { \\mathrm { i f ~ } k < K } \\\\ { \\qquad } \\\\ { \\prod _ { j = 0 } ^ { K - 1 } \\lambda ^ { j } } & { \\mathrm { o t h e r w i s e . } } \\end{array} \\right.\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where 1 is the identity matrix. This $\\lambda$ -preturn is analogous to the $\\lambda$ -return in the forward-view $\\mathrm { T D } ( \\lambda )$ algorithm (Sutton, 1988; Sutton and Barto, 1998). It may also be computed by a backward accumulation through intermediate steps $\\mathbf { g } ^ { k , \\lambda }$ , ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/3bcf3f07b5596719b14bfb35b0fae8902269d7bcf989870314babc28e4648e57.jpg",
+        "text": "$$\n\\mathbf { g } ^ { k , \\lambda } = ( \\mathbf { 1 } - \\lambda ^ { k } ) \\mathbf { v } ^ { k } + \\lambda ^ { k } \\left( \\mathbf { r } ^ { k + 1 } + \\gamma ^ { k + 1 } \\mathbf { g } ^ { k + 1 , \\lambda } \\right) ,\n$$",
+        "text_format": "latex",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "where $\\mathbf { g } ^ { K , \\lambda } = \\mathbf { v } ^ { K }$ , and then using $\\mathbf { g } ^ { \\lambda } = \\mathbf { g } ^ { 0 , \\lambda }$ . Computation in the $\\lambda$ -predictron operates in a sweep, iterating first through the model from $k = 0 \\ldots K$ and then back through the accumulator from $k = K \\ldots 0$ in a single “forward” pass of the network (see Figure 1b). Each $\\lambda ^ { k }$ weight acts as a gate on the computation of the $\\lambda$ -preturn: a value of $\\lambda ^ { k } = 0$ will truncate the $\\lambda$ -preturn at layer $k$ , while a value of $\\mathbf { \\hat { \\lambda } } \\mathbf { \\lambda } ^ { k } = \\mathbf { 1 }$ will utilise deeper layers based on additional steps of the model $m$ ; the final weight is always $\\pmb { \\lambda } ^ { K } = \\mathbf { 0 }$ . The individual $\\dot { \\lambda } ^ { k }$ weights may depend on the corresponding abstract state $\\mathbf { s } ^ { k }$ and can differ per prediction. This enables the predictron to compute to an adaptive depth (Graves, 2016) depending on the internal state and learning dynamics of the network. ",
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+    {
+        "type": "text",
+        "text": "4 PREDICTRON LEARNING UPDATES ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We first consider updates that optimise the joint parameters $\\pmb { \\theta }$ of the state representation, model, and value function. We begin with the $k$ -step predictron. We update the $k$ -step predictron $\\mathbf { g } ^ { k }$ towards a target outcome $\\mathbf { g }$ , such as the Monte-Carlo return from the real environment, by minimising a mean-squared error loss, ",
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+        "type": "equation",
+        "img_path": "images/351eac7a2de69730f3dab1f5189c90d52d764ae134a2439b606e7ef12358b6b9.jpg",
+        "text": "$$\nL ^ { k } = { \\frac { 1 } { 2 } } \\left\\| \\mathbb { E } _ { p } \\left[ \\mathbf { g } \\mid s \\right] - \\mathbb { E } _ { m } \\left[ \\mathbf { g } ^ { k } \\mid s \\right] \\right\\| ^ { 2 } . \\qquad { \\frac { \\partial l ^ { k } } { \\partial \\theta } } = \\left( \\mathbf { g } - \\mathbf { g } ^ { k } \\right) { \\frac { \\partial \\mathbf { g } ^ { k } } { \\partial \\theta } } .\n$$",
+        "text_format": "latex",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "where $l ^ { k } = \\textstyle { \\frac { 1 } { 2 } } \\left\\| \\mathbf { g } - \\mathbf { g } ^ { k } \\right\\| ^ { 2 }$ is the sample loss. We can use the gradient of the sample loss to update parameters, e.g. by stochastic gradient descent. For stochastic models, two independent samples are required for $\\mathbf { g } ^ { k }$ and ∂ g k to get unbiased samples for the gradient of $L ^ { k }$ . ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The $\\lambda$ -predictron combines together many $k$ -step preturns. To update the joint parameters $\\pmb \\theta$ , we can uniformly average the losses on the individual preturns $\\mathbf { g } ^ { k }$ , ",
+        "bbox": [
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+    {
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+        "img_path": "images/0c90f66f7c185d870095fba4c191fd03f8dfa64dd7bf7c1c35ee13b6c046dadd.jpg",
+        "text": "$$\nL ^ { 0 : K } = \\frac { 1 } { 2 K } \\sum _ { k = 0 } ^ { K } \\left\\| \\mathbb { E } _ { p } \\left[ \\mathbf { g } \\mid s \\right] - \\mathbb { E } _ { m } \\left[ \\mathbf { g } ^ { k } \\mid s \\right] \\right\\| ^ { 2 } , \\qquad \\frac { \\partial l ^ { 0 : K } } { \\partial \\theta } = \\frac { 1 } { K } \\sum _ { k = 0 } ^ { K } \\left( \\mathbf { g } - \\mathbf { g } ^ { k } \\right) \\frac { \\partial \\mathbf { g } ^ { k } } { \\partial \\theta } .\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
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+    {
+        "type": "text",
+        "text": "Alternative, we could weight each loss by the usage $\\boldsymbol { w } ^ { k }$ of the corresponding preturn, such that the gradient is $\\begin{array} { r } { \\sum _ { k = 0 } ^ { K } \\pmb { w } ^ { k } \\left( \\mathbf { g } - \\mathbf { g } ^ { k } \\right) \\frac { \\partial \\mathbf { g } ^ { k } } { \\partial \\pmb { \\theta } } } \\end{array}$ \u0001 ∂ g k∂ θ . ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The $\\lambda$ -predictron uses an accumulator with additional parameters $\\eta$ that determine the relative weighting of the $k$ -step preturns. These weights are also updated so as to minimise a mean-squared error loss $L ^ { \\lambda }$ , ",
+        "bbox": [
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+    {
+        "type": "equation",
+        "img_path": "images/01e9a10653c8121ca7431bc9d38a2316a64da433a9cd12cbede9880710b232ad.jpg",
+        "text": "$$\nL ^ { \\lambda } = \\frac { 1 } { 2 } \\left\\| \\mathbb { E } _ { p } \\left[ \\mathbf { g } \\mid s \\right] - \\mathbb { E } _ { m } \\left[ \\mathbf { g } ^ { \\lambda } \\mid s \\right] \\right\\| ^ { 2 } , \\qquad \\frac { \\partial l ^ { \\lambda } } { \\partial \\eta } = \\left( \\mathbf { g } - \\mathbf { g } ^ { \\lambda } \\right) \\frac { \\partial \\mathbf { g } ^ { \\lambda } } { \\partial \\eta } .\n$$",
+        "text_format": "latex",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In summary, the joint parameters $\\pmb \\theta$ of the state representation $f$ , the model $m$ , and the value function $v$ are updated to make each of the $k$ -step preturns $\\mathbf { g } ^ { k }$ more similar to the target $\\mathbf { g }$ , and the parameters $\\eta$ of the $\\lambda$ -accumulator are updated to make the aggregate $\\lambda$ -preturn $\\mathbf { g } ^ { \\lambda }$ more similar to the target g. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "4.1 CONSISTENCY (SEMI-SUPERVISED) LEARNING WITH THE $\\lambda$ -PREDICTRON ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Ideally, the predictron $( f , m , v )$ learns preturns that are all equal in expectation to the true value function of the environment, $\\mathbb { E } _ { m } \\left[ \\mathbf { g } ^ { k } \\mid s \\right] = \\mathbb { E } _ { p } \\left[ \\mathbf { g } _ { t } \\mid s \\right] = v _ { p } ( s )$ , in which case the preturns must be equal in expectation, $\\mathbb { E } _ { m } \\left[ \\mathbf { g } ^ { 0 } \\mid s \\right] = \\mathbb { E } _ { m } \\left[ \\mathbf { g } ^ { 1 } \\mid s \\right] = \\ldots = \\mathbb { E } _ { m } \\left[ \\mathbf { g } ^ { K } \\mid s \\right]$ . In addition, each $k$ -step preturn must then be equal in expectation to th $: \\lambda - p$ return, $\\mathbb { E } _ { m } \\left[ \\mathbf { \\bar { g } } ^ { k } \\mid s \\right] \\mathbf { \\bar { \\Lambda } } = \\mathbb { E } _ { m } \\left[ \\mathbf { g } ^ { \\lambda } \\mid s \\right]$ , for any $\\lambda$ parameters. All these consistency relations between preturns give rise to additional constraints upon the predictron. Specifically, we may adjust the parameters of the predictron to lead to consistent preturns, even in the absence of labelled targets. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Concretely, we can adjust each preturn $\\mathbf { g } ^ { k }$ towards the $\\lambda$ -preturn $\\mathbf { g } ^ { \\lambda }$ ; in other words, we can update each individual value estimate towards the best aggregated estimate by minimizing ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/01111d8b32de3dca2ecfde14ec4f99c730d6eb5016758fe903611948268c3209.jpg",
+        "text": "$$\nL = \\frac { 1 } { 2 } \\sum _ { k = 0 } ^ { K } \\left\\| \\mathbb { E } _ { m } \\left[ \\mathbf { g } ^ { \\lambda } \\mid s \\right] - \\mathbb { E } _ { m } \\left[ \\mathbf { g } ^ { k } \\mid s \\right] \\right\\| ^ { 2 } , \\qquad \\quad \\quad \\frac { \\partial l } { \\partial \\theta } = \\sum _ { k = 0 } ^ { K } \\left( \\mathbf { g } ^ { \\lambda } - \\mathbf { g } ^ { k } \\right) \\frac { \\partial \\mathbf { g } ^ { k } } { \\partial \\theta } .\n$$",
+        "text_format": "latex",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Here $\\mathbf { g } ^ { \\lambda }$ is considered fixed; the parameters $\\pmb \\theta$ are only updated to make $\\mathbf { g } ^ { k }$ more similar to $\\mathbf { g } ^ { \\lambda }$ , not vice versa. This consistency update does not require any labels $\\mathbf { g }$ or samples from the environment. As a result, it can be applied to (potentially hypothetical) states that have no associated ‘real’ (e.g. Monte-Carlo) outcome: we update the value estimates to be self-consistent with each other. Note the similarity with the semi-supervised setting, where we may have unlabelled inputs. ",
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+    {
+        "type": "text",
+        "text": "5 EXPERIMENTS ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We conducted experiments on two domains. The first domain consists of randomly generated $2 0 \\times 2 0$ mazes in which each location either is empty or contains a wall. Two locations in a maze are considered connected if they are both empty and we can reach one from the other by moving horizontally or vertically through adjacent empty cells. The goal is to predict, for each of the locations on the diagonal from top-left to bottom-right of the maze, whether the bottom-right corner is connected to that location, given the entire maze as an input image. Some of these predictions will be straightforward, for instance for locations on the diagonal that contain a wall themselves and for locations close to the bottom right. Many other predictive questions seem to require a simple algorithm, such as some form of a flood fill or search; our hypothesis is that an internal model can learn to emulate such algorithms, where naive approximation may struggle. A few example mazes are shown in Figure 2. ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Our second domain is a simulation of the game of pool, using four balls and four pockets. The simulator is implemented in the physics engine Mujoco (Todorov et al., 2012). We generate sequences of RGB frames starting from a random arrangement of balls on the table. The goal is to simultaneously learn to predict future events for each of the four balls, given 5 RGB frames as input. These events include: collision with any other ball, collision with any boundary of the table, entering a quadrant $\\times 4$ , for each quadrant), being located in a quadrant $\\times 4$ , for each quadrant), and entering a pocket $( \\times 4$ , for each pocket). Each of these $1 4 \\times 4$ events provides a binary pseudo-reward that we combine with 5 different discount factors $\\{ 0 , 0 . 5 , 0 . 9 , 0 . 9 8 , 1 \\}$ and predict their cumulative discounted sum over various time spans. This yields a total of 280 general value functions. An example trajectory is shown in Figure 2. In both domains, inputs are presented as minibatches of i.i.d. samples with their regression targets. Additional domain details are provided in Appendix E. ",
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+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/8a31c76eabf685b5e20aa0765cb76bf5f66494f925957476c5705091f578ef29.jpg",
+        "image_caption": [
+            "Figure 2: Left: Two sample mazes from the random-maze domain. Light blue cells are empty, darker blue cells contain a wall. One maze is connected from top-left to bottom-right (indicated in black), the other is not. Right: An example trajectory in the pool domain (before downsampling). It was selected by maximising the prediction of pocketing balls, using the predictron. "
+        ],
+        "image_footnote": [],
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+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/e602264f049e19e6be76364d251d62f7e9f44ac88523eb8c4214db23eff3de07.jpg",
+        "image_caption": [
+            "Figure 3: Exploring predictron variants. Aggregated prediction errors over all predictions (20 for mazes, 280 for pool) for the eight predictron variants corresponding to the cube on the left (as described in the main text), for both random mazes (top) and pool (bottom). Each line is the median of RMSE over five seeds; shaded regions encompass all seeds. The full $( r , \\gamma , \\lambda )$ -prediction (red) consistently performed best. "
+        ],
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+        "type": "text",
+        "text": "5.1 EXPLORING THE PREDICTRON ARCHITECTURE ",
+        "text_level": 1,
+        "bbox": [
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+        "type": "text",
+        "text": "Our first set of experiments examines three binary dimensions that differentiate the predictron from standard deep networks. We compare eight predictron variants corresponding to the corners of the cube on the left in Figure 3. ",
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+        "type": "text",
+        "text": "The first dimension corresponds to whether or not the predictron architecture utilises the structure of an MRP model. In the MRP case, labelled $r , \\gamma$ , internal rewards and discounts are both learned. In the non- $r$ , $\\gamma$ case, which corresponds to a vanilla hidden-to-hidden neural network module, internal rewards and discounts are ignored by fixing their values to $\\mathbf { r } ^ { k } = \\mathbf { 0 }$ and $\\gamma ^ { k } = \\mathbf { 1 }$ . ",
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+        "type": "text",
+        "text": "The second dimension is whether a $K$ -step accumulator or $\\lambda$ -accumulator is used to aggregate over preturns. When a $\\lambda$ -accumulator is used, a $\\lambda$ -preturn is computed as described in Section 3. Otherwise, intermediate preturns are ignored by fixing their values to $\\lambda ^ { k } = 1$ for $k < K$ . In this case, the overall output of the predictron is simply the maximum-depth preturn $\\mathbf { g } ^ { K }$ . ",
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+        "type": "text",
+        "text": "The third dimension, labelled usage weighting, defines the loss that is used to update the parameters $\\pmb \\theta$ . On this dimension, we consider two options: the preturn losses can either be weighted uniformly (see Equation 6), or the update for each preturn $\\mathbf { g } ^ { k }$ can be weighted according to the weight $\\boldsymbol { w } ^ { k }$ that determines how much it is used in the $\\lambda$ -predictron’s overall output. We call the latter loss ‘usage weighted‘. Note that for architectures without a $\\lambda$ -accumulator, $\\bar { \\boldsymbol { w } } ^ { k } = 0$ for $k < K$ , and $\\mathbf { \\Delta } w ^ { K } = \\mathbf { \\bar { \\mu } }$ , thus usage weighting then implies backpropagating only the loss on the final preturn $\\mathbf { g } ^ { K }$ . ",
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+        "type": "text",
+        "text": "All variants utilise a convolutional core with 2 intermediate hidden layers (see Appendix A); parameters were updated by supervised learning (see Appendix $\\mathbf { B }$ for more details). Root mean squared prediction errors for each architecture, aggregated over all predictions, are shown in Figure 3. The top row corresponds to the random mazes and the bottom row to the pool domain. The main conclusion is that learning an MRP model improved performance greatly. The inclusion of $\\lambda$ weights helped as well, especially on pool. Usage weighting further improved performance. ",
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+        "img_path": "images/dba61ef00d493777d067bc381985a11c743383fcb9df81dc1d0a496239d6428e.jpg",
+        "image_caption": [
+            "Figure 4: Comparing predictron to baselines. Aggregated prediction errors on random mazes (top) and pool (bottom) over all predictions for the eight architectures corresponding to the cube on the left. Each line is the median of RMSE over five seeds; shaded regions encompass all seeds. The full $( r , \\gamma , \\lambda )$ -predictron (red), consistently outperformed conventional deep network architectures (black), with and without skips and with and without weight sharing. "
+        ],
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+        "text": "",
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+    {
+        "type": "text",
+        "text": "5.2 COMPARING THE PREDICTRON TO OTHER DEEP NETWORKS ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Our second set of experiments compares the predictron to feedforward and recurrent deep learning architectures, with and without skip connections. We compare the corners of a new cube, as depicted on the left in Figure 4, based on three different binary dimensions. ",
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+    {
+        "type": "text",
+        "text": "The first dimension of this second cube is whether we use a predictron, or a (non- $\\boldsymbol { \\cdot } \\lambda$ , non- $\\cdot r , \\gamma$ ) deep network that does not have an internal model and does not output or learn from intermediate predictions. We use the most effective predictron from the previous section, i.e., the $( r , \\gamma , \\lambda )$ -predictron with usage weighting. ",
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+    {
+        "type": "text",
+        "text": "The second dimension is whether weights are shared between all cores (as in a recurrent network), or whether each core uses separate weights (as in a feedforward network). We note that the non$\\lambda$ , non- $\\cdot r , \\gamma$ variants of the predictron then correspond to standard (convolutional) feedforward and (unrolled) recurrent neural networks respectively. ",
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+    {
+        "type": "text",
+        "text": "The third dimension is whether we include skip connections. This is equivalent to defining the model step to output a change to the current state, $\\Delta \\mathbf { s } .$ , and then defining $\\mathbf { s } ^ { \\hat { k } + 1 } = h ( \\mathbf { s } ^ { k } + \\Delta \\mathbf { s } ^ { \\tilde { k } } )$ , where $h$ is the non-linear function—in our case a ReLU, $h ( x ) = \\operatorname* { m a x } ( \\bar { 0 , x } )$ . The deep network with skip connections is a variant of ResNet (He et al., 2015). ",
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+    {
+        "type": "text",
+        "text": "Root mean squared prediction errors for each architecture are shown in Figure 4. All $( r , \\gamma , \\lambda )$ - predictrons (red lines) outperformed the corresponding feedforward or recurrent neural network baselines (black lines) both in the random mazes and in pool. We also investigated the effect of changing the depth of the networks (see Appendix C). The predictron outperformed the corresponding feedforward or recurrent baselines for all depths, with and without skip connections. ",
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+    {
+        "type": "text",
+        "text": "5.3 SEMI-SUPERVISED LEARNING BY CONSISTENCY ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "We now consider how to use the predictron for semi-supervised learning, training the model on a combination of labelled and unlabelled random mazes. Semi-supervised learning is important because a common bottleneck in applying machine learning in the real world is the difficulty of collecting labelled data, whereas often large quantities of unlabelled data exist. ",
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+    {
+        "type": "text",
+        "text": "We trained a full $( r , \\gamma , \\lambda )$ -predictron by alternating standard supervised updates with consistency updates, obtained by stochastically minimizing the consistency loss (8), on the unlabelled samples. For each supervised update we apply either 0, 1, or 9 consistency updates. Figure 5 shows that the performance improved monotonically with the number of consistency updates, measured as a function of the number of labelled samples consumed. ",
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+    {
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+        "img_path": "images/a6a297ad344d3d9b89961b40f0a239cf9bf15e8964e2525c883b866251e3e396.jpg",
+        "image_caption": [
+            "Figure 5: Semi-supervised learning. Prediction errors of the $( r , \\gamma , \\lambda )$ -predictrons (shared core, no skips) using 0, 1, or 9 consistency updates for every update with labelled data, plotted as function of the number of labels consumed. Learning performance improves with more consistency updates. "
+        ],
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+    {
+        "type": "text",
+        "text": "5.4 ANALYSIS OF ADAPTIVE DEPTH ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "In principle, the predictron can adapt its depth to ‘think more’ about some predictions than others, perhaps depending on the complexity of the underlying target. We investigate this by looking at qualitatively different prediction types in pool: ball collisions, rail collisions, pocketing balls, and entering or staying in quadrants. For each prediction type we consider several different time-spans (determined by the real-world discount factors associated with each pseudo-reward). Figure 6 shows distributions of depth for each type of prediction. The ‘depth’ of a predictron is here defined as the effective number of model steps. If the predictron relies fully on the very first value (i.e., $\\lambda ^ { 0 } = 0$ ), this counts as 0 steps. If, instead, it learns to place equal weight on all rewards and on the final value, this counts as 16 steps. Concretely, the depth $^ d$ can be defined recursively as $\\pmb { d } = \\pmb { d } ^ { 0 }$ where $\\pmb { d } ^ { k } = \\lambda ^ { k } ( 1 + \\gamma ^ { k } \\pmb { d } ^ { k + 1 } )$ and $\\mathbf { { \\mathbf { { \\mathbf { { \\mathbf { { \\mathbf { \\alpha } } } } } } } } } \\mathbf { { \\mathbf { { \\mathbf { { d } } } } } } ^ { K } = \\mathbf { { \\mathbf { 0 } } }$ . Note that even for the same input state, each prediction has a separate depth. ",
+        "bbox": [
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+        "page_idx": 6
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+    {
+        "type": "text",
+        "text": "The depth distributions exhibit three properties. First, different types of predictions used different depths. Second, depth was correlated with the real-world discount for the first four prediction types. Third, the distributions are not strongly peaked, which implies that the depth can differ per input even for a single real-world discount and prediction type. In a control experiment (not shown) we used a scalar $\\lambda$ shared among all predictions, which reduced performance in all scenarios, indicating that the heterogeneous depth is a valuable form of flexibility. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "5.5 VISUALIZING THE PREDICTIONS IN THE POOL DOMAIN ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We test the quality of the predictions in the pool domain to evaluate whether they are well-suited to making decisions. For each sampled pool position, we consider a set $I$ of different initial conditions (different angles and velocity of the white ball), and ask which is more likely to lead to pocketing coloured balls. For each initial condition $s \\in I$ , we apply the $( r , \\gamma , \\lambda )$ -predictron (shared cores, 16 model steps, no skip connections) to obtain predictions $\\mathbf { g } ^ { \\lambda }$ . We sum the predictions that correspond to pocketing any ball except the white ball, and to real-world discounts $\\gamma = 0 . 9 8$ and $\\gamma = 1$ . We select the condition $s ^ { * }$ that maximises this sum. ",
+        "bbox": [
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+    {
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+        "img_path": "images/9e5eda1ba0817010e3a899cfcd39b4555fece7632765839f1302bb06efcfea60.jpg",
+        "image_caption": [
+            "Figure 6: Thinking depth. Distributions of thinking depth on pool for different types of predictions and for different real-world discounts. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        "page_idx": 7
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+    {
+        "type": "text",
+        "text": "We then roll forward the pool simulator from $s ^ { * }$ and log the number of pocketing events. Figure 2 shows a sampled rollout, using the predictron to pick $s ^ { * }$ . When providing the choice of 128 angles and two velocities for initial conditions $\\left. \\vert I \\right. = 2 5 6 )$ , this procedure resulted in pocketing 27 coloured balls in 50 episodes. Using the same procedure with an equally deep convolutional network only resulted in 10 pocketing events. These results suggest that the lower loss of the learned $( r , \\gamma , \\lambda )$ -predictron translated into meaningful improvements when informing decisions. A video of the rollouts selected by the predictron is available here: https://youtu.be/BeaLdaN2C3Q. ",
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+    {
+        "type": "text",
+        "text": "6 RELATED WORK ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Lee et al. (2015) introduced a neural network architecture where classifications branch off intermediate hidden layers. An important difference with respect to the $\\lambda$ -predictron, is that the weights are hand-tuned as hyper-parameters, whereas in the predictron the $\\lambda$ weights are learnt and, more importantly, conditional on the input. Another difference is that the loss on the auxiliary classifications is used to speed up learning, but the classifications themselves are not combined into an aggregate prediction; the output of the model itself is the deepest prediction. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Graves (2016) introduced an architecture with adaptive computation time (ACT), with a discrete (but differentiable) decision on when to halt, and aggregating over the outputs at each pondering step. This is related to our $\\lambda$ weights, but obtains depth in a different way; one notable difference is that the $\\lambda$ -predictron can choose different pondering depths for each of its predictions. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Value iteration networks (VINs) (Tamar et al., 2016) also learn value functions end-to-end using an internal model, similar to the (non- $\\lambda$ ) predictron. However, VINs plan via convolutional operations over the full input state space; whereas the predictron plans via imagined trajectories through an abstract state space. This may allow the predictron architecture to scale much more effectively in domains that do not have a natural two-dimensional encoding of the state space. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "The notion of learning about many predictions of the future relates to work on predictive state representations (PSRs; Littman et al., 2001), general value functions (GVFs; Sutton et al., 2011), and nexting (Modayil et al., 2012). Such predictions have been shown to be useful as representations (Schaul and Ring, 2013) and for transfer (Schaul et al., 2015). So far, however, none of these have been considered for learning abstract models. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Schmidhuber (2015) discusses learning abstract models, but maintains separate losses for the model and a controller, and suggests training the model unsupervised to compactly encode the entire history of observations, through predictive coding. The predictron’s abstract model is instead trained endto-end to obtain accurate values. ",
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+    },
+    {
+        "type": "text",
+        "text": "7 CONCLUSION ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "The predictron is a single differentiable architecture that rolls forward an internal model to estimate external values. This internal model may be given both the structure and the semantics of traditional reinforcement learning models. But unlike most approaches to model-based reinforcement learning, the model is fully abstract: it need not correspond to the real environment in any human understandable fashion, so long as its rolled-forward “plans” accurately predict outcomes in the true environment. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "The predictron may be viewed as a novel network architecture that incorporates several separable ideas. First, the predictron outputs a value by accumulating rewards over a series of internal planning steps. Second, each forward pass of the predictron outputs values at multiple planning depths. Third, these values may be combined together, also within a single forward pass, to output an overall ensemble value. Finally, the different values output by the predictron may be encouraged to be self-consistent with each other, to provide an additional signal during learning. Our experiments demonstrate that these differences result in more accurate predictions of value, in reinforcement learning environments, than more conventional network architectures. ",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "We have focused on value prediction tasks in uncontrolled environments. However, these ideas may transfer to the control setting, for example by using the predictron as a Q-network (Mnih et al., 2015). Even more intriguing is the possibility of learning an internal MDP with abstract internal actions, rather than the MRP considered in this paper. We aim to explore these ideas in future work. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
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+    {
+        "type": "text",
+        "text": "E. Todorov, T. Erez, and Y. Tassa. Mujoco: A physics engine for model-based control. In 2012 IEEE/RSJ International Conference on Intelligent Robots and Systems, pages 5026–5033. IEEE, 2012. ",
+        "bbox": [
+            174,
+            244,
+            826,
+            286
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "image",
+        "img_path": "images/470c195ad3d74763aaa60fca5f7047608345478b942bb4154c2bfe8bc163ff2a.jpg",
+        "image_caption": [
+            "Figure 7: The predictron core used in our experiments. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            434,
+            102,
+            557,
+            295
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "A ARCHITECTURE ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            352,
+            343,
+            367
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "The state representation $f$ is a two-layer convolutional neural network (LeCun et al., 1998). There is a core $c$ , again based on convolutions, that combines both MRP model and $\\lambda$ -network into a single repeatable module, such that $\\mathbf { s } ^ { k + 1 } , \\mathbf { r } ^ { k + 1 } , \\gamma ^ { k + 1 } , \\lambda ^ { k } = c ( \\mathbf { s } ^ { k } )$ . This core is deterministic, and is duplicated $K$ times in the predictron with shared weights. (The predictron with unshared weights has $K$ distinct cores.) Finally, the value network $v$ is a fully connected neural network that computes $\\mathbf { v } ^ { k } = v ( \\mathbf { s } ^ { k } )$ . ",
+        "bbox": [
+            174,
+            378,
+            825,
+            463
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Concretely, the core (Figure 7) consists first of a convolutional layer that maps into an intermediate (hidden) layer. From this layer, another two convolutions compute the next abstract state of the predictron. Additionally, this same hidden layer is flattened and fed into three separate networks, with two fully connected layers each. The outputs of these three networks represent the internal rewards, discounts, and lambdas. A similar small network also hangs off the internal states, in addition to the core, and computes the values. All convolutions use $3 \\times 3$ filters and a stride of one, and use padding to retain the size of the feature maps. All feature maps have 32 channels. The hidden layers within the MLPs have 32 hidden units. ",
+        "bbox": [
+            173,
+            465,
+            825,
+            577
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "In Figure 7 the convolutional layers are schematically drawn with three channels, flattening is represented by curly brakets, while the arrows represent the small multi-layer perceptrons which compute values, rewards, discounts and lambdas. ",
+        "bbox": [
+            176,
+            579,
+            820,
+            621
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "We allow up to 16 model steps in our experiments, resulting in 52-layer deep networks—two convolutional layers for the state representations, $3 \\times 1 6 = 4 8$ convolutional layers for the core steps, and two fully-connected layers for the values on top of the final state. Between each two layers we apply batch normalization (Ioffe and Szegedy, 2015) followed by a ReLU non-linearity (Glorot et al., 2011). The value and reward networks end with a linear layer, whereas the discount and $\\lambda$ -networks additionally add a sigmoid non-linearity to ensure that these quantities are in $[ 0 , 1 ]$ . ",
+        "bbox": [
+            174,
+            625,
+            825,
+            708
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "B TRAINING ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            724,
+            294,
+            741
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "All experiments used the supervised (Monte-Carlo) update described in Section 4 except for the semi-supervised experiment which used the consistency update described in Section 4.1. We update all parameters by applying the Adam optimiser (Kingma and Ba, 2015) to stochastic gradients of the corresponding loss functions. Each return is normalised by dividing it by its standard deviation (as measured, prior to the experiment, on a set of 20,000 episodes). In all experiments, the learning rate was 0.001, and the other parameters of the Adam optimiser were $\\beta _ { 1 } = 0 . 9$ , $\\beta _ { 2 } = 0 . 9 9 9$ , and $\\epsilon = 1 0 ^ { - 8 }$ . We used mini-batches of 100 samples. ",
+        "bbox": [
+            173,
+            752,
+            825,
+            851
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "C COMPARING ARCHITECTURES OF DIFFERENT DEPTHS ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            868,
+            651,
+            883
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "We investigated the effect of changing the depth of the networks, with and without skip connections. Figure 8 in shows that skip connections (dashed lines) make the conventional architectures ",
+        "bbox": [
+            174,
+            895,
+            818,
+            924
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "image",
+        "img_path": "images/b6658dee23cb96957d5c8447b1e18b5490b5e092b78dedcaac61ba8d741f03c4.jpg",
+        "image_caption": [
+            "Figure 8: Comparing depths. Comparing the $( r , \\gamma , \\lambda )$ -predictron (red) against more conventional deep networks (black) for various depths (2, 4, 8, or 16 model steps, corresponding to 10, 16, 28, or 52 total layers of depth). Lighter colours correspond to shallower networks. Dashed lines correspond to networks with skip connections. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            246,
+            106,
+            740,
+            344
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "(black/grey lines) more robust to the depth (i.e., the black/grey dashed lines almost overlap, especially on pool), and that the predictron outperforms the corresponding feedforward or recurrent baselines for all depths, with and without skips. ",
+        "bbox": [
+            174,
+            455,
+            825,
+            497
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "D CAPACITY COMPARISONS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            521,
+            421,
+            536
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "In this section, we present some additional experiments comparing the predictron to more conventional deep networks. The purposes of these experiments are 1) to show that the conclusions obtained above do not depend on the precise architecture used, and 2) to show that the structure of the network—whether we use a predictron or not—is more important than the raw number of parameters. ",
+        "bbox": [
+            174,
+            551,
+            825,
+            622
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Specifically, we again consider the same 20 by 20 random mazes, and the pool task described in the main text. As described in Section A, for the results in the paper we used an encoder that preserved the size of the input plans, $2 0 \\times 2 0$ for the mazes and $2 8 \\times 2 8$ for pool. Each convolution had 32 channels and therefore the abstract states were $2 0 \\times 2 0 \\times 3 2$ for the mazes and $2 8 \\times 2 8 \\times 3 2$ for pool. ",
+        "bbox": [
+            174,
+            626,
+            823,
+            695
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "We now consider a different architecture, where we no longer pad the convolutions used in the encoder. For the mazes, we still use two layers of $3 \\times 3$ stride-1 convolutions, which means the planes reduce in size to $1 6 \\times 1 6$ . This means that the abstract states are about one third smaller. For pool, we use three $5 \\times 5$ stride-1 convolutions, which bring us from $2 8 \\times 2 8$ down to $1 6 \\times 1 6$ as well. So, the abstract states are now of equal size for both experiments. For pool, this is approximately a two-thirds reduction, which helps reduce the compute needed to run the model. ",
+        "bbox": [
+            173,
+            698,
+            825,
+            782
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Most of the parameters in the predictron are in the fully connected layers. Previously, the first fully connected layer for each of the internal values, rewards, discounts, and $\\lambda$ -parameters would take a flattened abstract state, and then go into 32 hidden nodes. This means the number of parameters in this layer were $2 0 \\times 2 0 \\times 3 2 \\times 3 2 = 4 0 9 , 6$ 00 for the mazes and $2 8 \\times 2 8 \\times 3 2 \\times 3 2 = 8 0 2 , 8 1$ 6 for pool. The predictron with shared core would have four of these layers, one for each of the internal values, rewards, discounts, and $\\lambda s$ , compared to one for the deep network which only has values. We change this in two ways. First, we add a $1 \\times 1$ convolution with a stride of 1 and 8 channels before the first fully connected layer for each of these outputs. This reduces the number of channels, and therefore the number of parameters in the subsequent fully-connected layer, by one fourth. Second, we tested three different numbers of hidden nodes: 32, 128, or 512. ",
+        "bbox": [
+            173,
+            785,
+            825,
+            924
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "image",
+        "img_path": "images/93fd02c8270d80a1af3e7ef67faee6943d3152147776544fec0ca60f183fb98d.jpg",
+        "image_caption": [
+            "Figure 9: Comparing depths. Comparing the $( r , \\gamma , \\lambda )$ -predictron (red) against more conventional deep networks (blue) for different numbers hidden nodes in the fully connected layers, and therefore different total numbers of parameters. The deep networks with 32, 128, and 512 nodes respectively have 381,416, 1,275,752, and 4,853,096 parameters in total. The predictrons with 32 and 128 nodes respectively have 1,275,752, and 4,853,096 parameters in total. Note that the number of parameters for the 32 and 128 node predictrons are exactly equal to the number of parameters for the 128 and 512 node deep networks. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            199,
+            102,
+            799,
+            340
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "The deep network with 128 hidden nodes for its values has the exact same number of parameters as the $( r , \\gamma , \\lambda )$ -predictron with 32 hidden nodes for each of its outputs. Before, the deep network had fewer parameters, because we kept this number fixed at 32 across experiments. This opens the question of whether the improved performance of the predictron was not just an artifact of having more parameters. We tested this hypothesis, and the results are shown in Figure 9. ",
+        "bbox": [
+            174,
+            486,
+            825,
+            556
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Figure 9 shows that in each setting—on the mazes and pool, and with or without shared cores— both. The predictrons always performed better than all the deep networks. This includes the 32 node predictron (darkest red) compared to the 512 node deep network (lightest blue), even though the latter has approximately 4 times as many parameters (1.27M vs 4.85M). This means that the number of parameters mattered less than whether or not we use a predictron. ",
+        "bbox": [
+            174,
+            559,
+            825,
+            628
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "E ADDITIONAL DOMAIN DETAILS ",
+        "text_level": 1,
+        "bbox": [
+            178,
+            648,
+            467,
+            662
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "We now provide some additional details of domains. ",
+        "bbox": [
+            176,
+            676,
+            516,
+            690
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "E.1 POOL ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            707,
+            254,
+            720
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "To generate sequences in the Pool domain, the initial locations of 4 balls of different colours are sampled at random. The white ball is the only one moving initially. Its velocity has a norm sampled uniformly between 7 and 14. The initial angle is sampled uniformly in the range $( 0 , 2 \\pi )$ . From the initial condition, the Mujoco simulation is run forward until all balls have stopped moving; sequences that last more than 151 frames are rejected, and a new one is generated as replacement. Each frame is rendered by Mujoco as a $2 8 0 \\mathbf { x } 2 8 0$ RGB image, and subsequently downsampled through bilinear interpolation to a 28x28 RGB input (see Figure 10 for an example). Since the 280 signals described in Section 6.1 as targets for the Pool experiments have very different levels of sparsity, resulting in values with very different scales, we have normalised the pseudo returns. The normalization procedure consisted in dividing all targets by their standard deviation, as empirically measured across an initial set of 20,000 sequences. ",
+        "bbox": [
+            174,
+            729,
+            552,
+            924
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "image",
+        "img_path": "images/5d383c73a965d3d3933c82e67191cd7d3082ff03872892bee902b7940be8a77b.jpg",
+        "image_caption": [
+            "Figure 10: Pool input frame. An example of a $2 8 \\mathbf { x } 2 8$ RGB input frame in the pool domain. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            622,
+            695,
+            772,
+            811
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            176,
+            103,
+            823,
+            145
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "E.2 RANDOM MAZES ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            159,
+            338,
+            172
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "To generate mazes we first determine, with a stochastic line search, a number of walls so that the topleft corner is connected to the bottom-right corner (both always forced to be empty) in approximately $50 \\%$ of the mazes. We then shuffle the walls uniformly randomly. For 20 by 20 mazes this means $70 \\%$ of locations are empty and $30 \\%$ contain walls. More than a googol different such 20-by-20 mazes exist (as $\\mathrm { \\binom { 3 9 8 } { 1 2 0 } } > \\mathrm { \\bar { 1 0 } ^ { \\bar { 1 } 0 0 } } ,$ ). ",
+        "bbox": [
+            174,
+            181,
+            825,
+            253
+        ],
+        "page_idx": 13
+    }
+]

parse/train/Byl8hhNYPS/Byl8hhNYPS.md

@@ -0,0 +1,282 @@
+# NEURAL MACHINE TRANSLATION WITH UNIVERSAL VISUAL REPRESENTATION
+
+Zhuosheng Zhang1,2,3, Kehai Chen4, Rui Wang4,∗, Masao Utiyama4, Eiichiro Sumita4, Zuchao Li1,2,3 , Hai Zhao1,2,3,∗
+
+1Department of Computer Science and Engineering, Shanghai Jiao Tong University 2Key Laboratory of Shanghai Education Commission for Intelligent Interaction and Cognitive Engineering, Shanghai Jiao Tong University, Shanghai, China 3MoE Key Lab of Artificial Intelligence, AI Institute, Shanghai Jiao Tong University 4National Institute of Information and Communications Technology (NICT), Kyoto, Japan zhangzs@sjtu.edu.cn, charlee@sjtu.edu.cn, zhaohai@cs.sjtu.edu.cn, {khchen, wangrui, mutiyama, eiichiro.sumita}@nict.go.jp
+
+# ABSTRACT
+
+Though visual information has been introduced for enhancing neural machine translation (NMT), its effectiveness strongly relies on the availability of large amounts of bilingual parallel sentence pairs with manual image annotations. In this paper, we present a universal visual representation learned over the monolingual corpora with image annotations, which overcomes the lack of largescale bilingual sentence-image pairs, thereby extending image applicability in NMT. In detail, a group of images with similar topics to the source sentence will be retrieved from a light topic-image lookup table learned over the existing sentence-image pairs, and then is encoded as image representations by a pretrained ResNet. An attention layer with a gated weighting is to fuse the visual information and text information as input to the decoder for predicting target translations. In particular, the proposed method enables the visual information to be integrated into large-scale text-only NMT in addition to the multimodal NMT. Experiments on four widely used translation datasets, including the WMT’16 English-to-Romanian, WMT’14 English-to-German, WMT’14 Englishto-French, and Multi30K, show that the proposed approach achieves significant improvements over strong baselines.
+
+# 1 INTRODUCTION
+
+Visual information has been introduced for neural machine translation in some previous studies (NMT) (Specia et al., 2016; Elliott et al., 2017; Barrault et al., 2018; Ive et al., 2019) though the contribution of images is still an open question (Elliott, 2018; Caglayan et al., 2019). Typically, each bilingual (or multilingual) parallel sentence pair is annotated manually by one image describing the content of this sentence pair. The bilingual parallel corpora with manual image annotations are used to train a multimodal NMT model by an end-to-end framework, and results are reported on a specific data set, Multi30K (Calixto & Liu, 2017; Calixto et al., 2017).
+
+One strong point of the multimodal NMT model is the ability to use visual information to improve the quality of the target translation. However, the effectiveness heavily relies on the availability of bilingual parallel sentence pairs with manual image annotations, which hinders the image applicability to the NMT. As a result, the visual information is only applied to the translation task over a small and specific multimodal data set Multi30K (Elliott et al., 2016), but not to large-scale text-only NMT (Bahdanau et al., 2014; Gehring et al., 2017; Vaswani et al., 2017) and low-resource text-only NMT (Fadaee et al., 2017; Lample et al., 2018; Ma et al., 2019; Zhou et al., 2019). In addition, because of the high cost of annotation, the content of one bilingual parallel sentence pair is only represented by a single image, which is weak in capturing the diversity of visual information. The current situation of introducing visual information results in a bottleneck in the multimodal NMT and is not feasible for text-only NMT and low-resource NMT.
+
+In this paper, we present a universal visual representation (VR) method1 relying only on image-monolingual annotations instead of the existing approach that depends on image-bilingual annotations, thus breaking the bottleneck of using visual information in NMT. In detail, we transform the existing sentence-image pairs into a topic-image lookup table from a small-scale multimodal data set Multi30K. During the training and decoding process, a group of images with a similar topic to the source sentence will be retrieved from the topic-image lookup table learned by the term frequency-inverse document frequency, and thus is encoded as image representations by a pretrained ResNet (He et al., 2016). A simple and effective attention layer is then designed to fuse the image representations and the original source sentence representations as input to the decoder for predicting target translations. In particular, the proposed approach can be easily integrated into the text-only NMT model without annotating large-scale bilingual parallel corpora. The proposed method was evaluated on four widely-used translation datasets, including the WMT’16 Englishto-Romanian, WMT’14 English-to-German, WMT’14 English-to-French, and Multi30K which are standard corpora for NMT and multimodal machine translation (MMT) evaluation. Experiments and analyses show effectiveness. In summary, our contributions are primarily three-fold:
+
+1. We present a universal visual representation method that overcomes the shortcomings of the bilingual (or multilingual) parallel data with manual image annotations for MMT.   
+2. The proposed method enables the text-only NMT to use the multimodality of visual information without annotating the existing large scale bilingual parallel data.   
+3. Experiments on different scales of translation tasks verified the effectiveness and generality of the proposed approach.
+
+# 2 RELATED WORK
+
+Building fine-grained representation with extra knowledge is an essential topic in language modeling (Li et al., 2020a;b; Zhang et al., 2020b;a), among which adopting visual modality could potentially benefit the machine with a more comprehensive perception of the real world. Inspired by the studies on the image description generation (IDG) task (Mao et al., 2014; Elliott et al., 2015; Venugopalan et al., 2015; Xu et al., 2015), a new shared translation task for multimodal machine translation was addressed by the machine translation community (Specia et al., 2016). In particular, the released dataset Multi30K (Elliott et al., 2016) includes 29,000 multilingual (English, German, and French) parallel sentence pairs with image annotations (Elliott et al., 2017; Barrault et al., 2018). Subsequently, there has been a rise in the number of studies (Caglayan et al., 2016; 2017; Calixto et al., 2016; Huang et al., 2016; Libovicky & Helcl, 2017; Helcl et al., 2018). For \` example, Calixto et al. (2017) proposed a doubly-attentive multimodal NMT model to incorporate spatial-visual features, improving translation performance. Compared with spatial-visual features, Calixto & Liu (2017) further incorporated global image features as words in the source sentence and to enhance the encoder or decoder hidden state. In contrast, some recent studies indicated that the visual modality is either unnecessary (Zhang et al., 2017) or only marginally beneficial (Gronroos ¨ et al., 2018). More recently, Ive et al. (2019) showed that visual information is only needed in particular cases, such as for ambiguous words where the textual context is not sufficient.
+
+However, these approaches only center around a small and specific Multi30K data set to build a multimodal NMT model, which hinders image applicability to NMT. The reason would be the high cost of image annotations, resulting potentially in the image information not being adequately discovered. We believe that the capacity of MMT has not yet been excavated sufficiently, and there is still a long way to go before the potential of MMT is fully discovered. In this work, we seek to break this constraint and enable visual information to benefit NMT, especially text-only NMT.
+
+# 3 UNIVERSAL VISUAL RETRIEVAL
+
+<table><tr><td colspan="2">Algorithm1 Topic-image Lookup Table Conversion Algorithm</td></tr><tr><td>Require: Input sentences, S= {Xi, X2,... X1} and paired images E = {e1,e2,...,e1} 1:Obtain the TF-IDF dictionary F= TF-IDF(S) 2: 3: procedure TF-IDF(S)</td><td>Ensure: Topic-image lookup table Q where each word is associated with a group of images Transform sentence-image pair to topic-image lookup table Q= LookUp(S,E,F)</td></tr><tr><td>4: for each sentence in S do 5: end for</td><td>Filter stop-words in the sentence</td></tr><tr><td>6:</td><td>Calculate the TF-IDF weight for each word</td></tr><tr><td>7: 8:</td><td></td></tr><tr><td>9:</td><td></td></tr><tr><td></td><td>return TF-IDF dictionary F</td></tr><tr><td>10:</td><td>end procedure</td></tr><tr><td>11:</td><td>procedure LOOKUP(S,E,F)</td></tr><tr><td>12:</td><td>for For each pair{Ti,ei} ∈zip{S,E}do</td></tr><tr><td></td><td>Rank and pick out the top-w“topic” words in the sentence according to the TF-IDF</td></tr><tr><td>13:</td><td>score in the dictionary F,and each sentence is reformed as T= {t1,t2,...,tw}</td></tr><tr><td>14:</td><td>Pair the w words with the corresponding image ei</td></tr><tr><td>15:</td><td>for For each word tjin T do</td></tr><tr><td></td><td>if ei not in Q[tj] then</td></tr><tr><td>16:</td><td></td></tr><tr><td>17:</td><td>Add ej to the corresponding image set Q[tj] for word t j</td></tr><tr><td>18:</td><td>end if</td></tr><tr><td></td><td></td></tr><tr><td>19:</td><td>end for</td></tr><tr><td></td><td></td></tr><tr><td>20:</td><td>end for</td></tr><tr><td></td><td></td></tr><tr><td>21:</td><td>return Topic-image lookup table Q</td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td>end procedure</td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr></table>
+
+In this section, we will introduce the proposed universal visual representation method. Generally, the default input setting of the MMT is a sentence-image pair. Our basic intuition is to transform the existing sentence-image pairs into topic-image lookup table2, which assumes the topic words in a sentence should be relevant to the paired image. Consequently, a sentence can possess a group of images by retrieving the topic-image lookup table.
+
+Topic-image Lookup Table Conversion To focus on the major part of the sentence and suppress the noise such as stopwords and low-frequency words, we design a filtering method to extract the “topic” words of the sentence through the term frequency-inverse document frequency $( \mathrm { T F - I D F } ) ^ { 3 }$ inspired by Chen et al. (2019). Specifically, given an original input sentence $X = \{ x _ { 1 } , x _ { 2 } , \dots , x _ { I } \}$ of length $I$ and its paired image $e$ , $X$ is first filtered by a stopword list4 and then the sentence is treated as a document $g$ . We then compute TF-IDF $T I _ { i , j }$ for each word $x _ { i }$ in $g$ ,
+
+$$
+T I _ { i , j } = \frac { o _ { i , j } } { \sum _ { k } o _ { k , j } } \times \log \frac { | { G } | } { 1 + | { j } : { x } _ { i } \in { g } | } ,
+$$
+
+where $o _ { i , j }$ represents the number of occurrences of the word $x _ { i }$ in the input sentence $g$ , $| G |$ the total number of source language sentences in the training data, and $| j : x _ { i } \in g |$ the number of source sentences including word $x _ { i }$ in the training data. We then select the top- $w$ high TF-IDF words as the new image description $T = \{ t _ { 1 } , t _ { 2 } , \dots , t _ { w } \}$ for the input sentence $X$ . After preprocessing, each filtered sentence $T$ is paired with an image $e$ , and each word $t _ { i } \in T$ is regarded as the topic word for image $e$ . After processing the whole corpus (i.e., Multi30K), we form a topic-image lookup table $\mathcal { Q }$ as described in Algorithm 1, in which each topic word $t _ { i }$ would be paired with dozens of images.
+
+Image Retrieval For the input sentence, we first obtain its topic words according to the text preprocessing method described above. Then we retrieve the associated images for each topic word from the lookup table $\mathcal { Q }$ and group all the retrieved images together to form an image list $\mathcal { G }$ . We observe that an image might be associated with multiple topic words so that it would occur multiple times in the list $\mathcal { G }$ . Therefore, we sort the images according to the frequency of occurrences in $\mathcal { G }$ to maintain the total number of images for each sentence at $m$ .
+
+![](images/ec6ef9a373972526443f987670429f17c4cfcb962c73244ef05b7230b637fbcc.jpg)  
+Figure 1: Illustration of the proposed visual retrieval.
+
+Figure 1 illustrates the retrieval process5. In the left block, we show six examples of sentence-image pairs in which the topic words are in boldface. Then we process the corpus using the topic-image transformation method demonstrated above and obtain the topic-image lookup table. For example, the word dog is associated with 1,512 images. For an input source sentence, we obtain the topic words (in boldface) using the same preprocessing. Then we retrieve the corresponding images from the lookup table for each topic word. Now we have a list of images, and some images appear multiple times as they have various topics (like the boxed image in Figure 1). So we sort the retrieved image list by the count of occurrence to pick out the top- $m$ images that cover the most topics of the sentence.
+
+At test time, the process of getting images is done using the image lookup table built by the training set, so we do not need to use the images from the dev and test sets in Multi30K dataset6. Intuitively, we do not strictly require the manual alignment of the word (or concept) and image, but rely on the co-occurrence of topic word and image, which is simpler and more general. In this way, we call our method as universal visual retrieval.
+
+# 4 NMT WITH UNIVERSAL VISUAL REPRESENTATION
+
+In this section, we introduce the proposed universal visual representation (VR) method for NMT.   
+The overview of the framework of our proposed method is shown in Figure 2.
+
+# 4.1 SOURCE REPRESENTATION FOR NEURAL MACHINE TRANSLATION
+
+In the state-of-the-art Transformer-based NMT (Vaswani et al., 2017), source information is encoded as source representation by an SAN-based encoder with multiple layers. Specifically, the encoder is composed of a stack of $L$ identical layers, each of which includes two sub-layers. The first sublayer is a self-attention module, whereas the second is a position-wise, fully connected feed-forward network. A residual connection (He et al., 2016) is applied between the two sub-layers, and then a layer normalization (Ba et al., 2016) is performed. Formally, the stack of learning the source representation is organized as follows:
+
+![](images/c4aaf77a9b3f70bdd6db859235887c88b50e0497f0bb88b7a5d30fb871a689b9.jpg)  
+Figure 2: Overview of the framework of our proposed method.
+
+$$
+\begin{array} { r l } & { \overline { { \mathbf { H } } } ^ { l } = \mathrm { L N } ( \mathrm { A T T } ^ { l } ( \mathbf { Q } ^ { l - 1 } , \mathbf { K } ^ { l - 1 } , \mathbf { V } ^ { l - 1 } ) + \mathbf { H } ^ { l - 1 } ) , } \\ & { \mathbf { H } ^ { l } = \mathrm { L N } ( \mathrm { F F N } ^ { l } ( \overline { { \mathbf { H } } } ^ { l } ) + \overline { { \mathbf { H } } } ^ { l } ) , } \end{array}
+$$
+
+where $\mathrm { A T T } ^ { l } ( \cdot ) , \mathrm { L N } ( \cdot )$ , and $\mathrm { F F N } ^ { l } ( \cdot )$ are the attention module, layer normalization, and the feedforward network for the $l$ -th identical layer, respectively. $\{ \mathbf { Q } ^ { l - 1 } , \mathbf { K } ^ { l - 1 } , \mathbf { V } ^ { l - 1 } \}$ are query, key, and value vectors that are transformed from the (l-1)-th layer $\mathbf { H } ^ { l - 1 }$ . For example, $\{ Q ^ { 0 } , K ^ { 0 } , V ^ { 0 } \}$ are packed from the summation $\mathbf { H } ^ { 0 }$ of the positional embeddings and word embeddings. Finally, the output of the stack of $L$ identical layers $\mathbf { \bar { H } } ^ { L }$ is the final source sentence representation.
+
+# 4.2 AGGREGATION FOR TEXT AND IMAGE REPRESENTATIONS
+
+After retrieval as described in Section 3, each original sentence $X ~ = ~ \{ x _ { 1 } , x _ { 2 } , \ldots , x _ { I } \}$ is paired with $m$ images $E = \{ e _ { 1 } , e _ { 2 } , \ldots , e _ { m } \}$ retrieved from the topic-image lookup table $\mathcal { Q }$ . First, the source sentence $X { = } \{ x _ { 1 } , x _ { 2 } , \ldots , x _ { I } \}$ is fed into the encoder (Eq.2) to learn the source sentence representation $\mathbf { H } ^ { L }$ . Second, the images $E = \{ e _ { 1 } , e _ { 2 } , \dots , e _ { m } \}$ are the inputs to a pre-trained ResNet (He et al., 2016) followed by a feed forward layer to learn the source image representation $t e x t M \in$ $R ^ { m \times 2 0 4 8 }$ . Then, we apply an attention mechanism7 to append the image representation to the text representation:
+
+$$
+\begin{array} { r } { \overline { { \mathscr { H } } } = \mathrm { A T T } _ { \mathcal { M } } ( \mathbf { H } ^ { L } , \mathbf { K } _ { \mathcal { M } } , \mathbf { V } _ { \mathcal { M } } ) , } \end{array}
+$$
+
+where $\{ \mathbf { K } _ { \mathcal { M } } , \mathbf { V } _ { \mathcal { M } } \}$ are packed from the learned source image representation $\mathbf { \mathcal { M } }$
+
+Intuitively, NMT aims to produce a target word sequence with the same meaning as the source sentence rather than a group of images. In other words, the image information may play an auxiliary effect during the translation prediction. Therefore, we compute $\lambda \in [ 0 , 1 ]$ to weight the expected importance of source image representation for each source word:
+
+$$
+\lambda = \mathrm { s i g m o i d } ( \mathbf { W } _ { \lambda } \overline { { \pmb { \mathscr { H } } } } + \mathbf { U } _ { \lambda } \mathbf { H } ^ { L } ) ,
+$$
+
+where $\mathbf { W } _ { \lambda }$ and $\mathbf { U } _ { \lambda }$ are model parameters. We then fuse $\mathbf { H } ^ { L }$ and $\overline { { \mathcal { H } } }$ to learn an effective source representation:
+
+$$
+\pmb { \mathcal { H } } = \mathbf { H } ^ { L } + \lambda \overline { { \pmb { \mathcal { H } } } } .
+$$
+
+Finally, $\varkappa$ is fed to the decoder to learn a dependent-time context vector for predicting target translation. Note that there is a single aggregation layer to fuse image and text information.
+
+# 5 EXPERIMENTS
+
+# 5.1 DATA
+
+The proposed method was evaluated on four widely-used translation datasets, including WMT’16 English-to-Romanian (EN-RO), WMT’14 English-to-German (EN-DE), WMT’14 English-toFrench (EN-DE), and Multi30K which are standard corpora for NMT and MMT evaluation.
+
+1) For the EN-RO task, we experimented with the officially provided parallel corpus: Europarl v7 and SETIMES2 from WMT’16 with 0.6M sentence pairs. We used newsdev2016 as the dev set and newstest2016 as the test set.
+
+2) For the EN-DE translation task, 4.43M bilingual sentence pairs of the WMT14 dataset were used as training data, including Common Crawl, News Commentary, and Europarl v7. The newstest2013 and newstest2014 datasets were used as the dev set and test set, respectively.
+
+3) For the EN-FR translation task, 36M bilingual sentence pairs from the WMT14 dataset were used as training data. Newstest12 and newstest13 were combined for validation and newstest14 was used as the test set, following the setting of Gehring et al. (2017).
+
+4) The Multi30K dataset contains 29K English {German, French} parallel sentence pairs with visual annotations. The 1,014 English {German, French $\}$ sentence pairs visual annotations are as dev set. The test sets are test2016 and test2017 with 1,000 pairs for each.
+
+# 5.2 SYSTEM SETTING
+
+Image Retrieval Implementation We used 29,000 sentence-image pairs from Multi30K to build the topic-image lookup table. We segmented the sentences using the same BPE vocabulary as that for each source language. We selected top-8 $\omega = 8$ ) high TF-IDF words, and the default number of images $m$ was set 5. The detailed case study is shown in Section 6.2. After preprocessing, we had about 3K topic words, associated with a total of 10K images for retrieval. Image features were extracted from the averaged pooled features of a pre-trained ResNet50 CNN (He et al., 2016). This led to feature maps V ∈ R2048.
+
+Baseline Our baseline was text-only Transformer (Vaswani et al., 2017). We used six layers for the encoder and the decoder. The number of dimensions of all input and output layers was set to 512 and 1024 for base and big models. The inner feed-forward neural network layer was set to 2048. The heads of all multi-head modules were set to eight in both encoder and decoder layers. For the Multi30K dataset, we further evaluated a multimodal baseline (denoted as MMT) where each source sentence was paired with an original image. The other settings were the same as our proposed model.
+
+Model Implementation The byte pair encoding algorithm was adopted, and the size of the vocabulary was set to 40,000. In each training batch, a set of sentence pairs contained approximately $4 0 9 6 \times 4$ source tokens and $4 0 9 6 \times 4$ target tokens. During training, the value of label smoothing was set to 0.1, and the attention dropout and residual dropout were $p = 0 . 1$ . We used Adam optimizer (Kingma & Ba, 2014) to tune the parameters of the model. The learning rate was varied
+
+<table><tr><td rowspan="2">System</td><td rowspan="2">Architecture</td><td colspan="2">EN-RO</td><td colspan="2">EN-DE</td><td colspan="2">EN-FR</td></tr><tr><td>BLEU #Param</td><td>BLEU</td><td></td><td>#Param</td><td>BLEU</td><td>#Param</td></tr><tr><td colspan="7">ExistingNMTsystems</td></tr><tr><td>Vaswani et al. (2017)</td><td>Trans.(base)</td><td>N/A</td><td>N/A</td><td>27.3</td><td>N/A</td><td>38.1</td><td>N/A</td></tr><tr><td></td><td>Trans.(big)</td><td>N/A</td><td>N/A</td><td>28.4</td><td>N/A</td><td>41.0</td><td>N/A</td></tr><tr><td>Lee et al. (2018)</td><td>Trans.(base)</td><td>32.40</td><td>N/A</td><td>24.57</td><td>N/A</td><td>N/A</td><td>N/A</td></tr><tr><td colspan="8">OurNMTsystems</td></tr><tr><td rowspan="4">This work</td><td>Trans.(base)</td><td>32.66</td><td>61.54M</td><td>27.31</td><td>63.44M</td><td>38.52</td><td>63.83M</td></tr><tr><td>+VR</td><td>33.78++</td><td>63.04M</td><td>28.14++</td><td>64.94M</td><td>39.64++</td><td>65.33M</td></tr><tr><td>Trans. (big)</td><td>33.85</td><td>207.02M</td><td>28.45</td><td>210.88M</td><td>41.10</td><td>211.66M</td></tr><tr><td>+VR</td><td>34.46+</td><td>211.02M</td><td>29.14++</td><td>214.89M</td><td>41.83+</td><td>215.66M</td></tr></table>
+
+Table 1: Results on EN-RO, EN-DE, and EN-FR for the NMT tasks. Trans. is short for transformer. N/A denotes that those numbers are not reported in the corresponding literature. $" + + / + "$ after the BLEU score indicate that the proposed method was significantly better than the corresponding baseline Transformer (base or big) at significance level $p { < } 0 . 0 1 / 0 . 0 5$ .
+
+under a warm-up strategy with 8,000 steps. For evaluation, we validated the model with an interval of 1,000 batches on the dev set. For the Multi30K dataset, we trained the model up to 10,000 steps, and the training was early-stopped if dev set BLEU score did not improve for ten epochs. For the ENDE, EN-RO, and EN-FR tasks, following the training of 200,000 batches, the model with the highest BLEU score of the dev set was selected to evaluate the test sets. During the decoding, the beam size was set to five. All models were trained and evaluated on a single V100 GPU. Multi-bleu.perl8 was used to compute case-sensitive 4-gram BLEU scores for all test sets. The signtest (Collins et al., 2005) is a standard statistical-significance test. In addition, we followed the model configurations of Vaswani et al. (2017) to train Big models for WMT EN-RO, EN-DE, and EN-FR translation tasks. All experiments were conducted with fairseq9 (Ott et al., 2019). The analysis in Section 6 is conducted on base models.
+
+# 5.3 RESULTS
+
+Table 1 shows the results for the WMT’14 EN-DE, EN-FR, and WMT’16 EN-RO translation tasks. Our implemented Transformer (base/big) models showed similar BLEU scores with the original Transformer (Vaswani et al., 2017), ensuring that the proposed method can be evaluated over strong baseline NMT systems. As seen, the proposed $+ \mathrm { V R }$ significantly outperformed the baseline Transformer (base), demonstrating the effectiveness of modeling visual information for text-only NMT. In particular, the effectiveness was adapted to the translation tasks of the three language pairs, which have different scales of training data, verifying that the proposed approach is a universal method for improving translation performance.
+
+Our method introduced only $1 . 5 \mathbf { M }$ and $4 . 0 \mathbf { M }$ parameters for the base and big transformers, respectively. The number is less than $3 \%$ of the baseline parameters as we used the fixed image embeddings from the pre-trained ResNet feature extractor. Besides, the training time was basically the same as the baseline model (Section 6.4).
+
+In addition, the proposed method was also evaluated for MMT on the multimodal dataset, Multi30K. Results in Table 2 show that our model also outperformed the transformer baseline. Compared with the results in text-only NMT, we find that the image presentation gave marginal contribution, which was consistent with the findings in previous work (Zhang et al., 2017; Gronroos et al., 2018; ¨ Caglayan et al., 2019). The most plausible reason might be that the sentences in Multi30K are so simple, short, and repetitive that the source text is sufficient to perform the translation (Caglayan et al., 2019; Ive et al., 2019). This verifies our assumption of the current bottleneck of MMT due to the limitation of Multi30K and shows the necessity of our new setting of transferring multimodality into more standard and mature text-only NMT tasks.
+
+<table><tr><td rowspan="2">System</td><td rowspan="2">Architecture</td><td colspan="3">EN-DE</td><td colspan="3">EN-FR</td></tr><tr><td>Test2016</td><td>Test2017</td><td>#Param</td><td>Test2016</td><td>Test2017</td><td>#Param</td></tr><tr><td colspan="8">Existing NMTsystems</td></tr><tr><td>Calixto et al. (2017)</td><td>RNN</td><td>33.7</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td></tr><tr><td>Elliott et al. (2017)</td><td>RNN</td><td>N/A</td><td>19.3</td><td>N/A</td><td>N/A</td><td>44.3</td><td>N/A</td></tr><tr><td>Elliott &amp; Kadar (2017)</td><td>Imagination</td><td>36.8</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td></tr><tr><td rowspan="2">Ive et al. (2019)</td><td>Trans. (big)</td><td>36.4</td><td>N/A</td><td>N/A</td><td>59.0</td><td>N/A</td><td>N/A</td></tr><tr><td>Del</td><td>38.0</td><td>N/A</td><td>N/A</td><td>60.1</td><td>N/A</td><td>N/A</td></tr><tr><td colspan="8">Our MMTsystems</td></tr><tr><td rowspan="6">This work</td><td>MMT.(base)</td><td>35.09</td><td>27.10</td><td>50.72M</td><td>57.40</td><td>48.02</td><td>50.65M</td></tr><tr><td>MMT.(big)</td><td>35.60</td><td>28.02</td><td>190.58M</td><td>57.87</td><td>49.63</td><td>190.43M</td></tr><tr><td>Trans.(base)</td><td>35.59</td><td>26.31</td><td>49.15M</td><td>57.88</td><td>48.55</td><td>49.07M</td></tr><tr><td>+VR</td><td>35.72</td><td>26.87</td><td>50.72M</td><td>58.32</td><td>48.69</td><td>50.65M</td></tr><tr><td>Trans. (big)</td><td>36.86</td><td>27.62</td><td>186.38M</td><td>56.97</td><td>48.17</td><td>186.23M</td></tr><tr><td>+VR</td><td>36.94</td><td>28.63</td><td>190.58M</td><td>57.53</td><td>48.46</td><td>190.43M</td></tr></table>
+
+Table 2: Results from the test2016 and test2017 for the MMT task. Del denotes the deliberation network in (Ive et al., 2019). Elliott et al. (2017) is the official baseline (text-only NMT) on WMT17- Multi30K 2017 test data. Trans. is short for transformer and MMT is the multimodal baseline described in Section 5.2. Because we used the same model for test2016 and test2017 evaluation, the numbers of parameters are the same.
+
+# 6 ANALYSIS
+
+# 6.1 WHY DOES THE LOOKUP TABLE WORK
+
+The contribution of the lookup table could be two folds: 1) the content connection of the sentences and images; 2) the topic-aware co-occurrence of similar images and sentences. There are cases when paired images are not accurately related to the given sentence. A simple solution is to set a threshold heuristically for the TF-IDF retrieval to filter out the “improper” images. However, we maintain the specific number of the images in this work because of the second potential benefits of the cooccurrence, by taking images as diverse topic information. According to Distributional Hypothesis (Harris, 1954), which states that words that occur in similar contexts tend to have similar meanings, we are inspired to extend the concept in the multimodal world, the sentences with similar meanings would be likely to pair with similar even the same images. Therefore, the consistent images (with a related topic) could play the role of topic or type hints for similar sentence modeling.
+
+This is also very similar to the idea of word embedding by taking each image as a “word”. Because we use the average pooled output of ResNet, each image is represented as a 2400-d vector. For all the 29,000 images, we have an embedding layer with size (29000, 2400). The “content” of the image is regarded as the embedding initialization. It indeed makes effects, but the capacity of the neural network is not up to it. In contrast, the mapping from text word to the index in the word embedding is critical. Similarly, the mapping of sentence to image in image embedding would be essential, i.e., the similar sentences (with the same topic words) tend to map the same or similar image.
+
+To verify the hypotheses, we replace our ResNet features with 1) Shuffle: shuffle the image features but keep the lookup table; 2) Random Init: randomly initialize the image embedding but keep the lookup table; 3) Random Mapping: randomly retrieve unrelated images. The BLEU scores are on EN-RO are 33.53, 33,28, 32.14, respectively. The results of 1-2 are close to the proposed VR (33.78) and outperform the baseline (32.66), which shows that the content of images would not be very important. The ablation 3) gives a lower result, which verifies the necessity of the mapping, especially the topic relationship.
+
+# 6.2 INFLUENCE OF THE NUMBER OF IMAGES
+
+To evaluate the influence of the number of paired images $m$ , we constrained $m$ in $\{ 0 , 1 , 3 , 5 , 7 , 9 ,$ $1 5 , 2 0 , 3 0 \}$ for experiments on the EN-RO test set, as shown in Figure 4. When $m = 0$ , the model is the baseline NMT model, whose BLEU score was lower than all the models with images. As the number of images increases, the BLEU score also increased at the beginning (from 32.66 to 33.78)
+
+and then slightly decreased when $m$ exceeds 5. The reason might be that too many images for a sentence would have a higher chance of noise. Therefore, we set $m = 5$ in our models.
+
+The number of sentence-image pairs to create the lookup table could also make effects. We randomly split the pairs of Multi30K into the proportion in [0.1, 0.3, 0.5, 0.7, 0.9], the corresponding BLEU scores for EN-RO are [33.07, 33.44, 34.01, 34.06, 33.80]. Furthermore, we also evaluate the performance by adding external sentence-pairs from the training set of MS COCO image caption dataset (Lin et al., 2014). The BLEU scores are 33.55 and 33.71, respectively, for COCO only and Mult $1 3 0 \mathrm { K + C O C O }$ . These results indicate that a modest number of pairs would be beneficial.
+
+# 6.3 THE INFLUENCE OF GATING WEIGHT λ
+
+![](images/4afe8a65f062ea1895711881c063117fba5d70ddc29a026e2c577a7da5e5e8cd.jpg)  
+Figure 4: Influence of the number of images on the BLEU score.
+
+![](images/2cf68d92dc3d17de00225cf8437e911eec88366d65a4a253c5cc7df8c22e8536.jpg)  
+Figure 5: Quantitative study of the gating weight $\lambda$ .
+
+In our model, the weight $\lambda$ of the gated aggregation method was learned automatically to measure the importance of the visual information. We compared by manually setting the weight $\lambda$ into scalar values in $\{ 0 . 1 , 0 . 3 , 0 . 5 , 0 . 7 , 0 . 9 \}$ for experiments on the EN-RO test set. Figure 5 shows that all models with manual $\lambda$ outperformed the baseline Trans. (base), indicating the effectiveness of image information. In contrast, they were inferior to the performance of our model. This means that the degree of dependency for image information varies for each source sentence, indicating the necessity of automatically learning the gating weights of image representations.
+
+# 6.4 EXTRA COMPUTATION TIME
+
+There are mainly two extra computation costs using our method, including 1) obtaining image data for sentences and 2) learning image representations, which are negligible compared with training an NMT model. The time of obtaining image data for MT sentences for the EN-RO dataset is less than 1 minute using GPU. The lookup table is formed as the mapping of token (only topic words) index to image id. Then, the retrieval method is applied as the tensor indexing from the sentence token indices (only topic words) to image ids, which is the same as the procedure of word embedding. The retrieved image ids are then sorted by frequency. Learning image representations takes about 2 minutes for all the 29,000 images in Multi30K using 6G GPU memory for feature extraction and eight threads of CPU for transforming images. The extracted features are formed as the “image embedding layer” with the size of (29000, 2400) for quick access in the neural network.
+
+# 7 CONCLUSION
+
+This work presents a universal visual representation method for neural machine translation relying on monolingual image annotations, which breaks the restraint of heavy dependency on bilingual sentence-image pairs in the current multimodal NMT setting. In particular, this method enables visual information to be applied to large-scale text-only NMT through a topic-image lookup. We hope this work sheds some light on future MMT research. In the future, we will try to adopt the proposed method for other tasks.
+
+# REFERENCES
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+Chunting Zhou, Xuezhe Ma, Junjie Hu, and Graham Neubig. Handling syntactic divergence in low-resource machine translation. arXiv preprint arXiv:1909.00040, 2019.
+
+A APPENDIX
+
+A.1 EXAMPLES OF RETRIEVED IMAGES
+
+![](images/293a5463d7433f9fcf3db43d8f8e360e7f0c0a86cb0f1e2cbf762a4bcdf0de49.jpg)  
+Figure 5: Examples of the topic-image lookup table and retrieved images for sentences in Multi30K dataset. We only show six images for each topic or sentence for instance. The topics in each sentence are in boldface.
+
+The old system of private arbitration courts is off the table
+
+![](images/e5ba119ecb4055c44d9ac56f8f958a5bf101cbc9dfd928f44a8f71b79e2c460d.jpg)
+
+This issue is shaping as a potential early rift with the business community
+
+![](images/42433a729a2739381d56bd5a48c8efe8b2f45ab2f7e88db467ebdf9f4a94fba9.jpg)
+
+He said he then heard his friend , Hamza calling to him
+
+![](images/3ef3ba5df5780e6c074b6b54dd18c1288a6010c367ada066a6c05dccf074ad88.jpg)
+
+The red flag has been risen
+
+![](images/feaeea2efe7f95fcdd779fa0dfcbc2340d2b06448715b7e1cbee82ec6754e002.jpg)
+
+The character attempts to pass human smugglers and then border police on his way to a refugee centre in the European Union .
+
+![](images/6a2a396fc01022d989bc1aaf0e76e67498ceb7789654193b875e7f01d6cafe83.jpg)  
+Figure 6: Examples of the retrieved images for sentences in WMT datasets. We only show six images for each sentence for instance. The topics in each sentence are in boldface.

parse/train/Byl8hhNYPS/Byl8hhNYPS_content_list.json

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+    {
+        "type": "text",
+        "text": "NEURAL MACHINE TRANSLATION WITH UNIVERSAL VISUAL REPRESENTATION ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Zhuosheng Zhang1,2,3, Kehai Chen4, Rui Wang4,∗, Masao Utiyama4, Eiichiro Sumita4, Zuchao Li1,2,3 , Hai Zhao1,2,3,∗ ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "1Department of Computer Science and Engineering, Shanghai Jiao Tong University 2Key Laboratory of Shanghai Education Commission for Intelligent Interaction and Cognitive Engineering, Shanghai Jiao Tong University, Shanghai, China 3MoE Key Lab of Artificial Intelligence, AI Institute, Shanghai Jiao Tong University 4National Institute of Information and Communications Technology (NICT), Kyoto, Japan zhangzs@sjtu.edu.cn, charlee@sjtu.edu.cn, zhaohai@cs.sjtu.edu.cn, {khchen, wangrui, mutiyama, eiichiro.sumita}@nict.go.jp ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "ABSTRACT ",
+        "text_level": 1,
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+    },
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+        "type": "text",
+        "text": "Though visual information has been introduced for enhancing neural machine translation (NMT), its effectiveness strongly relies on the availability of large amounts of bilingual parallel sentence pairs with manual image annotations. In this paper, we present a universal visual representation learned over the monolingual corpora with image annotations, which overcomes the lack of largescale bilingual sentence-image pairs, thereby extending image applicability in NMT. In detail, a group of images with similar topics to the source sentence will be retrieved from a light topic-image lookup table learned over the existing sentence-image pairs, and then is encoded as image representations by a pretrained ResNet. An attention layer with a gated weighting is to fuse the visual information and text information as input to the decoder for predicting target translations. In particular, the proposed method enables the visual information to be integrated into large-scale text-only NMT in addition to the multimodal NMT. Experiments on four widely used translation datasets, including the WMT’16 English-to-Romanian, WMT’14 English-to-German, WMT’14 Englishto-French, and Multi30K, show that the proposed approach achieves significant improvements over strong baselines. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
+        "bbox": [
+            176,
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+            334,
+            646
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Visual information has been introduced for neural machine translation in some previous studies (NMT) (Specia et al., 2016; Elliott et al., 2017; Barrault et al., 2018; Ive et al., 2019) though the contribution of images is still an open question (Elliott, 2018; Caglayan et al., 2019). Typically, each bilingual (or multilingual) parallel sentence pair is annotated manually by one image describing the content of this sentence pair. The bilingual parallel corpora with manual image annotations are used to train a multimodal NMT model by an end-to-end framework, and results are reported on a specific data set, Multi30K (Calixto & Liu, 2017; Calixto et al., 2017). ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "One strong point of the multimodal NMT model is the ability to use visual information to improve the quality of the target translation. However, the effectiveness heavily relies on the availability of bilingual parallel sentence pairs with manual image annotations, which hinders the image applicability to the NMT. As a result, the visual information is only applied to the translation task over a small and specific multimodal data set Multi30K (Elliott et al., 2016), but not to large-scale text-only NMT (Bahdanau et al., 2014; Gehring et al., 2017; Vaswani et al., 2017) and low-resource text-only NMT (Fadaee et al., 2017; Lample et al., 2018; Ma et al., 2019; Zhou et al., 2019). In addition, because of the high cost of annotation, the content of one bilingual parallel sentence pair is only represented by a single image, which is weak in capturing the diversity of visual information. The current situation of introducing visual information results in a bottleneck in the multimodal NMT and is not feasible for text-only NMT and low-resource NMT. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In this paper, we present a universal visual representation (VR) method1 relying only on image-monolingual annotations instead of the existing approach that depends on image-bilingual annotations, thus breaking the bottleneck of using visual information in NMT. In detail, we transform the existing sentence-image pairs into a topic-image lookup table from a small-scale multimodal data set Multi30K. During the training and decoding process, a group of images with a similar topic to the source sentence will be retrieved from the topic-image lookup table learned by the term frequency-inverse document frequency, and thus is encoded as image representations by a pretrained ResNet (He et al., 2016). A simple and effective attention layer is then designed to fuse the image representations and the original source sentence representations as input to the decoder for predicting target translations. In particular, the proposed approach can be easily integrated into the text-only NMT model without annotating large-scale bilingual parallel corpora. The proposed method was evaluated on four widely-used translation datasets, including the WMT’16 Englishto-Romanian, WMT’14 English-to-German, WMT’14 English-to-French, and Multi30K which are standard corpora for NMT and multimodal machine translation (MMT) evaluation. Experiments and analyses show effectiveness. In summary, our contributions are primarily three-fold: ",
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+    {
+        "type": "text",
+        "text": "1. We present a universal visual representation method that overcomes the shortcomings of the bilingual (or multilingual) parallel data with manual image annotations for MMT.   \n2. The proposed method enables the text-only NMT to use the multimodality of visual information without annotating the existing large scale bilingual parallel data.   \n3. Experiments on different scales of translation tasks verified the effectiveness and generality of the proposed approach. ",
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+    {
+        "type": "text",
+        "text": "2 RELATED WORK ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Building fine-grained representation with extra knowledge is an essential topic in language modeling (Li et al., 2020a;b; Zhang et al., 2020b;a), among which adopting visual modality could potentially benefit the machine with a more comprehensive perception of the real world. Inspired by the studies on the image description generation (IDG) task (Mao et al., 2014; Elliott et al., 2015; Venugopalan et al., 2015; Xu et al., 2015), a new shared translation task for multimodal machine translation was addressed by the machine translation community (Specia et al., 2016). In particular, the released dataset Multi30K (Elliott et al., 2016) includes 29,000 multilingual (English, German, and French) parallel sentence pairs with image annotations (Elliott et al., 2017; Barrault et al., 2018). Subsequently, there has been a rise in the number of studies (Caglayan et al., 2016; 2017; Calixto et al., 2016; Huang et al., 2016; Libovicky & Helcl, 2017; Helcl et al., 2018). For \\` example, Calixto et al. (2017) proposed a doubly-attentive multimodal NMT model to incorporate spatial-visual features, improving translation performance. Compared with spatial-visual features, Calixto & Liu (2017) further incorporated global image features as words in the source sentence and to enhance the encoder or decoder hidden state. In contrast, some recent studies indicated that the visual modality is either unnecessary (Zhang et al., 2017) or only marginally beneficial (Gronroos ¨ et al., 2018). More recently, Ive et al. (2019) showed that visual information is only needed in particular cases, such as for ambiguous words where the textual context is not sufficient. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "However, these approaches only center around a small and specific Multi30K data set to build a multimodal NMT model, which hinders image applicability to NMT. The reason would be the high cost of image annotations, resulting potentially in the image information not being adequately discovered. We believe that the capacity of MMT has not yet been excavated sufficiently, and there is still a long way to go before the potential of MMT is fully discovered. In this work, we seek to break this constraint and enable visual information to benefit NMT, especially text-only NMT. ",
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+    {
+        "type": "text",
+        "text": "3 UNIVERSAL VISUAL RETRIEVAL ",
+        "text_level": 1,
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+    {
+        "type": "table",
+        "img_path": "images/defc9f518dc7533012149235c5366d1974794c375d0f02385a9512b421bf3035.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td colspan=\"2\">Algorithm1 Topic-image Lookup Table Conversion Algorithm</td></tr><tr><td>Require: Input sentences, S= {Xi, X2,... X1} and paired images E = {e1,e2,...,e1} 1:Obtain the TF-IDF dictionary F= TF-IDF(S) 2: 3: procedure TF-IDF(S)</td><td>Ensure: Topic-image lookup table Q where each word is associated with a group of images Transform sentence-image pair to topic-image lookup table Q= LookUp(S,E,F)</td></tr><tr><td>4: for each sentence in S do 5: end for</td><td>Filter stop-words in the sentence</td></tr><tr><td>6:</td><td>Calculate the TF-IDF weight for each word</td></tr><tr><td>7: 8:</td><td></td></tr><tr><td>9:</td><td></td></tr><tr><td></td><td>return TF-IDF dictionary F</td></tr><tr><td>10:</td><td>end procedure</td></tr><tr><td>11:</td><td>procedure LOOKUP(S,E,F)</td></tr><tr><td>12:</td><td>for For each pair{Ti,ei} ∈zip{S,E}do</td></tr><tr><td></td><td>Rank and pick out the top-w“topic” words in the sentence according to the TF-IDF</td></tr><tr><td>13:</td><td>score in the dictionary F,and each sentence is reformed as T= {t1,t2,...,tw}</td></tr><tr><td>14:</td><td>Pair the w words with the corresponding image ei</td></tr><tr><td>15:</td><td>for For each word tjin T do</td></tr><tr><td></td><td>if ei not in Q[tj] then</td></tr><tr><td>16:</td><td></td></tr><tr><td>17:</td><td>Add ej to the corresponding image set Q[tj] for word t j</td></tr><tr><td>18:</td><td>end if</td></tr><tr><td></td><td></td></tr><tr><td>19:</td><td>end for</td></tr><tr><td></td><td></td></tr><tr><td>20:</td><td>end for</td></tr><tr><td></td><td></td></tr><tr><td>21:</td><td>return Topic-image lookup table Q</td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td>end procedure</td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr></table>",
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In this section, we will introduce the proposed universal visual representation method. Generally, the default input setting of the MMT is a sentence-image pair. Our basic intuition is to transform the existing sentence-image pairs into topic-image lookup table2, which assumes the topic words in a sentence should be relevant to the paired image. Consequently, a sentence can possess a group of images by retrieving the topic-image lookup table. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Topic-image Lookup Table Conversion To focus on the major part of the sentence and suppress the noise such as stopwords and low-frequency words, we design a filtering method to extract the “topic” words of the sentence through the term frequency-inverse document frequency $( \\mathrm { T F - I D F } ) ^ { 3 }$ inspired by Chen et al. (2019). Specifically, given an original input sentence $X = \\{ x _ { 1 } , x _ { 2 } , \\dots , x _ { I } \\}$ of length $I$ and its paired image $e$ , $X$ is first filtered by a stopword list4 and then the sentence is treated as a document $g$ . We then compute TF-IDF $T I _ { i , j }$ for each word $x _ { i }$ in $g$ , ",
+        "bbox": [
+            173,
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+    },
+    {
+        "type": "equation",
+        "img_path": "images/5e6adfd4a11803de2c3e651c913f01404a6b2137ee63c87007ff743efb324361.jpg",
+        "text": "$$\nT I _ { i , j } = \\frac { o _ { i , j } } { \\sum _ { k } o _ { k , j } } \\times \\log \\frac { | { G } | } { 1 + | { j } : { x } _ { i } \\in { g } | } ,\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where $o _ { i , j }$ represents the number of occurrences of the word $x _ { i }$ in the input sentence $g$ , $| G |$ the total number of source language sentences in the training data, and $| j : x _ { i } \\in g |$ the number of source sentences including word $x _ { i }$ in the training data. We then select the top- $w$ high TF-IDF words as the new image description $T = \\{ t _ { 1 } , t _ { 2 } , \\dots , t _ { w } \\}$ for the input sentence $X$ . After preprocessing, each filtered sentence $T$ is paired with an image $e$ , and each word $t _ { i } \\in T$ is regarded as the topic word for image $e$ . After processing the whole corpus (i.e., Multi30K), we form a topic-image lookup table $\\mathcal { Q }$ as described in Algorithm 1, in which each topic word $t _ { i }$ would be paired with dozens of images. ",
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+    {
+        "type": "text",
+        "text": "Image Retrieval For the input sentence, we first obtain its topic words according to the text preprocessing method described above. Then we retrieve the associated images for each topic word from the lookup table $\\mathcal { Q }$ and group all the retrieved images together to form an image list $\\mathcal { G }$ . We observe that an image might be associated with multiple topic words so that it would occur multiple times in the list $\\mathcal { G }$ . Therefore, we sort the images according to the frequency of occurrences in $\\mathcal { G }$ to maintain the total number of images for each sentence at $m$ . ",
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+        "type": "image",
+        "img_path": "images/ec6ef9a373972526443f987670429f17c4cfcb962c73244ef05b7230b637fbcc.jpg",
+        "image_caption": [
+            "Figure 1: Illustration of the proposed visual retrieval. "
+        ],
+        "image_footnote": [],
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+        "type": "text",
+        "text": "",
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+    {
+        "type": "text",
+        "text": "Figure 1 illustrates the retrieval process5. In the left block, we show six examples of sentence-image pairs in which the topic words are in boldface. Then we process the corpus using the topic-image transformation method demonstrated above and obtain the topic-image lookup table. For example, the word dog is associated with 1,512 images. For an input source sentence, we obtain the topic words (in boldface) using the same preprocessing. Then we retrieve the corresponding images from the lookup table for each topic word. Now we have a list of images, and some images appear multiple times as they have various topics (like the boxed image in Figure 1). So we sort the retrieved image list by the count of occurrence to pick out the top- $m$ images that cover the most topics of the sentence. ",
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+        "type": "text",
+        "text": "At test time, the process of getting images is done using the image lookup table built by the training set, so we do not need to use the images from the dev and test sets in Multi30K dataset6. Intuitively, we do not strictly require the manual alignment of the word (or concept) and image, but rely on the co-occurrence of topic word and image, which is simpler and more general. In this way, we call our method as universal visual retrieval. ",
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+    {
+        "type": "text",
+        "text": "4 NMT WITH UNIVERSAL VISUAL REPRESENTATION ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In this section, we introduce the proposed universal visual representation (VR) method for NMT.   \nThe overview of the framework of our proposed method is shown in Figure 2. ",
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+    {
+        "type": "text",
+        "text": "4.1 SOURCE REPRESENTATION FOR NEURAL MACHINE TRANSLATION ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In the state-of-the-art Transformer-based NMT (Vaswani et al., 2017), source information is encoded as source representation by an SAN-based encoder with multiple layers. Specifically, the encoder is composed of a stack of $L$ identical layers, each of which includes two sub-layers. The first sublayer is a self-attention module, whereas the second is a position-wise, fully connected feed-forward network. A residual connection (He et al., 2016) is applied between the two sub-layers, and then a layer normalization (Ba et al., 2016) is performed. Formally, the stack of learning the source representation is organized as follows: ",
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+    {
+        "type": "image",
+        "img_path": "images/c4aaf77a9b3f70bdd6db859235887c88b50e0497f0bb88b7a5d30fb871a689b9.jpg",
+        "image_caption": [
+            "Figure 2: Overview of the framework of our proposed method. "
+        ],
+        "image_footnote": [],
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+        "type": "text",
+        "text": "",
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+    {
+        "type": "equation",
+        "img_path": "images/cc0b3aa12284535f464095aa3124201fde3ed32ba427b49331568468b9474b0d.jpg",
+        "text": "$$\n\\begin{array} { r l } & { \\overline { { \\mathbf { H } } } ^ { l } = \\mathrm { L N } ( \\mathrm { A T T } ^ { l } ( \\mathbf { Q } ^ { l - 1 } , \\mathbf { K } ^ { l - 1 } , \\mathbf { V } ^ { l - 1 } ) + \\mathbf { H } ^ { l - 1 } ) , } \\\\ & { \\mathbf { H } ^ { l } = \\mathrm { L N } ( \\mathrm { F F N } ^ { l } ( \\overline { { \\mathbf { H } } } ^ { l } ) + \\overline { { \\mathbf { H } } } ^ { l } ) , } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
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+            563,
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+    },
+    {
+        "type": "text",
+        "text": "where $\\mathrm { A T T } ^ { l } ( \\cdot ) , \\mathrm { L N } ( \\cdot )$ , and $\\mathrm { F F N } ^ { l } ( \\cdot )$ are the attention module, layer normalization, and the feedforward network for the $l$ -th identical layer, respectively. $\\{ \\mathbf { Q } ^ { l - 1 } , \\mathbf { K } ^ { l - 1 } , \\mathbf { V } ^ { l - 1 } \\}$ are query, key, and value vectors that are transformed from the (l-1)-th layer $\\mathbf { H } ^ { l - 1 }$ . For example, $\\{ Q ^ { 0 } , K ^ { 0 } , V ^ { 0 } \\}$ are packed from the summation $\\mathbf { H } ^ { 0 }$ of the positional embeddings and word embeddings. Finally, the output of the stack of $L$ identical layers $\\mathbf { \\bar { H } } ^ { L }$ is the final source sentence representation. ",
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+    },
+    {
+        "type": "text",
+        "text": "4.2 AGGREGATION FOR TEXT AND IMAGE REPRESENTATIONS ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "After retrieval as described in Section 3, each original sentence $X ~ = ~ \\{ x _ { 1 } , x _ { 2 } , \\ldots , x _ { I } \\}$ is paired with $m$ images $E = \\{ e _ { 1 } , e _ { 2 } , \\ldots , e _ { m } \\}$ retrieved from the topic-image lookup table $\\mathcal { Q }$ . First, the source sentence $X { = } \\{ x _ { 1 } , x _ { 2 } , \\ldots , x _ { I } \\}$ is fed into the encoder (Eq.2) to learn the source sentence representation $\\mathbf { H } ^ { L }$ . Second, the images $E = \\{ e _ { 1 } , e _ { 2 } , \\dots , e _ { m } \\}$ are the inputs to a pre-trained ResNet (He et al., 2016) followed by a feed forward layer to learn the source image representation $t e x t M \\in$ $R ^ { m \\times 2 0 4 8 }$ . Then, we apply an attention mechanism7 to append the image representation to the text representation: ",
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+    {
+        "type": "equation",
+        "img_path": "images/185e5439db35160603490c27b9c92a26ad5c51777553cad91e3658049e84e79b.jpg",
+        "text": "$$\n\\begin{array} { r } { \\overline { { \\mathscr { H } } } = \\mathrm { A T T } _ { \\mathcal { M } } ( \\mathbf { H } ^ { L } , \\mathbf { K } _ { \\mathcal { M } } , \\mathbf { V } _ { \\mathcal { M } } ) , } \\end{array}\n$$",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "where $\\{ \\mathbf { K } _ { \\mathcal { M } } , \\mathbf { V } _ { \\mathcal { M } } \\}$ are packed from the learned source image representation $\\mathbf { \\mathcal { M } }$ ",
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+        "type": "text",
+        "text": "Intuitively, NMT aims to produce a target word sequence with the same meaning as the source sentence rather than a group of images. In other words, the image information may play an auxiliary effect during the translation prediction. Therefore, we compute $\\lambda \\in [ 0 , 1 ]$ to weight the expected importance of source image representation for each source word: ",
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+    {
+        "type": "equation",
+        "img_path": "images/d444fefa305388b408ca9b6a434b610fc66bd2b15a1e0d9cd3bec9bd1acc68aa.jpg",
+        "text": "$$\n\\lambda = \\mathrm { s i g m o i d } ( \\mathbf { W } _ { \\lambda } \\overline { { \\pmb { \\mathscr { H } } } } + \\mathbf { U } _ { \\lambda } \\mathbf { H } ^ { L } ) ,\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where $\\mathbf { W } _ { \\lambda }$ and $\\mathbf { U } _ { \\lambda }$ are model parameters. We then fuse $\\mathbf { H } ^ { L }$ and $\\overline { { \\mathcal { H } } }$ to learn an effective source representation: ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "img_path": "images/c8ad9ce2aeb2b3a0bda97c9e25e990f4b12208e45970b8458cae5e2b3e5055e6.jpg",
+        "text": "$$\n\\pmb { \\mathcal { H } } = \\mathbf { H } ^ { L } + \\lambda \\overline { { \\pmb { \\mathcal { H } } } } .\n$$",
+        "text_format": "latex",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Finally, $\\varkappa$ is fed to the decoder to learn a dependent-time context vector for predicting target translation. Note that there is a single aggregation layer to fuse image and text information. ",
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+    {
+        "type": "text",
+        "text": "5 EXPERIMENTS ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "5.1 DATA ",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "The proposed method was evaluated on four widely-used translation datasets, including WMT’16 English-to-Romanian (EN-RO), WMT’14 English-to-German (EN-DE), WMT’14 English-toFrench (EN-DE), and Multi30K which are standard corpora for NMT and MMT evaluation. ",
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+    {
+        "type": "text",
+        "text": "1) For the EN-RO task, we experimented with the officially provided parallel corpus: Europarl v7 and SETIMES2 from WMT’16 with 0.6M sentence pairs. We used newsdev2016 as the dev set and newstest2016 as the test set. ",
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+    },
+    {
+        "type": "text",
+        "text": "2) For the EN-DE translation task, 4.43M bilingual sentence pairs of the WMT14 dataset were used as training data, including Common Crawl, News Commentary, and Europarl v7. The newstest2013 and newstest2014 datasets were used as the dev set and test set, respectively. ",
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+    },
+    {
+        "type": "text",
+        "text": "3) For the EN-FR translation task, 36M bilingual sentence pairs from the WMT14 dataset were used as training data. Newstest12 and newstest13 were combined for validation and newstest14 was used as the test set, following the setting of Gehring et al. (2017). ",
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+    },
+    {
+        "type": "text",
+        "text": "4) The Multi30K dataset contains 29K English {German, French} parallel sentence pairs with visual annotations. The 1,014 English {German, French $\\}$ sentence pairs visual annotations are as dev set. The test sets are test2016 and test2017 with 1,000 pairs for each. ",
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+    {
+        "type": "text",
+        "text": "5.2 SYSTEM SETTING ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Image Retrieval Implementation We used 29,000 sentence-image pairs from Multi30K to build the topic-image lookup table. We segmented the sentences using the same BPE vocabulary as that for each source language. We selected top-8 $\\omega = 8$ ) high TF-IDF words, and the default number of images $m$ was set 5. The detailed case study is shown in Section 6.2. After preprocessing, we had about 3K topic words, associated with a total of 10K images for retrieval. Image features were extracted from the averaged pooled features of a pre-trained ResNet50 CNN (He et al., 2016). This led to feature maps V ∈ R2048. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Baseline Our baseline was text-only Transformer (Vaswani et al., 2017). We used six layers for the encoder and the decoder. The number of dimensions of all input and output layers was set to 512 and 1024 for base and big models. The inner feed-forward neural network layer was set to 2048. The heads of all multi-head modules were set to eight in both encoder and decoder layers. For the Multi30K dataset, we further evaluated a multimodal baseline (denoted as MMT) where each source sentence was paired with an original image. The other settings were the same as our proposed model. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Model Implementation The byte pair encoding algorithm was adopted, and the size of the vocabulary was set to 40,000. In each training batch, a set of sentence pairs contained approximately $4 0 9 6 \\times 4$ source tokens and $4 0 9 6 \\times 4$ target tokens. During training, the value of label smoothing was set to 0.1, and the attention dropout and residual dropout were $p = 0 . 1$ . We used Adam optimizer (Kingma & Ba, 2014) to tune the parameters of the model. The learning rate was varied ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/31ba0171280d6bb266d7f31e0843bfbed84ca390f0bb738fbd08fdee8047d1d3.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">System</td><td rowspan=\"2\">Architecture</td><td colspan=\"2\">EN-RO</td><td colspan=\"2\">EN-DE</td><td colspan=\"2\">EN-FR</td></tr><tr><td>BLEU #Param</td><td>BLEU</td><td></td><td>#Param</td><td>BLEU</td><td>#Param</td></tr><tr><td colspan=\"7\">ExistingNMTsystems</td></tr><tr><td>Vaswani et al. (2017)</td><td>Trans.(base)</td><td>N/A</td><td>N/A</td><td>27.3</td><td>N/A</td><td>38.1</td><td>N/A</td></tr><tr><td></td><td>Trans.(big)</td><td>N/A</td><td>N/A</td><td>28.4</td><td>N/A</td><td>41.0</td><td>N/A</td></tr><tr><td>Lee et al. (2018)</td><td>Trans.(base)</td><td>32.40</td><td>N/A</td><td>24.57</td><td>N/A</td><td>N/A</td><td>N/A</td></tr><tr><td colspan=\"8\">OurNMTsystems</td></tr><tr><td rowspan=\"4\">This work</td><td>Trans.(base)</td><td>32.66</td><td>61.54M</td><td>27.31</td><td>63.44M</td><td>38.52</td><td>63.83M</td></tr><tr><td>+VR</td><td>33.78++</td><td>63.04M</td><td>28.14++</td><td>64.94M</td><td>39.64++</td><td>65.33M</td></tr><tr><td>Trans. (big)</td><td>33.85</td><td>207.02M</td><td>28.45</td><td>210.88M</td><td>41.10</td><td>211.66M</td></tr><tr><td>+VR</td><td>34.46+</td><td>211.02M</td><td>29.14++</td><td>214.89M</td><td>41.83+</td><td>215.66M</td></tr></table>",
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Table 1: Results on EN-RO, EN-DE, and EN-FR for the NMT tasks. Trans. is short for transformer. N/A denotes that those numbers are not reported in the corresponding literature. $\" + + / + \"$ after the BLEU score indicate that the proposed method was significantly better than the corresponding baseline Transformer (base or big) at significance level $p { < } 0 . 0 1 / 0 . 0 5$ . ",
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+    },
+    {
+        "type": "text",
+        "text": "under a warm-up strategy with 8,000 steps. For evaluation, we validated the model with an interval of 1,000 batches on the dev set. For the Multi30K dataset, we trained the model up to 10,000 steps, and the training was early-stopped if dev set BLEU score did not improve for ten epochs. For the ENDE, EN-RO, and EN-FR tasks, following the training of 200,000 batches, the model with the highest BLEU score of the dev set was selected to evaluate the test sets. During the decoding, the beam size was set to five. All models were trained and evaluated on a single V100 GPU. Multi-bleu.perl8 was used to compute case-sensitive 4-gram BLEU scores for all test sets. The signtest (Collins et al., 2005) is a standard statistical-significance test. In addition, we followed the model configurations of Vaswani et al. (2017) to train Big models for WMT EN-RO, EN-DE, and EN-FR translation tasks. All experiments were conducted with fairseq9 (Ott et al., 2019). The analysis in Section 6 is conducted on base models. ",
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "5.3 RESULTS ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Table 1 shows the results for the WMT’14 EN-DE, EN-FR, and WMT’16 EN-RO translation tasks. Our implemented Transformer (base/big) models showed similar BLEU scores with the original Transformer (Vaswani et al., 2017), ensuring that the proposed method can be evaluated over strong baseline NMT systems. As seen, the proposed $+ \\mathrm { V R }$ significantly outperformed the baseline Transformer (base), demonstrating the effectiveness of modeling visual information for text-only NMT. In particular, the effectiveness was adapted to the translation tasks of the three language pairs, which have different scales of training data, verifying that the proposed approach is a universal method for improving translation performance. ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Our method introduced only $1 . 5 \\mathbf { M }$ and $4 . 0 \\mathbf { M }$ parameters for the base and big transformers, respectively. The number is less than $3 \\%$ of the baseline parameters as we used the fixed image embeddings from the pre-trained ResNet feature extractor. Besides, the training time was basically the same as the baseline model (Section 6.4). ",
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "In addition, the proposed method was also evaluated for MMT on the multimodal dataset, Multi30K. Results in Table 2 show that our model also outperformed the transformer baseline. Compared with the results in text-only NMT, we find that the image presentation gave marginal contribution, which was consistent with the findings in previous work (Zhang et al., 2017; Gronroos et al., 2018; ¨ Caglayan et al., 2019). The most plausible reason might be that the sentences in Multi30K are so simple, short, and repetitive that the source text is sufficient to perform the translation (Caglayan et al., 2019; Ive et al., 2019). This verifies our assumption of the current bottleneck of MMT due to the limitation of Multi30K and shows the necessity of our new setting of transferring multimodality into more standard and mature text-only NMT tasks. ",
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+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">System</td><td rowspan=\"2\">Architecture</td><td colspan=\"3\">EN-DE</td><td colspan=\"3\">EN-FR</td></tr><tr><td>Test2016</td><td>Test2017</td><td>#Param</td><td>Test2016</td><td>Test2017</td><td>#Param</td></tr><tr><td colspan=\"8\">Existing NMTsystems</td></tr><tr><td>Calixto et al. (2017)</td><td>RNN</td><td>33.7</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td></tr><tr><td>Elliott et al. (2017)</td><td>RNN</td><td>N/A</td><td>19.3</td><td>N/A</td><td>N/A</td><td>44.3</td><td>N/A</td></tr><tr><td>Elliott &amp; Kadar (2017)</td><td>Imagination</td><td>36.8</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td></tr><tr><td rowspan=\"2\">Ive et al. (2019)</td><td>Trans. (big)</td><td>36.4</td><td>N/A</td><td>N/A</td><td>59.0</td><td>N/A</td><td>N/A</td></tr><tr><td>Del</td><td>38.0</td><td>N/A</td><td>N/A</td><td>60.1</td><td>N/A</td><td>N/A</td></tr><tr><td colspan=\"8\">Our MMTsystems</td></tr><tr><td rowspan=\"6\">This work</td><td>MMT.(base)</td><td>35.09</td><td>27.10</td><td>50.72M</td><td>57.40</td><td>48.02</td><td>50.65M</td></tr><tr><td>MMT.(big)</td><td>35.60</td><td>28.02</td><td>190.58M</td><td>57.87</td><td>49.63</td><td>190.43M</td></tr><tr><td>Trans.(base)</td><td>35.59</td><td>26.31</td><td>49.15M</td><td>57.88</td><td>48.55</td><td>49.07M</td></tr><tr><td>+VR</td><td>35.72</td><td>26.87</td><td>50.72M</td><td>58.32</td><td>48.69</td><td>50.65M</td></tr><tr><td>Trans. (big)</td><td>36.86</td><td>27.62</td><td>186.38M</td><td>56.97</td><td>48.17</td><td>186.23M</td></tr><tr><td>+VR</td><td>36.94</td><td>28.63</td><td>190.58M</td><td>57.53</td><td>48.46</td><td>190.43M</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Table 2: Results from the test2016 and test2017 for the MMT task. Del denotes the deliberation network in (Ive et al., 2019). Elliott et al. (2017) is the official baseline (text-only NMT) on WMT17- Multi30K 2017 test data. Trans. is short for transformer and MMT is the multimodal baseline described in Section 5.2. Because we used the same model for test2016 and test2017 evaluation, the numbers of parameters are the same. ",
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+    {
+        "type": "text",
+        "text": "6 ANALYSIS ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "6.1 WHY DOES THE LOOKUP TABLE WORK ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "The contribution of the lookup table could be two folds: 1) the content connection of the sentences and images; 2) the topic-aware co-occurrence of similar images and sentences. There are cases when paired images are not accurately related to the given sentence. A simple solution is to set a threshold heuristically for the TF-IDF retrieval to filter out the “improper” images. However, we maintain the specific number of the images in this work because of the second potential benefits of the cooccurrence, by taking images as diverse topic information. According to Distributional Hypothesis (Harris, 1954), which states that words that occur in similar contexts tend to have similar meanings, we are inspired to extend the concept in the multimodal world, the sentences with similar meanings would be likely to pair with similar even the same images. Therefore, the consistent images (with a related topic) could play the role of topic or type hints for similar sentence modeling. ",
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+        "type": "text",
+        "text": "This is also very similar to the idea of word embedding by taking each image as a “word”. Because we use the average pooled output of ResNet, each image is represented as a 2400-d vector. For all the 29,000 images, we have an embedding layer with size (29000, 2400). The “content” of the image is regarded as the embedding initialization. It indeed makes effects, but the capacity of the neural network is not up to it. In contrast, the mapping from text word to the index in the word embedding is critical. Similarly, the mapping of sentence to image in image embedding would be essential, i.e., the similar sentences (with the same topic words) tend to map the same or similar image. ",
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+        "type": "text",
+        "text": "To verify the hypotheses, we replace our ResNet features with 1) Shuffle: shuffle the image features but keep the lookup table; 2) Random Init: randomly initialize the image embedding but keep the lookup table; 3) Random Mapping: randomly retrieve unrelated images. The BLEU scores are on EN-RO are 33.53, 33,28, 32.14, respectively. The results of 1-2 are close to the proposed VR (33.78) and outperform the baseline (32.66), which shows that the content of images would not be very important. The ablation 3) gives a lower result, which verifies the necessity of the mapping, especially the topic relationship. ",
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+    {
+        "type": "text",
+        "text": "6.2 INFLUENCE OF THE NUMBER OF IMAGES ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "To evaluate the influence of the number of paired images $m$ , we constrained $m$ in $\\{ 0 , 1 , 3 , 5 , 7 , 9 ,$ $1 5 , 2 0 , 3 0 \\}$ for experiments on the EN-RO test set, as shown in Figure 4. When $m = 0$ , the model is the baseline NMT model, whose BLEU score was lower than all the models with images. As the number of images increases, the BLEU score also increased at the beginning (from 32.66 to 33.78) ",
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+    {
+        "type": "text",
+        "text": "and then slightly decreased when $m$ exceeds 5. The reason might be that too many images for a sentence would have a higher chance of noise. Therefore, we set $m = 5$ in our models. ",
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+    {
+        "type": "text",
+        "text": "The number of sentence-image pairs to create the lookup table could also make effects. We randomly split the pairs of Multi30K into the proportion in [0.1, 0.3, 0.5, 0.7, 0.9], the corresponding BLEU scores for EN-RO are [33.07, 33.44, 34.01, 34.06, 33.80]. Furthermore, we also evaluate the performance by adding external sentence-pairs from the training set of MS COCO image caption dataset (Lin et al., 2014). The BLEU scores are 33.55 and 33.71, respectively, for COCO only and Mult $1 3 0 \\mathrm { K + C O C O }$ . These results indicate that a modest number of pairs would be beneficial. ",
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+    {
+        "type": "text",
+        "text": "6.3 THE INFLUENCE OF GATING WEIGHT λ",
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+    {
+        "type": "image",
+        "img_path": "images/4afe8a65f062ea1895711881c063117fba5d70ddc29a026e2c577a7da5e5e8cd.jpg",
+        "image_caption": [
+            "Figure 4: Influence of the number of images on the BLEU score. "
+        ],
+        "image_footnote": [],
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+    {
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+        "img_path": "images/2cf68d92dc3d17de00225cf8437e911eec88366d65a4a253c5cc7df8c22e8536.jpg",
+        "image_caption": [
+            "Figure 5: Quantitative study of the gating weight $\\lambda$ . "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "In our model, the weight $\\lambda$ of the gated aggregation method was learned automatically to measure the importance of the visual information. We compared by manually setting the weight $\\lambda$ into scalar values in $\\{ 0 . 1 , 0 . 3 , 0 . 5 , 0 . 7 , 0 . 9 \\}$ for experiments on the EN-RO test set. Figure 5 shows that all models with manual $\\lambda$ outperformed the baseline Trans. (base), indicating the effectiveness of image information. In contrast, they were inferior to the performance of our model. This means that the degree of dependency for image information varies for each source sentence, indicating the necessity of automatically learning the gating weights of image representations. ",
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+    {
+        "type": "text",
+        "text": "6.4 EXTRA COMPUTATION TIME ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "There are mainly two extra computation costs using our method, including 1) obtaining image data for sentences and 2) learning image representations, which are negligible compared with training an NMT model. The time of obtaining image data for MT sentences for the EN-RO dataset is less than 1 minute using GPU. The lookup table is formed as the mapping of token (only topic words) index to image id. Then, the retrieval method is applied as the tensor indexing from the sentence token indices (only topic words) to image ids, which is the same as the procedure of word embedding. The retrieved image ids are then sorted by frequency. Learning image representations takes about 2 minutes for all the 29,000 images in Multi30K using 6G GPU memory for feature extraction and eight threads of CPU for transforming images. The extracted features are formed as the “image embedding layer” with the size of (29000, 2400) for quick access in the neural network. ",
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+    {
+        "type": "text",
+        "text": "7 CONCLUSION ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "This work presents a universal visual representation method for neural machine translation relying on monolingual image annotations, which breaks the restraint of heavy dependency on bilingual sentence-image pairs in the current multimodal NMT setting. In particular, this method enables visual information to be applied to large-scale text-only NMT through a topic-image lookup. We hope this work sheds some light on future MMT research. In the future, we will try to adopt the proposed method for other tasks. ",
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+    {
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+    {
+        "type": "text",
+        "text": "A APPENDIX ",
+        "bbox": [
+            176,
+            599,
+            299,
+            614
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "A.1 EXAMPLES OF RETRIEVED IMAGES ",
+        "bbox": [
+            176,
+            630,
+            460,
+            645
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "image",
+        "img_path": "images/293a5463d7433f9fcf3db43d8f8e360e7f0c0a86cb0f1e2cbf762a4bcdf0de49.jpg",
+        "image_caption": [
+            "Figure 5: Examples of the topic-image lookup table and retrieved images for sentences in Multi30K dataset. We only show six images for each topic or sentence for instance. The topics in each sentence are in boldface. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            207,
+            167,
+            792,
+            833
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "The old system of private arbitration courts is off the table ",
+        "bbox": [
+            209,
+            209,
+            534,
+            220
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "image",
+        "img_path": "images/e5ba119ecb4055c44d9ac56f8f958a5bf101cbc9dfd928f44a8f71b79e2c460d.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
+            209,
+            226,
+            787,
+            316
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "This issue is shaping as a potential early rift with the business community ",
+        "bbox": [
+            207,
+            327,
+            630,
+            339
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "image",
+        "img_path": "images/42433a729a2739381d56bd5a48c8efe8b2f45ab2f7e88db467ebdf9f4a94fba9.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
+            209,
+            347,
+            787,
+            435
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "He said he then heard his friend , Hamza calling to him ",
+        "bbox": [
+            209,
+            445,
+            521,
+            457
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "image",
+        "img_path": "images/3ef3ba5df5780e6c074b6b54dd18c1288a6010c367ada066a6c05dccf074ad88.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
+            209,
+            467,
+            789,
+            555
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "The red flag has been risen ",
+        "bbox": [
+            209,
+            564,
+            364,
+            575
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "image",
+        "img_path": "images/feaeea2efe7f95fcdd779fa0dfcbc2340d2b06448715b7e1cbee82ec6754e002.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
+            209,
+            585,
+            789,
+            674
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "The character attempts to pass human smugglers and then border police on his way to a refugee centre in the European Union . ",
+        "bbox": [
+            209,
+            683,
+            764,
+            705
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "image",
+        "img_path": "images/6a2a396fc01022d989bc1aaf0e76e67498ceb7789654193b875e7f01d6cafe83.jpg",
+        "image_caption": [
+            "Figure 6: Examples of the retrieved images for sentences in WMT datasets. We only show six images for each sentence for instance. The topics in each sentence are in boldface. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            209,
+            717,
+            787,
+            805
+        ],
+        "page_idx": 13
+    }
+]

parse/train/SJgEl3A5tm/SJgEl3A5tm.md

@@ -0,0 +1,416 @@
+# CAMOU: LEARNING A VEHICLE CAMOUFLAGE FOR PHYSICAL ADVERSARIAL ATTACK ON OBJECT DETECTORS IN THE WILD
+
+Yang Zhang1, Hassan Foroosh1, Philip David2, and Boqing Gong3
+
+1 Department of Computer Science, University of Central Florida 2 Computational and Information Sciences Directorate, U.S. Army Research Laboratory 3 Tencent A.I. Lab yangzhang@knights.ucf.edu, foroosh@cs.ucf.edu, philip.j.david4.civ@mail.mil, boqinggo@outlook.com
+
+# ABSTRACT
+
+In this paper, we conduct an intriguing experimental study about the physical adversarial attack on object detectors in the wild. In particular, we learn a camouflage pattern to hide vehicles from being detected by state-of-the-art convolutional neural network based detectors. Our approach alternates between two threads. In the first, we train a neural approximation function to imitate how a simulator applies a camouflage to vehicles and how a vehicle detector performs given images of the camouflaged vehicles. In the second, we minimize the approximated detection score by searching for the optimal camouflage. Experiments show that the learned camouflage can not only hide a vehicle from the image-based detectors under many test cases but also generalizes to different environments, vehicles, and object detectors.
+
+# 1 INTRODUCTION
+
+Is it possible to paint a unique pattern on a vehicle’s body and hence hide it from being detected by surveillance cameras? We conjecture the answer is affirmative mainly for two reasons. First, deep neural networks will be widely used in modern surveillance and autonomous driving systems for automatic vehicle detection. Second, unfortunately, these neural networks are intriguingly vulnerable to adversarial examples (Akhtar & Mian, 2018).
+
+Szegedy et al. (2013) found that adding imperceptible perturbations to clean images can result in the failure of neural networks trained for image classification. This motivates a rich line of work on developing defense techniques for the neural networks (Akhtar & Mian, 2018) and powerful attack methods to defeat those defenses (Athalye et al., 2018a). Moreover, the adversarial attack has been extended to other tasks, such as semantic segmentation (Arnab et al., 2018), object detection (Xie et al., 2017), image captioning (Chen et al., 2018a), etc.
+
+![](images/3ad224d7c17be423dca32355e7c6ddef678bcbb31b6b826558d694ad25125977.jpg)  
+Figure 1: A Toyota Camry XLE in the center of the image fools the Mask R-CNN object detector after we apply the learned camouflage to it (on the right), whereas neither plain colors (on the left) nor a random camouflage (in the middle) is able to escape the Camry from being detected.
+
+It is worth noting that the adversarial examples in the works mentioned above are not physical, i.e., the adversary directly manipulates image pixels. Although it is arguably more challenging to create physical adversarial objects than to produce adversarial images, some existing works have shown promising results with adversarial patches (Brown et al., 2017), stop signs (Eykholt et al., 2018b; Chen et al., 2018b), and small objects like baseballs and 3D turtle models (Athalye et al., 2018b).
+
+To this end, we are reasonably optimistic about designing a special pattern to camouflage a 3D car, in order to make it difficult to detect by the deep learning based vehicle detectors.
+
+It is undoubtedly challenging to run experiments in the real world considering financial and time constraints. In this paper, we instead demonstrate results using a simulation engine (Unreal) with a high-fidelity 3D sedan model and a 3D SUV. Fig. 1 shows that the vehicle in the simulation is photo-realistic such that, even covered with random camouflage, it can still be detected by the Mask R-CNN detector (He et al., 2017) trained on COCO (Lin et al., 2014).
+
+The simulation engine enables us to test the physically adversarial cars under a considerable spectrum of environmental conditions: lighting, backgrounds, camera-to-object distances, viewing angles, occlusions, etc. In contrast, existing experiments on physical adversarial attacks are all executed in simplified scenarios. Eykholt et al. (2018b), Eykholt et al. (2018a), and Chen et al. (2018b) attack neural classifiers and detectors of stop signs. While projective transformations could be used to render the planar stop signs to various images, it is more involved to image the nonplanar 3D vehicles considered in this paper; we learn a neural approximation function instead. Athalye et al. (2018b) synthesize objects (e.g., baseball, turtle, etc.) which are adversarial within a small range of camera-to-object distances and viewing angles.
+
+Given a 3D vehicle model in the simulation engine, we learn a camouflage for it by following the expectation over transformation (EoT) principle first formalized by Athalye et al. (2018b). The main idea is to consider a variety of transformations under which the camouflage can consistently hide the vehicle from a neural detector. A transformation imitates the imaging procedure and produces an image of the 3D vehicle model in the simulated environment. If a camouflage works under many transformations seen in the training phase, it is expected to also generalize to unseen transformations in the test phase.
+
+One of the major challenges is that the simulator’s image generation procedure is non-differentiable. A seemingly plausible solution is to train a neural network to approximate this procedure. The network takes as input the environment, a camouflage pattern, and the 3D vehicle model and outputs an image as close as possible to the one rendered by the simulator. Although this approach is viable, it is extremely difficult to generate high-resolution images. State-of-the-art methods (e.g., RenderNet (Nguyen-Phuoc et al., 2018)) can only generate simple 3D objects without any backgrounds.
+
+We tackle the above challenge by drawing the following observation. In EoT (Athalye et al., 2018b; Chen et al., 2018b), the gradients propagate back to the physical object from the detector/classifier’s decision values. If we jointly consider the object detector and the imaging procedure of the simulator as a whole black box, it is easier to learn a function to approximate this black box’s behavior than to train the image generation neural network. Hence, we learn a substitute neural network which takes as input a camouflage, the vehicle model, and the environment and outputs the vehicle detector’s decision value. Equipped with this substitute network, we can readily run the EoT algorithm (Athalye et al., 2018b) over our simulator in order to infer an adversarial camouflage for the vehicles.
+
+Finally, we make some remarks about the significance and potential impact of this work. In the real world, multiclass visual object detection neural networks (He et al., 2017; Redmon & Farhadi, 2018) have become the cornerstone of multiple industrial applications, such as surveillance systems (Nair et al., 2018), autonomous driving (Huval et al., 2015), and military systems (Pellerin, 2017). Among these applications, cars are one of the most crucial objects. Attacking vehicle detectors in the physical world will be enormously valuable and impactful from the perspective of the malicious adversaries. Compared with the stop sign, it is legal in the United States to paint a car while defacing a stop sign is criminal. This poses a more significant threat to autonomous driving systems since anyone has access to perturb public machine learning based systems legally. This observation motivates us to focus our approach on cars. We limit our camouflage within the legally paintable car body parts, which means that we will leave discriminative visual cues, such as the tires, windows, grille, lights, etc. unaltered for the detectors.
+
+# 2 RELATED WORK
+
+# 2.1 ADVERSARIAL ATTACK AND ITS GENERALIZATION
+
+Currently, the adversarial attack is powerful enough to attack image classification (MoosaviDezfooli et al., 2017), object detection (Arnab et al., 2018), semantic segmentation (Xie et al., 2017), audio recognition (Carlini & Wagner, 2018) and even bypass most of the defense mechanism (Athalye et al., 2018a). The mainstream adversarial machine learning research focuses on the in silico ones or the generalization within in silico (Liu et al., 2017). Such learned perturbations are practically unusable in the real world as shown in the experiments by Lu et al. (2017b), who found that almost all perturbation methods failed to prevent a detector from detecting real stop signs.
+
+The first physical world adversarial attack by Kurakin et al. (2016) found perturbations remain effective on the printed paper. Eykholt et al. (2018b) found a way to train perturbations that remain effective against a classifier on real stop signs for different viewing angles and such. Athalye et al. (2018b) trained another perturbation that successfully attacks an image classifier on 3D-printed objects. However Lu et al. (2017c) found that Eykholt et al. (2018b)’s perturbation does not fool the object detectors YOLO9000 (Redmon & Farhadi, 2017) and Faster RCNN (Ren et al., 2015). They argue that fooling an image classifier is different and easier than fooling an object detector because the detector is able to propose object bounding boxes on its own. In the meanwhile, Lu et al. (2017a)’s and Chen et al. (2018b)’s work could be generalized to attack the stop sign detector in the physical world more effectively. However, all the above methods aim to perturb detecting the stop signs.
+
+Blackbox attack is another relevant topic. Among the current blackbox attack literature, Papernot et al. (2017) trained a target model substitution based on the assumption that the gradient between the image and the perturbation is available. We do not have the gradient since the simulation is nondifferentiable. Chen et al. (2017) proposed a coordinate descent to attack the model. However, we found that our optimization problem is time-consuming, noisy (see Sec. G.2), empirically nonlinear and non-convex (see Sec. H). Time constraints made this approach unavailable to us since it requires extensive evaluations during coordinate descent. Besides, coordinate descent generally requires precise evaluation at each data-point.
+
+# 2.2 SIMULATION AIDED MACHINE LEARNING
+
+Since the dawn of deep learning, data collection has always been of fundamental importance as deep learning model performance is generally correlated with the amount of training data used. Given the sometimes unrealistically expensive annotation costs, some machine learning researchers use synthetic data to train their models. This is especially true in computer vision applications since state-of-the-art computer-generated graphics are truly photo-realistic. Ros et al. (2016); Richter et al. (2017) proposed synthetic datasets for semantic segmentation. Gaidon et al. (2016) proposed virtual KITTI as a synthetic replica of the famous KITTI dataset (Geiger et al., 2012) for tracking, segmentation, etc. And Varol et al. (2017) proposed using synthetic data for human action learning. Zhang et al. (2017); Bousmalis et al. (2017) adapt RL-trained robot grasping models from the synthetic environment to the real environment. Tremblay et al. (2018) trained a detection network using the same Unreal engine that we are using.
+
+# 3 PROBLEM STATEMENT
+
+In this paper, we investigate physical adversarial attack on state-of-the-art neural network based object detectors. The objective is to find a camouflage pattern such that, when it is painted on the body of a vehicle, the Mask R-CNN (He et al., 2017) and YOLO (Redmon & Farhadi, 2018) detectors fail to detect the vehicle under a wide spectrum of variations (e.g., locations, lighting conditions, viewing angles, etc.). We learn the camouflage in a black-box fashion, without the need for accessing the detectors’ network architecture or weights.
+
+Expectation-over-transformation (EoT). We formalize the physical adversarial attack problem with the EoT framework (Athalye et al., 2018b). Denote by $t$ a transformation which converts a camouflage pattern $c$ to a real photo. Such a transformation actually represents an involved procedure: paint the pattern to a vehicle’s body, drive the vehicle to a location, configure a camera, and take a picture of the vehicle. The transformation conveniently abstracts away enormous factors (e.g., quality of painting, camera, etc.), each of which could play a role in this procedure. Denote by $V _ { t } ( c )$ the detection score (e.g., by Mask-RCNN) over an image which is a result of a transformation $t$ and a camouflage $c$ . The physical adversarial attack problem is then described by
+
+![](images/8ce40e4e065c748809fb4d2c823c310987f3288f7931797026338a31e4250c30.jpg)  
+Figure 2: Example procedure of a transformation $t$ . From left to right: a $1 6 \times 1 6$ camouflage, a highfidelity vehicle, a location in our simulated environment, and an image due to this transformation over the camouflage.
+
+$$
+\arg \operatorname* { m i n } _ { c } \quad \mathbb { E } _ { t \sim \mathcal { T } } V _ { t } ( c )
+$$
+
+where $\tau$ is a distribution over all the possible transformations $\{ t \}$ . In other words, we search for a camouflage $c$ that minimizes the vehicle detection score in expectation.
+
+Transformation in simulation. Due to financial and time constraints, we conduct our study with the photo-realistic Unreal 4 game engine. It supplies us sufficient configuration parameters, such as the resolution and pattern of the camouflage, 3D models of vehicles, parameters of cameras and environments, etc. Fig. 2 shows a camouflage pattern, a high-fidelity 3D model of Toyota Camry, a corner of the virtual city used in this paper, and finally the picture taken by a camera after we apply the camouflage to the Camry and drive it to that corner — in other words, the rightmost image is the result of a certain transformation $t$ acting on the three images on the left of Fig. 2.
+
+# 4 APPROACH
+
+In this section, we present two key techniques for solving the problem $\operatorname* { m i n } _ { c }$ $\mathbb { E } _ { t } V _ { t } ( c )$ (cf. Eq. (1) and the text there). One is to estimate the expectation $\mathbb { E } _ { t }$ by an empirical mean over many transformations. The other is to train a neural network to clone the joint behavior $V _ { t } ( c )$ of the black-box detector and the non-differentiable simulator.
+
+# 4.1 SAMPLING TRANSFORMATIONS TO ESTIMATE $\mathbb { E } _ { t }$
+
+Recall that a transformation $t$ specifies a particular procedure from applying the camouflage $c$ to a vehicle until the corresponding image captured by a camera. In the context of the simulation engine, the camouflage $c$ is first programmed as textures, which are then warped onto the 3D model of an object. The simulator can teleport the object to different locations in the environment. The simulator also has multiple cameras to photograph the teleported object from various distances and viewing angles.
+
+We identify some key factors involved in this procedure, including vehicle, location, camera-toobject distance, and viewing angle. The combinations of them also give rise to variations along other dimensions. For instance, the lighting condition changes from one location to another. The vehicle of interest is occluded to different degrees in the images captured by the cameras. Denote by $T _ { S }$ all the sampled transformations that are used for learning the camouflage.
+
+Fig. 3 illustrates the positions where the cameras are placed. We can see how the viewing angles and camera-to-object distances vary. The ones shown in the green color are used in the training. We left out some cameras shown in the red color for the testing. Since it is computationally expensive to utilize the cameras, we randomly arrange them in different heights and distances to create as much variations as possible instead of traversing all possible height-distance combinations.
+
+![](images/0d907c35ed2ec5e62bc129613a2d8e17a9180e32ee9bc41fc30a8b1c8b9bb81f.jpg)  
+Figure 3: The camera setup as well as some exemplar locations. The cameras depicted in the green color are used to learn the camouflage while those in red are unseen cameras used for testing the camouflage’s generalization. (H: camera height, L: vehicle-to-camera distance.)
+
+4.2 LEARNING A CLONE NETWORK $V _ { \theta } ( c , t )$ TO APPROXIMATE $V _ { t } ( c )$
+
+If we unroll the detection score $V _ { t } ( c )$ , it contains two major components. The first renders an image based on the camouflage $c$ by following the procedure specified by the transformation $t$ . The second obtains the detection score of a vehicle detector (e.g., Mask-RCNN) over the rendered image. The first component is non-differentiable while the second one could be a black box in practice. Therefore, we propose to consider them jointly as a single black box. Furthermore, we learn a clone neural network $V _ { \theta } ( c , t )$ to imitate the input-output behavior of this extended black box. As the transformation $t$ itself is involved and hard to represent, we instead input its consequence to the network: a background image and the cropped foreground of the vehicle.
+
+Fig. 4b shows the network architecture. It takes as input a camouflage pattern $c$ , the background image due to a sampled transformation $t$ , and the cropped foreground. The network $V _ { \theta } ( c , t )$ has a single output to approximate the detection score $V _ { t } ( c )$ .
+
+To this end, we are ready to write down an approximate form of problem (1),
+
+$$
+\underset { c } { \arg \operatorname* { m i n } } \quad \frac { 1 } { \left| T _ { S } \right| } \sum _ { t \in T _ { S } } V _ { \theta } ( c , t ) .
+$$
+
+Thanks to the differentiable network $V _ { \theta } ( c , t )$ with respect to the camouflage $c$ , we can solve the problem above by standard (stochastic) gradient descent.
+
+It is important to note that the fidelity of problem (2) depends on the size and diversity of the sampled set of transformations $T _ { S }$ as well as the quality of the clone network $V _ { \theta } ( c , t )$ . It is straightforward to generate a large training set for the clone network by randomizing the camouflages and transformations and “labeling” the resulting images with the detection scores. However, if the optimal camouflage is unfortunately not covered by this training set, a discrepancy would occur when we solve problem (2). In other words, the network may fail to well approximate the detection scores at the region around the optimal camouflage. We address this discrepancy by an alternative learning algorithm as follows.
+
+# 4.3 JOINTLY LEARNING THE CLONE NETWORK AND THE OPTIMAL CAMOUFLAGE
+
+We alternatively learn the clone network $V _ { \theta } ( c , t )$ and solve the problem (2). Once a new camouflage pattern is found due to optimizing problem (2), it is converted to multiple images by the training
+
+![](images/d80a830f80f9ae6649a361a1b2126f31e0602e65c93d2ec5d5144632a8b1de4c.jpg)  
+Figure 4: Overview of our optimization pipeline and the clone network $V _ { \theta } ( c , t )$ .
+
+transformations $T _ { S }$ . We obtain the detection score for each of the images by querying a detector. The camouflage pattern, along with the detection scores are then added to the training set for learning the clone network $V _ { \theta } ( c , t )$ . Fig. 4a illustrates this process.
+
+Implementation details. Denote by $H [ p , q ] : = - p \log q - ( 1 - p ) \log ( 1 - q )$ the cross-entropy loss. We alternately solve the following two problems,
+
+$$
+\arg \operatorname* { m i n } _ { \theta } \ \frac { 1 } { | C | | T s | } \sum _ { c \in C } \sum _ { t \in T s } H \big [ s , V _ { \theta } ( c , t ) \big ] + \lambda \| \theta \| _ { 2 } , \qquad \arg \operatorname* { m i n } _ { c } \ \frac { 1 } { | T | } \sum _ { t \in T s } H \big [ 0 , V _ { \theta } ( c , t ) \big ] 
+$$
+
+where $C$ is the collection of all camouflages in the training set for learning the clone network $V _ { \theta } ( c , t )$ , and $s : = V _ { t } ( c )$ is the detection score corresponding to the camouflage $c$ and the transformation $t$ . The $\ell _ { 2 }$ regularization $\lambda \| \boldsymbol { \theta } \| _ { 2 }$ over the clone network’s weights is essential. Without this term, the two loss functions may cause oscillations or degeneration of the solutions. We set $\lambda = 1 0$ in the experiments. Since the approximation accuracy of the clone network near the optimal camouflage is more important than in other regions, we weigh the newly added samples to the training set 10 times higher than the old ones at each iteration. Algorithm 1 in the Appendix gives more details.
+
+# 5 EXPERIMENTS
+
+Since the primary objective of this paper is to learn camouflage patterns that deceive vehicle detectors, we introduce two baseline camouflage patterns in the experiments: 6 most popular car colors and 800 random camouflages in different resolutions. We then analyze how the resolution of the camouflage affects the detection performance. For the vehicles, we employ two 3D models: a 2015 Toyota Camry and a virtual SUV. In addition to the main comparison results, we also test the transferability of the learned camouflage across different car models, environments, camera positions, and object detectors.
+
+# 5.1 EXPERIMENT SETUP
+
+We describe the detailed experimental setup in this section, including the simulator, vehicle detector, evaluation metrics, and the baseline camouflage patterns.
+
+# 5.1.1 THE SIMULATOR
+
+As shown in Fig. 5a, we use the Unreal engine to build our first simulation environment from the photo-realistic DownTown environment. It is modeled after the downtown Manhattan in New York. There are skyscrapers, cars, traffic signs, a park, and roads in this environment, resembling a typical urban environment. We sample 32 different locations along the streets. Eight cameras perch at each location, each taking pictures of the size $7 2 0 \times 3 6 0$ . The relative position of a camera is indexed by the viewing angle and camera-to-object distance, as shown in Fig. 3. In addition, we install another 16 cameras to test the generalization of the learned camouflage across viewing angles, distances, etc. In total, we use 18 locations for training and another 18 for testing. Note that the vehicles are invisible to some cameras due to occlusion.
+
+![](images/8f13124eb918205339bb84dfbafd604190b286290f3672c52eedcfc46b983cd3.jpg)  
+(b) A mountain environment.   
+Figure 5: The two environments we built to learn and test the vehicle camouflage. Zoom in for more details. These images are of the higher resolution but the same rendering quality (anti-aliasing level, shadow quality, rendering distance, texture resolution etc.) the detector perceived.
+
+Our second environment is based on a totally different countryside scene called Landscape Mountains, shown in Fig. 5b. The roads lie on high-altitude mountains and cross bridges, forest, snow, and a lake. We use this scene to test the transferability of our camouflage across different environments; this scene is not used in the training. Like the DownTown environment, we sample 18 locations along the roads for the purpose of testing.
+
+The two vehicles used in the experiments are shown in Fig. 6. One is a 2015 Toyota Camry XLE sold in the European Union. The other is a virtual SUV from AirSim (Shah et al., 2017). It is worth noting that the Toyota sedan appears multiple times in the MS-COCO dataset (Lin et al., 2014) (cf. some examples in Fig. 12). Since the object detectors are trained on MS-COCO, the Camry is more challenging to hide than the virtual SUV.
+
+# 5.1.2 VEHICLE DETECTORS
+
+We study two state-of-the-art detectors: Mask R-CNN (He et al., 2017) and YOLOv3-SPP (Redmon & Farhadi, 2018). Mask R-CNN is one of the most powerful publicly available object detectors; it currently ranks in the 4th place in the MS COCO detection leaderboard. Both detectors are pretrained on MS COCO. For Mask R-CNN, we use the one implemented by Abdulla (2017). Its backbone network is ResNet-101 (He et al., 2016). YOLOv3 has comparable performance with
+
+![](images/7bf363407a0ec8a0ce821f3d8fed8cd94affbd9f25a1dc00014589c6b9bc392f.jpg)  
+Figure 6: Orthogonal views of the Toyota Carmy XLE 2015 (second row) and the virtual SUV (first row) used in our simulation.
+
+Mask R-CNN. Its network architecture is very different from Mask R-CNN’s, causing challenges to the transfer of the camouflage between the two detectors. We use the spatial pyramid pooling (SPP) variant of YOLOv3 in the experiments.
+
+In the rest of the paper, we experiment with Mask R-CNN except the transfer experiments in Sec. 5.4.
+
+# 5.1.3 EVALUATION METRICS
+
+We adopt two metrics to evaluate the detection performance. The first one is a variation of the Intersection over Union proposed by Everingham et al. (2015). The IoU between a predicted box and the groundtruth bounding box is defined as $\begin{array} { r } { \mathsf { \bar { I } } o U ( A , B ) = \frac { A \bigcap B } { A \bigcup B } } \end{array}$ . Since IoU was originally proposed to evaluate the results of multi-object detection, as opposed to the single vehicle detection in our context, we modify it to the following to better capture the vehicle of interest: $\mathrm { m a x } _ { p \in P } I o U ( p , G T )$ , where $P$ is the set of all detection proposals in an image. We average this quantity across all the test images and denote by mIoU the mean value.
+
+Our second metric is precision at 0.5 or $\mathrm { P @ 0 . 5 }$ . Everingham et al. (2015) set a 0.5 threshold for the detection IoU in the PASCAL VOC detection challenge to determine whether a detection is a hit or miss. We report the percentage of the hit detections out of all observations as our $\mathrm { P @ 0 . 5 }$ . We also report the relative precision drop of the camouflage against the baseline colors whenever possible.
+
+# 5.1.4 BASELINES
+
+Our first baseline is when a vehicle is colored in popular real car colors. We select 6 basic car colors (red, black, silver, grey, blue, and white) which cover over $90 \%$ of the car colors worldwide (Axalta). We obtain their RGB values according to the X11 Color Names.
+
+As the second baseline, we generate 800 random camouflages in different resolutions ranging in $\{ 2 ^ { i } \times 2 ^ { i } ; i \in [ 1 . . 8 ] \}$ . Since we find that camouflages with strong contrasts work better, we generate half of the camouflages using RGB values $\in \ [ 0 , 2 5 5 ]$ and the other half using RGB values $\in \ \{ 0 , 2 5 5 \}$ . After we obtain these camouflages and the corresponding detection scores, we use those with proper resolutions to initialize the training set for the clone network $V _ { \theta } ( c , t )$ .
+
+The two baselines partially resolve the concern one might have that the learned camouflage successfully attacks the detector not because it exploits the CNN’s structural weakness, but because it takes advantage of the domain gap between the real data used to train the detector and our simulated data used to test the detector. Results show that the baselines could not fail the detectors under most test cases, indicating that the detectors are fairly resilient to the domain gap between the simulated imagery and the real data (at least for the vehicle detection task).
+
+# 5.2 RESOLUTION OF THE CAMOUFLAGES
+
+We first report the random camouflages’ performance on hiding the Camry from the Mast R-CNN detector in the DownTown environment. Fig. 7 shows the results. The first observation is that, although random camouflages are visually very different from conventional car paintings (cf. Fig. 8), the Mask R-CNN detector is still able to detect most of them. Another slightly counter-intuitive yet interesting observation is that the detector’s performance does not always decrease as the camouflages’ resolutions increase. This is probably because some fine-grained patterns displayed by the high-resolution camouflage become harder to observe from a distance. Since the high-resolution camouflage does not bring any additional benefits beyond the $1 6 \times 1 6$ resolution, we use camouflages of size $1 6 \times 1 6$ in the remaining experiments.
+
+![](images/11a4ab5dbefbbf5e29ba8a2952b686f6f3f99b009e05bd12095189207c954e4a.jpg)  
+Figure 7: The mIoU and $\mathrm { P @ 0 . 5 }$ of the 800 random camouflages in different resolutions on Camry in the DownTown environment. There are 100 camouflages per resolution.
+
+![](images/217a875298bd410a386c9f2e08143f17befd7b1540cd894602391b3b94dc891d.jpg)  
+Figure 8: Visualization of three random camouflages of resolutions $4 \times 4$ , $1 6 \times 1 6$ , and $2 5 6 \times 2 5 6$ , respectively, as well as the resulting images by the same camera.
+
+# 5.3 CAMOUFLAGING TOYOTA CAMRY IN THE URBAN ENVIRONMENT
+
+Here we report the results on detecting the Camry in the urban environment. Table 1 summarizes the results for the Camry respectively with the baseline colors, random camouflages, and our learned camouflage. We can see from the table that the Mask R-CNN is surprisingly robust against different types of random camouflages. The random camouflages’ detection scores are close to the baseline colors’. Moreover, the standard deviation of the random camouflages’ scores is also very low, indicating that the difference in the random camouflages does not really change the detector’s performance. Note that we apply the camouflage to the body of the Camry, leaving tires, windows, grilles, etc. as informative visual cues to the detector. Despite that, our learned camouflage reduces the precision by around $3 0 \%$ over baseline colors in both training and testing scenes in the urban environment.
+
+Table 1: Mask R-CNN detection performance on the Camry in the urban environment.   
+
+<table><tr><td rowspan="2">Camouflages</td><td colspan="2">Training Scenes</td><td colspan="2">Testing Scenes</td></tr><tr><td>mIoU (%)</td><td>P@0.5 (%)</td><td>mIoU (%)</td><td>P@0.5 (%)</td></tr><tr><td>Baseline Colors</td><td>76.14</td><td>84.40</td><td>72.88</td><td>77.57</td></tr><tr><td>Random Camou</td><td>73.48± 0.80</td><td>82.17± 1.20</td><td>67.79± 0.79</td><td>71.42± 1.20</td></tr><tr><td>Ours</td><td>57.69</td><td>62.14</td><td>53.64</td><td>52.17</td></tr><tr><td>Relative Performance Drop</td><td>24.23%</td><td>26.37%</td><td>26.39%</td><td>32.74%</td></tr></table>
+
+Table 2: YOLOv3-SPP detection performance on the Camry in the urban environment. In addition to the camouflage inferred for YOLO, we also include the YOLO detection results on the camouflage learned for Mask R-CNN.   
+
+<table><tr><td rowspan="2">Camouflages</td><td colspan="2">Training Scenes</td><td colspan="2">Testing Scenes</td></tr><tr><td>mIoU (%)</td><td>P@0.5 (%)</td><td>mIoU (%)</td><td>P@0.5 (%)</td></tr><tr><td>Baseline colors</td><td>76.79</td><td>85.34</td><td>73.00</td><td>78.50</td></tr><tr><td>Random Camou</td><td>73.19±0.75</td><td>83.30±0.89</td><td>68.76±0.81</td><td>73.92±1.00</td></tr><tr><td>Ours (YOLO trained)</td><td>65.83</td><td>72.53</td><td>64.03</td><td>69.56</td></tr><tr><td>Ours (Mask R-CNN trained)</td><td>65.43</td><td>70.42</td><td>61.79</td><td>65.21</td></tr><tr><td>Relative Performance Drop</td><td>14.79%</td><td>17.48%</td><td>15.35%</td><td>16.92%</td></tr></table>
+
+Virtual SUV. Appendix A presents the results on the virtual SUV. The learned camouflage reduces Mask R-CNN’s detection precision by around $40 \%$ from the precision for the baseline colors.
+
+# 5.4 TRANSFERABILITY EXPERIMENTS
+
+We show that the camouflage learned to attack Mask R-CNN can actually also defeat YOLOv3 to a certain degree. The results are reported in Table 2. Similarly, appendices A to D report the transferabilities of the learned camouflage across different environments, vehicles, camera viewing angles, and distances from the camera to the object.
+
+# 5.5 QUALITATIVE RESULTS
+
+We present some of our detection results on the baseline colors, random camouflages, and the learned camouflages for the Camry in Fig. 11.
+
+We can draw a lot of interesting observations from the qualitative results which were hidden by the quantitative results. We find that there are 3 types of successful attacks: (1) Camouflages lower the objectiveness of the car and the car region is not proposed or only partially proposed as a candidate for the classifier of the detector; (2) The car region is successfully proposed but misclassified (e.g., to kite, cake, truck, or potted plant as shown in the examples) or the classification score is too low to pass the threshold for the detection score; (3) The car region is successfully proposed and classified, but the camouflage results in an incorrect detection which largely overlaps with the car (cf. the 5th row where the regions covering the car are detected as a car and a boat, respectively).
+
+One can see that the context or background plays a vital role in object detection. Although some images capture the Camry by the same pose, the detector makes completely different predictions for them. Besides, these qualitative results imply that the detector works in a way different from human vision. In the Landscape environment, our learned camouflage has the strongest contrast to the background compared to other baseline patterns. However, the detector is still sometimes not able to detect the camouflaged car or SUV.
+
+# 6 CONCLUSION
+
+In this paper, we investigate whether it is possible to physically camouflage 3D objects of complex shapes, i.e., vehicles, in order to hide them from state-of-the-art object detectors. We conduct extensive experimental studies with a photo-realistic simulation engine. We propose to use a clone network to mimic the simulator and the detector’s joint response to the 3D vehicles. Then, we infer a camouflage for a 3D vehicle by minimizing the output of the clone network. Our learned camouflage significantly reduces the detectability of a Toyota Camry and a SUV. Moreover, we find that the camouflage is transferable across different environments. For future work, We plan to look into possible ways to white-box the entire process so as to propose a more effective camouflage.
+
+# ACKNOWLEDGMENT
+
+This work was in part supported by the NSF grants IIS-1212948, IIS-1566511, and a gift from Uber Technologies Inc.
+
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+Table 3: Detection performance of camouflages on SUV in urban environment.   
+
+<table><tr><td rowspan="3">Camouflages</td><td colspan="2">Training Scenes</td><td colspan="2">Testing Scenes</td></tr><tr><td>mIoU (%)</td><td>P@0.5 (%)</td><td>mIoU (%)</td><td>P@0.5 (%)</td></tr><tr><td>Baseline Colors</td><td>82.35</td><td>91.07</td><td>81.06</td><td>89.22</td></tr><tr><td>Random Camou</td><td>83.53±3.26</td><td>93.21±3.48</td><td>78.02±2.53</td><td>84.79±2.81</td></tr><tr><td>Ours</td><td>53.27</td><td>55.79</td><td>48.91</td><td>50.36</td></tr><tr><td>Relative Performance Drop</td><td>35.31%</td><td>38.79%</td><td>39.66%</td><td>43.55%</td></tr></table>
+
+Table 4: Detection performance of camouflages on Camry in Landscape environment. Note that this camouflage is pretrained in urban environment and then transferred without any finetuning.   
+
+<table><tr><td rowspan="2">Camouflages</td><td colspan="2">Testing Scenes</td></tr><tr><td>mIoU (%)</td><td>P@0.5 (%)</td></tr><tr><td>Baseline Colors</td><td>74.81</td><td>82.04</td></tr><tr><td>Random Camou</td><td>72.45±4.26</td><td>77.11±5.45</td></tr><tr><td>Ours - Transferred</td><td>40.39</td><td>43.26</td></tr><tr><td>Relative Performance Drop</td><td>46.00%</td><td>47.26%</td></tr></table>
+
+# A VIRTUAL SUV IN URBAN AREA
+
+We then report the camouflage performance on the newly modeled SUV in the urban environment in Table 3.
+
+Judging by the results, it is clear that the Mask R-CNN is a very generalized detector. The SUV’s baseline color and random camouflage detection scores are even higher than the Camry correspondence although the detector has never seen it before. This might be because the SUV has much less polygon and is built to resemble the shape of a general SUV as shown in Fig. 6.
+
+However, the price for not seeing this vehicle during training is that Mask R-CNN is more likely to be affected by the camouflage. The standard deviation of the random camouflage mIoU/ precision is higher (3.26/3.48 vs. 0.8/1.2) than Camry. And our camouflage achieves lower detection precision despite both baseline colors and random camouflage’s detection scores are higher than Camry’s. The detectability is reduced by almost 1.5 times of Camry’s results in this case. This experiment shows that Mask R-CNN might well generalize to unseen vehicles, but it is easier to get attacked.
+
+# B TRANSFERABILITY ACROSS ENVIRONMENTS
+
+Another important question is that what if we transfer the camouflage to a not only previously unseen but a totally different environment? To quantitatively answer this question, we build the Landscape environment (Fig. 5b) to test our camouflages trained in urban environment (Fig. 5a) using the Camry vehicle. The results are reported in Table. 4. Some qualitative results are shown in Fig. 11.
+
+Given the barren landscape with few objects in sight, the detector detects the car better than it did in the urban environment for both baseline colors (82.04 vs. 77.57) and random camouflages (77.11 vs. 71.42) possibly due to the absence of distractions. However, our directly transferred camouflage is still able to beat both of them by more than $46 \%$ regarding both detection mIoU and precision without any fine-tuning.
+
+It is interesting to notice that the Camry with grey color looks almost identical to the background in this environment (Fig. 11). However, it still could be perfectly detected. Meanwhile, our leaned camouflage results in far better stealth despite it has a sharp contrast to the background.
+
+Table 5: Camouflage transferability across vehicle reported in testing $\mathrm { P @ 0 . 5 }$ in urban environment.   
+
+<table><tr><td></td><td></td><td colspan="2">Test</td></tr><tr><td></td><td></td><td>SUV</td><td>Camry</td></tr><tr><td>TTeil</td><td>SUV</td><td>50.36</td><td>47.44</td></tr><tr><td></td><td>Camry</td><td>58.39</td><td>52.17</td></tr></table>
+
+Table 6: Detection performance of pretrained camouflages on Camry with urban environment in 16 unseen cameras.   
+
+<table><tr><td rowspan="2">Camouflages</td><td colspan="2">Testing Scenes</td></tr><tr><td>mIoU (%)</td><td>P@0.5 (%)</td></tr><tr><td>Baseline Colors</td><td>78.43</td><td>86.16</td></tr><tr><td>Random Camou</td><td>77.26±0.96</td><td>84.61±1.06</td></tr><tr><td>Ours - Transferred</td><td>67.74</td><td>73.14</td></tr><tr><td>Relative Performance Drop</td><td>13.62%</td><td>15.11%</td></tr></table>
+
+# C TRANSFERABILITY ACROSS VEHICLES
+
+It will be impractical to retrain a specific camouflage for each vehicle whenever we need it. Hence it would be interesting to look into the transferability between vehicles in this scenario. We swap the camouflages of SUV and Camry and see how they would perform in the urban environment. We present the testing precision after swapping in Table. 5.
+
+First, both camouflages are definitely transferable. It is also interesting to see that the Camry learned camouflage is not as good as the SUV learned camouflage even when being applied on the Camry itself. This might be due to the fact that the SUV resembles a car with more generic features and hence learning camouflage on SUV is less likely to encounter local minima during optimization.
+
+# D TRANSFERABILITY ACROSS VIEWING POSITION
+
+One of the possibly most concerning questions is whether the learned camouflage is robust to the change of the camera position. To answer this question, we set up another 16 new cameras, as shown in Fig. 3, surrounding the vehicle in different relative locations. We then test the learned camouflage’s performance on these new cameras. The results are shown in Table 6.
+
+Our camouflage performance drop has a slightly decrease of $5 \%$ from Table 1. This indicates that the change of the camera locations would impact the performance, but the performance drop is still way beyond the standard deviation of random camouflages’ scores. Given that the new camera views cover more perspectives as shown in Fig. 3, this result is reasonable.
+
+# E IMPACT OF CLONE NETWORK QUALITY
+
+How does the clone network’s quality affect the camouflage’s performance? Is the alternative optimization necessary? We quantitatively show the first 300 simulation calls of our system in Fig. 9 and meanwhile evaluate the camouflages proposed by the clone network. Note that initially the clone network has already been trained with 800 random camouflages. However, the proposed camouflage’s score does not fall until the new camouflages from iteration scheme join the optimization. This suggests that without our iterative optimization mechanism, the clone network could only find camouflage with mIoU around $70 \%$ , which is the same as the random camouflage. Those new samples serve as the hard samples. They gradually calibrate the clone network’s global minima to $V _ { t } ( )$ ’s and help it to generate better camouflages. Note that although the score descends quicker during the first 50 iterations, it does not find the global best camouflage until near the end (296th iteration). This graph also shows the classification score is a suitable choice to be minimized as it is highly correlated with mIoU.
+
+Note that the system automatically re-initialize the clone network’s parameters to prevent it from falling into local minima during the optimization whenever we add a new sample to the training set $C$ . Hence, there are some spikes in the graph.
+
+![](images/e6cea3b0fef3f0adcba8636a06e8de8e20ff076673920721b5d123a99143cf71.jpg)  
+Figure 9: Clone network’s learned camouflage’s classification score and mIoU vs. Simulation called. We can see how the new samples helped the clone network to find the minimal.
+
+# F DETECTION ATTENTION
+
+How exactly does our camouflage work against the detector? We partially answer this question by visualizing Mask-RCNN’s completely/partially successful detection attention on our grey and camouflaged Camry. Since our Mask-RCNN implementation does not explicitly yield failed detection’s prediction, we are unable to visualize the failed detection’s attention w.r.t. the input image if the failed detection does not exist.
+
+There are two main visualization approaches: Grad-CAM (Selvaraju et al., 2017) and saliency (Simonyan et al., 2013). Approximately speaking, grad-CAM visualizes the gradient of output w.r.t. penultimate (pre-fully-connected layer) convolutional layer feature map output; Saliency visualizes the gradient of output w.r.t. initial input image. Grad-CAM is generally considered superior as the last convolutional layer’s feature map contains much more abstracted semantic information, leading to less noisy visualization. However, we find that it is hard to define the single “penultimate layer” in Mask-RCNN: It has multiple penultimate layers, tracing back to different stages of the network, prior to the ROI pooling layer. Each of those penultimate layers contains varying levels of information. We choose to use saliency in this case.
+
+It is clear how to define the “attention” in the image classification scenario: It is the gradient heatmap of the classification score scalar w.r.t. the entire input image. On the other hand, an end-to-end detection neural network often yields multiple structure predictions. Each structure contains bounding box and classification score, etc. We choose to visualize the gradient of the best bounding-box’s classification score w.r.t. the input image.
+
+Our visualizations are presented in Fig. 10. It is surprising that the window, roof and upper bodies are playing the predominant role in car detection. Upper body attention exists even when the upper body is not included in the detection bounding box (row 3). Given that the classification stage makes the classification decision based on the proposed feature map box region, such attention must have been already included in the detection proposal before the ROI layer, i.e. detection stage. This may also explain why it is easier to fail the front-viewing and the rear-view detectors: front-view (row 1) and the rear-view (row 5) detectors place their attention on the hood and trunk, where camouflage pattern is presented. A partially successful attack (row 4) was carried out by wiping out detector’s attention on the car hood. On the other hand, the side-view detector is harder to attack since the detector merely places any attention of the car body (row 2) where the camouflages are mainly located. However, our camouflages on the roof could still fail the side-view detector partially (row 3).
+
+Since we only visualize the (partially) successful detections, there are still many cases to explore.
+
+![](images/b49fa4ebb626dc4aa9b44f1f8895d991d5d6a97915956a86c42489b7211c7c33.jpg)  
+Figure 10: The best detections in each image and the gradient heatmap of their classification scores w.r.t. the input images. The detector places its attention predominantly on the upper car body, i.e., roof, hood, trunk, and windows.
+
+# G SIMULATION SETUP
+
+# G.1 SIMULATION IMPLEMENTATION
+
+The iterative optimization framework works on two Nvidia GTX 1080 Ti in our experiment. We use one to run the detector and another one to run the simulation and training/ prediction of evaluation network. The simulation was implemented partially using AirSim by Shah et al. (2017) and UnrealEnginePython. All submodules are implemented asynchronously to run in parallel and are communicating with each other using RPC/ RPyC. All the camouflages and the baseline colors are implemented either using or based on the official Unreal Automotive Material. Each evaluation in the simulation, which is the most time-consuming part, takes around 15 to 20 second.
+
+# G.2 SIMULATION ERROR
+
+Despite our best effort, we observe $V _ { t } ( c )$ come with a standard deviation of 0.008 due to the inherent and mostly necessary random processes in the rendering (i.e., Monte Carlo in path tracing, etc.). This unfortunately makes $V _ { t } ( c )$ a noisy function. We reduce this error by repeat sampling $\bar { V } _ { t } ( c )$ 5 times whenever we use it.
+
+# H NON-LINEARITY AND NON-CONVEXITY
+
+Since this is a blackbox optimization problem, it is important to examine some important features of the $\textstyle \mathbb { E } _ { t } V _ { t } ( \cdot )$ . We first verify its convexity via the convexity definition. We test the convexity of $\mathbb { E } _ { t } V _ { t } ( \cdot )$ by testing the convexity of subsampled correspondence $\begin{array} { r } { \frac { 1 } { \left| T _ { S } \right| } \sum _ { t \in T _ { S } } V _ { t } ( \cdot ) } \end{array}$ via:
+
+$$
+\forall c _ { 1 } , c _ { 2 } \in C : \quad \frac { 1 } { | T _ { S } | } \sum _ { t \in T _ { S } } V _ { t } ( \frac { c _ { 1 } + c _ { 2 } } { 2 } ) \leq \frac { 1 } { | T _ { S } | } \sum _ { t \in T _ { S } } V _ { t } \frac { V _ { T _ { S } } ( c _ { 1 } ) + V _ { T _ { S } } ( c _ { 2 } ) } { 2 }
+$$
+
+where $C$ is a set of camouflages. We sampled 1000 pairs of random camouflages from $C$ and half of them do not meet the equation. Hence $\begin{array} { r } { \frac { 1 } { | T _ { S } | } \sum _ { t \in T _ { S } } ^ { } { \bar { V } } _ { t } ( \cdot ) } \end{array}$ is nonconvex.
+
+Besides, we find a simple linear MLP is insufficient to approximate $\begin{array} { r } { \frac { 1 } { \left| T _ { S } \right| } \sum _ { t \in T _ { S } } V _ { t } ( \cdot ) } \end{array}$ , which empirically shows it is nonlinear.
+
+# I SUPPLEMENTAL FIGURES
+
+# Algorithm 1: Iterative Object Camouflage Learning
+
+Input : Clone network parameter $V _ { \theta } ( \cdot )$ ; Simulation and detection $V _ { T _ { S } } ( \cdot )$ ; Transformation $T _ { S }$ which are parameterized as rendered background and foreground images; Regularization tradeoff $\alpha$ ; Random camouflage set $C _ { R }$ .
+
+1 Initialize $V _ { \theta }$ with random weights $\theta$
+
+2 Set score record $s ^ { * }  + \infty$
+
+5 F $\begin{array} { r } { \theta  \arg \operatorname* { m i n } _ { \theta } \ \frac { 1 } { | C | | T _ { S } | } \sum _ { c \in C } \sum _ { t \in T _ { S } } H \big [ s , V _ { \theta } ( c , t ) \big ] + \lambda \| \theta \| _ { 2 } } \end{array}$   
+6 $\begin{array} { r } { c ^ { \prime } \gets \arg \operatorname* { m i n } _ { c } \frac { 1 } { | T | } \sum _ { t \in T _ { S } } H \big [ 0 , V _ { \theta } ( c , t ) \big ] } \end{array}$   
+7 s0 ← {Vt(c)|t ∈ T }   
+8 C ← C ∪ {c0}   
+9 if mea $1 ( s ^ { \prime } ) < s ^ { * }$ then   
+10 s∗ ← mean(s0)   
+11 c ∗ ← c 0
+
+12 until Reach maximum training steps output: Best learned camouflage $c ^ { * }$
+
+![](images/e53c10bceacd153d333f31b7e0cdfa3d6e757e1bc35df9f0780558ccc6b33f10.jpg)  
+Figure 11: Qualitative comparison of the Mask R-CNN detections results of the grey baseline color, random camouflages and our learned camouflages in different transformations. Zoom in for more details. 19
+
+![](images/b1188dd4fb2e6e0ce606158e83f009828d30947abde20b98c09f3a3ea6c18f4e.jpg)  
+Figure 12: A fraction of different Toyota sedan appearances in MS COCO dataset.

parse/train/SJgEl3A5tm/SJgEl3A5tm_content_list.json

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+[
+    {
+        "type": "text",
+        "text": "CAMOU: LEARNING A VEHICLE CAMOUFLAGE FOR PHYSICAL ADVERSARIAL ATTACK ON OBJECT DETECTORS IN THE WILD ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Yang Zhang1, Hassan Foroosh1, Philip David2, and Boqing Gong3 ",
+        "bbox": [
+            271,
+            200,
+            725,
+            217
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1 Department of Computer Science, University of Central Florida 2 Computational and Information Sciences Directorate, U.S. Army Research Laboratory 3 Tencent A.I. Lab yangzhang@knights.ucf.edu, foroosh@cs.ucf.edu, philip.j.david4.civ@mail.mil, boqinggo@outlook.com ",
+        "bbox": [
+            210,
+            227,
+            789,
+            299
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "ABSTRACT ",
+        "text_level": 1,
+        "bbox": [
+            454,
+            338,
+            544,
+            353
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "In this paper, we conduct an intriguing experimental study about the physical adversarial attack on object detectors in the wild. In particular, we learn a camouflage pattern to hide vehicles from being detected by state-of-the-art convolutional neural network based detectors. Our approach alternates between two threads. In the first, we train a neural approximation function to imitate how a simulator applies a camouflage to vehicles and how a vehicle detector performs given images of the camouflaged vehicles. In the second, we minimize the approximated detection score by searching for the optimal camouflage. Experiments show that the learned camouflage can not only hide a vehicle from the image-based detectors under many test cases but also generalizes to different environments, vehicles, and object detectors. ",
+        "bbox": [
+            233,
+            372,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            559,
+            336,
+            575
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Is it possible to paint a unique pattern on a vehicle’s body and hence hide it from being detected by surveillance cameras? We conjecture the answer is affirmative mainly for two reasons. First, deep neural networks will be widely used in modern surveillance and autonomous driving systems for automatic vehicle detection. Second, unfortunately, these neural networks are intriguingly vulnerable to adversarial examples (Akhtar & Mian, 2018). ",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Szegedy et al. (2013) found that adding imperceptible perturbations to clean images can result in the failure of neural networks trained for image classification. This motivates a rich line of work on developing defense techniques for the neural networks (Akhtar & Mian, 2018) and powerful attack methods to defeat those defenses (Athalye et al., 2018a). Moreover, the adversarial attack has been extended to other tasks, such as semantic segmentation (Arnab et al., 2018), object detection (Xie et al., 2017), image captioning (Chen et al., 2018a), etc. ",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/3ad224d7c17be423dca32355e7c6ddef678bcbb31b6b826558d694ad25125977.jpg",
+        "image_caption": [
+            "Figure 1: A Toyota Camry XLE in the center of the image fools the Mask R-CNN object detector after we apply the learned camouflage to it (on the right), whereas neither plain colors (on the left) nor a random camouflage (in the middle) is able to escape the Camry from being detected. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "It is worth noting that the adversarial examples in the works mentioned above are not physical, i.e., the adversary directly manipulates image pixels. Although it is arguably more challenging to create physical adversarial objects than to produce adversarial images, some existing works have shown promising results with adversarial patches (Brown et al., 2017), stop signs (Eykholt et al., 2018b; Chen et al., 2018b), and small objects like baseballs and 3D turtle models (Athalye et al., 2018b). ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "To this end, we are reasonably optimistic about designing a special pattern to camouflage a 3D car, in order to make it difficult to detect by the deep learning based vehicle detectors. ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "It is undoubtedly challenging to run experiments in the real world considering financial and time constraints. In this paper, we instead demonstrate results using a simulation engine (Unreal) with a high-fidelity 3D sedan model and a 3D SUV. Fig. 1 shows that the vehicle in the simulation is photo-realistic such that, even covered with random camouflage, it can still be detected by the Mask R-CNN detector (He et al., 2017) trained on COCO (Lin et al., 2014). ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "The simulation engine enables us to test the physically adversarial cars under a considerable spectrum of environmental conditions: lighting, backgrounds, camera-to-object distances, viewing angles, occlusions, etc. In contrast, existing experiments on physical adversarial attacks are all executed in simplified scenarios. Eykholt et al. (2018b), Eykholt et al. (2018a), and Chen et al. (2018b) attack neural classifiers and detectors of stop signs. While projective transformations could be used to render the planar stop signs to various images, it is more involved to image the nonplanar 3D vehicles considered in this paper; we learn a neural approximation function instead. Athalye et al. (2018b) synthesize objects (e.g., baseball, turtle, etc.) which are adversarial within a small range of camera-to-object distances and viewing angles. ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Given a 3D vehicle model in the simulation engine, we learn a camouflage for it by following the expectation over transformation (EoT) principle first formalized by Athalye et al. (2018b). The main idea is to consider a variety of transformations under which the camouflage can consistently hide the vehicle from a neural detector. A transformation imitates the imaging procedure and produces an image of the 3D vehicle model in the simulated environment. If a camouflage works under many transformations seen in the training phase, it is expected to also generalize to unseen transformations in the test phase. ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "One of the major challenges is that the simulator’s image generation procedure is non-differentiable. A seemingly plausible solution is to train a neural network to approximate this procedure. The network takes as input the environment, a camouflage pattern, and the 3D vehicle model and outputs an image as close as possible to the one rendered by the simulator. Although this approach is viable, it is extremely difficult to generate high-resolution images. State-of-the-art methods (e.g., RenderNet (Nguyen-Phuoc et al., 2018)) can only generate simple 3D objects without any backgrounds. ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "We tackle the above challenge by drawing the following observation. In EoT (Athalye et al., 2018b; Chen et al., 2018b), the gradients propagate back to the physical object from the detector/classifier’s decision values. If we jointly consider the object detector and the imaging procedure of the simulator as a whole black box, it is easier to learn a function to approximate this black box’s behavior than to train the image generation neural network. Hence, we learn a substitute neural network which takes as input a camouflage, the vehicle model, and the environment and outputs the vehicle detector’s decision value. Equipped with this substitute network, we can readily run the EoT algorithm (Athalye et al., 2018b) over our simulator in order to infer an adversarial camouflage for the vehicles. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Finally, we make some remarks about the significance and potential impact of this work. In the real world, multiclass visual object detection neural networks (He et al., 2017; Redmon & Farhadi, 2018) have become the cornerstone of multiple industrial applications, such as surveillance systems (Nair et al., 2018), autonomous driving (Huval et al., 2015), and military systems (Pellerin, 2017). Among these applications, cars are one of the most crucial objects. Attacking vehicle detectors in the physical world will be enormously valuable and impactful from the perspective of the malicious adversaries. Compared with the stop sign, it is legal in the United States to paint a car while defacing a stop sign is criminal. This poses a more significant threat to autonomous driving systems since anyone has access to perturb public machine learning based systems legally. This observation motivates us to focus our approach on cars. We limit our camouflage within the legally paintable car body parts, which means that we will leave discriminative visual cues, such as the tires, windows, grille, lights, etc. unaltered for the detectors. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "2 RELATED WORK ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            102,
+            344,
+            118
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2.1 ADVERSARIAL ATTACK AND ITS GENERALIZATION ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            135,
+            568,
+            148
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Currently, the adversarial attack is powerful enough to attack image classification (MoosaviDezfooli et al., 2017), object detection (Arnab et al., 2018), semantic segmentation (Xie et al., 2017), audio recognition (Carlini & Wagner, 2018) and even bypass most of the defense mechanism (Athalye et al., 2018a). The mainstream adversarial machine learning research focuses on the in silico ones or the generalization within in silico (Liu et al., 2017). Such learned perturbations are practically unusable in the real world as shown in the experiments by Lu et al. (2017b), who found that almost all perturbation methods failed to prevent a detector from detecting real stop signs. ",
+        "bbox": [
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+            162,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The first physical world adversarial attack by Kurakin et al. (2016) found perturbations remain effective on the printed paper. Eykholt et al. (2018b) found a way to train perturbations that remain effective against a classifier on real stop signs for different viewing angles and such. Athalye et al. (2018b) trained another perturbation that successfully attacks an image classifier on 3D-printed objects. However Lu et al. (2017c) found that Eykholt et al. (2018b)’s perturbation does not fool the object detectors YOLO9000 (Redmon & Farhadi, 2017) and Faster RCNN (Ren et al., 2015). They argue that fooling an image classifier is different and easier than fooling an object detector because the detector is able to propose object bounding boxes on its own. In the meanwhile, Lu et al. (2017a)’s and Chen et al. (2018b)’s work could be generalized to attack the stop sign detector in the physical world more effectively. However, all the above methods aim to perturb detecting the stop signs. ",
+        "bbox": [
+            174,
+            267,
+            825,
+            419
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Blackbox attack is another relevant topic. Among the current blackbox attack literature, Papernot et al. (2017) trained a target model substitution based on the assumption that the gradient between the image and the perturbation is available. We do not have the gradient since the simulation is nondifferentiable. Chen et al. (2017) proposed a coordinate descent to attack the model. However, we found that our optimization problem is time-consuming, noisy (see Sec. G.2), empirically nonlinear and non-convex (see Sec. H). Time constraints made this approach unavailable to us since it requires extensive evaluations during coordinate descent. Besides, coordinate descent generally requires precise evaluation at each data-point. ",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2.2 SIMULATION AIDED MACHINE LEARNING ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            558,
+            504,
+            571
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Since the dawn of deep learning, data collection has always been of fundamental importance as deep learning model performance is generally correlated with the amount of training data used. Given the sometimes unrealistically expensive annotation costs, some machine learning researchers use synthetic data to train their models. This is especially true in computer vision applications since state-of-the-art computer-generated graphics are truly photo-realistic. Ros et al. (2016); Richter et al. (2017) proposed synthetic datasets for semantic segmentation. Gaidon et al. (2016) proposed virtual KITTI as a synthetic replica of the famous KITTI dataset (Geiger et al., 2012) for tracking, segmentation, etc. And Varol et al. (2017) proposed using synthetic data for human action learning. Zhang et al. (2017); Bousmalis et al. (2017) adapt RL-trained robot grasping models from the synthetic environment to the real environment. Tremblay et al. (2018) trained a detection network using the same Unreal engine that we are using. ",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3 PROBLEM STATEMENT ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            761,
+            392,
+            776
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In this paper, we investigate physical adversarial attack on state-of-the-art neural network based object detectors. The objective is to find a camouflage pattern such that, when it is painted on the body of a vehicle, the Mask R-CNN (He et al., 2017) and YOLO (Redmon & Farhadi, 2018) detectors fail to detect the vehicle under a wide spectrum of variations (e.g., locations, lighting conditions, viewing angles, etc.). We learn the camouflage in a black-box fashion, without the need for accessing the detectors’ network architecture or weights. ",
+        "bbox": [
+            174,
+            794,
+            825,
+            877
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Expectation-over-transformation (EoT). We formalize the physical adversarial attack problem with the EoT framework (Athalye et al., 2018b). Denote by $t$ a transformation which converts a camouflage pattern $c$ to a real photo. Such a transformation actually represents an involved procedure: paint the pattern to a vehicle’s body, drive the vehicle to a location, configure a camera, and take a picture of the vehicle. The transformation conveniently abstracts away enormous factors (e.g., quality of painting, camera, etc.), each of which could play a role in this procedure. Denote by $V _ { t } ( c )$ the detection score (e.g., by Mask-RCNN) over an image which is a result of a transformation $t$ and a camouflage $c$ . The physical adversarial attack problem is then described by ",
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+        "type": "image",
+        "img_path": "images/8ce40e4e065c748809fb4d2c823c310987f3288f7931797026338a31e4250c30.jpg",
+        "image_caption": [
+            "Figure 2: Example procedure of a transformation $t$ . From left to right: a $1 6 \\times 1 6$ camouflage, a highfidelity vehicle, a location in our simulated environment, and an image due to this transformation over the camouflage. "
+        ],
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+        "type": "equation",
+        "img_path": "images/537bb3d41b6e15006c6c960fd8b87a23d139a51da1be19d6b521d07f5901d77d.jpg",
+        "text": "$$\n\\arg \\operatorname* { m i n } _ { c } \\quad \\mathbb { E } _ { t \\sim \\mathcal { T } } V _ { t } ( c )\n$$",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "where $\\tau$ is a distribution over all the possible transformations $\\{ t \\}$ . In other words, we search for a camouflage $c$ that minimizes the vehicle detection score in expectation. ",
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+        "type": "text",
+        "text": "Transformation in simulation. Due to financial and time constraints, we conduct our study with the photo-realistic Unreal 4 game engine. It supplies us sufficient configuration parameters, such as the resolution and pattern of the camouflage, 3D models of vehicles, parameters of cameras and environments, etc. Fig. 2 shows a camouflage pattern, a high-fidelity 3D model of Toyota Camry, a corner of the virtual city used in this paper, and finally the picture taken by a camera after we apply the camouflage to the Camry and drive it to that corner — in other words, the rightmost image is the result of a certain transformation $t$ acting on the three images on the left of Fig. 2. ",
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+    {
+        "type": "text",
+        "text": "4 APPROACH",
+        "text_level": 1,
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+        "type": "text",
+        "text": "In this section, we present two key techniques for solving the problem $\\operatorname* { m i n } _ { c }$ $\\mathbb { E } _ { t } V _ { t } ( c )$ (cf. Eq. (1) and the text there). One is to estimate the expectation $\\mathbb { E } _ { t }$ by an empirical mean over many transformations. The other is to train a neural network to clone the joint behavior $V _ { t } ( c )$ of the black-box detector and the non-differentiable simulator. ",
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+    {
+        "type": "text",
+        "text": "4.1 SAMPLING TRANSFORMATIONS TO ESTIMATE $\\mathbb { E } _ { t }$ ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Recall that a transformation $t$ specifies a particular procedure from applying the camouflage $c$ to a vehicle until the corresponding image captured by a camera. In the context of the simulation engine, the camouflage $c$ is first programmed as textures, which are then warped onto the 3D model of an object. The simulator can teleport the object to different locations in the environment. The simulator also has multiple cameras to photograph the teleported object from various distances and viewing angles. ",
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+        "type": "text",
+        "text": "We identify some key factors involved in this procedure, including vehicle, location, camera-toobject distance, and viewing angle. The combinations of them also give rise to variations along other dimensions. For instance, the lighting condition changes from one location to another. The vehicle of interest is occluded to different degrees in the images captured by the cameras. Denote by $T _ { S }$ all the sampled transformations that are used for learning the camouflage. ",
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+    {
+        "type": "text",
+        "text": "Fig. 3 illustrates the positions where the cameras are placed. We can see how the viewing angles and camera-to-object distances vary. The ones shown in the green color are used in the training. We left out some cameras shown in the red color for the testing. Since it is computationally expensive to utilize the cameras, we randomly arrange them in different heights and distances to create as much variations as possible instead of traversing all possible height-distance combinations. ",
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+    {
+        "type": "image",
+        "img_path": "images/0d907c35ed2ec5e62bc129613a2d8e17a9180e32ee9bc41fc30a8b1c8b9bb81f.jpg",
+        "image_caption": [
+            "Figure 3: The camera setup as well as some exemplar locations. The cameras depicted in the green color are used to learn the camouflage while those in red are unseen cameras used for testing the camouflage’s generalization. (H: camera height, L: vehicle-to-camera distance.) "
+        ],
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+    },
+    {
+        "type": "text",
+        "text": "4.2 LEARNING A CLONE NETWORK $V _ { \\theta } ( c , t )$ TO APPROXIMATE $V _ { t } ( c )$ ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "If we unroll the detection score $V _ { t } ( c )$ , it contains two major components. The first renders an image based on the camouflage $c$ by following the procedure specified by the transformation $t$ . The second obtains the detection score of a vehicle detector (e.g., Mask-RCNN) over the rendered image. The first component is non-differentiable while the second one could be a black box in practice. Therefore, we propose to consider them jointly as a single black box. Furthermore, we learn a clone neural network $V _ { \\theta } ( c , t )$ to imitate the input-output behavior of this extended black box. As the transformation $t$ itself is involved and hard to represent, we instead input its consequence to the network: a background image and the cropped foreground of the vehicle. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Fig. 4b shows the network architecture. It takes as input a camouflage pattern $c$ , the background image due to a sampled transformation $t$ , and the cropped foreground. The network $V _ { \\theta } ( c , t )$ has a single output to approximate the detection score $V _ { t } ( c )$ . ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "To this end, we are ready to write down an approximate form of problem (1), ",
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+    {
+        "type": "equation",
+        "img_path": "images/f2996211df5b2cbe73760a7068aaf9d7ff271d066a9dd81d87066e5af74e7a38.jpg",
+        "text": "$$\n\\underset { c } { \\arg \\operatorname* { m i n } } \\quad \\frac { 1 } { \\left| T _ { S } \\right| } \\sum _ { t \\in T _ { S } } V _ { \\theta } ( c , t ) .\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Thanks to the differentiable network $V _ { \\theta } ( c , t )$ with respect to the camouflage $c$ , we can solve the problem above by standard (stochastic) gradient descent. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "It is important to note that the fidelity of problem (2) depends on the size and diversity of the sampled set of transformations $T _ { S }$ as well as the quality of the clone network $V _ { \\theta } ( c , t )$ . It is straightforward to generate a large training set for the clone network by randomizing the camouflages and transformations and “labeling” the resulting images with the detection scores. However, if the optimal camouflage is unfortunately not covered by this training set, a discrepancy would occur when we solve problem (2). In other words, the network may fail to well approximate the detection scores at the region around the optimal camouflage. We address this discrepancy by an alternative learning algorithm as follows. ",
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+    },
+    {
+        "type": "text",
+        "text": "4.3 JOINTLY LEARNING THE CLONE NETWORK AND THE OPTIMAL CAMOUFLAGE",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We alternatively learn the clone network $V _ { \\theta } ( c , t )$ and solve the problem (2). Once a new camouflage pattern is found due to optimizing problem (2), it is converted to multiple images by the training ",
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+    {
+        "type": "image",
+        "img_path": "images/d80a830f80f9ae6649a361a1b2126f31e0602e65c93d2ec5d5144632a8b1de4c.jpg",
+        "image_caption": [
+            "Figure 4: Overview of our optimization pipeline and the clone network $V _ { \\theta } ( c , t )$ . "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "transformations $T _ { S }$ . We obtain the detection score for each of the images by querying a detector. The camouflage pattern, along with the detection scores are then added to the training set for learning the clone network $V _ { \\theta } ( c , t )$ . Fig. 4a illustrates this process. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Implementation details. Denote by $H [ p , q ] : = - p \\log q - ( 1 - p ) \\log ( 1 - q )$ the cross-entropy loss. We alternately solve the following two problems, ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "img_path": "images/74c41d2d113839749f73c6bcb38f6d9f2ede855417e083b92d0013e858063677.jpg",
+        "text": "$$\n\\arg \\operatorname* { m i n } _ { \\theta } \\ \\frac { 1 } { | C | | T s | } \\sum _ { c \\in C } \\sum _ { t \\in T s } H \\big [ s , V _ { \\theta } ( c , t ) \\big ] + \\lambda \\| \\theta \\| _ { 2 } , \\qquad \\arg \\operatorname* { m i n } _ { c } \\ \\frac { 1 } { | T | } \\sum _ { t \\in T s } H \\big [ 0 , V _ { \\theta } ( c , t ) \\big ] \n$$",
+        "text_format": "latex",
+        "bbox": [
+            192,
+            395,
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+            435
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where $C$ is the collection of all camouflages in the training set for learning the clone network $V _ { \\theta } ( c , t )$ , and $s : = V _ { t } ( c )$ is the detection score corresponding to the camouflage $c$ and the transformation $t$ . The $\\ell _ { 2 }$ regularization $\\lambda \\| \\boldsymbol { \\theta } \\| _ { 2 }$ over the clone network’s weights is essential. Without this term, the two loss functions may cause oscillations or degeneration of the solutions. We set $\\lambda = 1 0$ in the experiments. Since the approximation accuracy of the clone network near the optimal camouflage is more important than in other regions, we weigh the newly added samples to the training set 10 times higher than the old ones at each iteration. Algorithm 1 in the Appendix gives more details. ",
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+    {
+        "type": "text",
+        "text": "5 EXPERIMENTS ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Since the primary objective of this paper is to learn camouflage patterns that deceive vehicle detectors, we introduce two baseline camouflage patterns in the experiments: 6 most popular car colors and 800 random camouflages in different resolutions. We then analyze how the resolution of the camouflage affects the detection performance. For the vehicles, we employ two 3D models: a 2015 Toyota Camry and a virtual SUV. In addition to the main comparison results, we also test the transferability of the learned camouflage across different car models, environments, camera positions, and object detectors. ",
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+    {
+        "type": "text",
+        "text": "5.1 EXPERIMENT SETUP ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We describe the detailed experimental setup in this section, including the simulator, vehicle detector, evaluation metrics, and the baseline camouflage patterns. ",
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+    {
+        "type": "text",
+        "text": "5.1.1 THE SIMULATOR ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "As shown in Fig. 5a, we use the Unreal engine to build our first simulation environment from the photo-realistic DownTown environment. It is modeled after the downtown Manhattan in New York. There are skyscrapers, cars, traffic signs, a park, and roads in this environment, resembling a typical urban environment. We sample 32 different locations along the streets. Eight cameras perch at each location, each taking pictures of the size $7 2 0 \\times 3 6 0$ . The relative position of a camera is indexed by the viewing angle and camera-to-object distance, as shown in Fig. 3. In addition, we install another 16 cameras to test the generalization of the learned camouflage across viewing angles, distances, etc. In total, we use 18 locations for training and another 18 for testing. Note that the vehicles are invisible to some cameras due to occlusion. ",
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+    {
+        "type": "image",
+        "img_path": "images/8f13124eb918205339bb84dfbafd604190b286290f3672c52eedcfc46b983cd3.jpg",
+        "image_caption": [
+            "(b) A mountain environment. ",
+            "Figure 5: The two environments we built to learn and test the vehicle camouflage. Zoom in for more details. These images are of the higher resolution but the same rendering quality (anti-aliasing level, shadow quality, rendering distance, texture resolution etc.) the detector perceived. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Our second environment is based on a totally different countryside scene called Landscape Mountains, shown in Fig. 5b. The roads lie on high-altitude mountains and cross bridges, forest, snow, and a lake. We use this scene to test the transferability of our camouflage across different environments; this scene is not used in the training. Like the DownTown environment, we sample 18 locations along the roads for the purpose of testing. ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "The two vehicles used in the experiments are shown in Fig. 6. One is a 2015 Toyota Camry XLE sold in the European Union. The other is a virtual SUV from AirSim (Shah et al., 2017). It is worth noting that the Toyota sedan appears multiple times in the MS-COCO dataset (Lin et al., 2014) (cf. some examples in Fig. 12). Since the object detectors are trained on MS-COCO, the Camry is more challenging to hide than the virtual SUV. ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "5.1.2 VEHICLE DETECTORS ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "We study two state-of-the-art detectors: Mask R-CNN (He et al., 2017) and YOLOv3-SPP (Redmon & Farhadi, 2018). Mask R-CNN is one of the most powerful publicly available object detectors; it currently ranks in the 4th place in the MS COCO detection leaderboard. Both detectors are pretrained on MS COCO. For Mask R-CNN, we use the one implemented by Abdulla (2017). Its backbone network is ResNet-101 (He et al., 2016). YOLOv3 has comparable performance with ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/7bf363407a0ec8a0ce821f3d8fed8cd94affbd9f25a1dc00014589c6b9bc392f.jpg",
+        "image_caption": [
+            "Figure 6: Orthogonal views of the Toyota Carmy XLE 2015 (second row) and the virtual SUV (first row) used in our simulation. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Mask R-CNN. Its network architecture is very different from Mask R-CNN’s, causing challenges to the transfer of the camouflage between the two detectors. We use the spatial pyramid pooling (SPP) variant of YOLOv3 in the experiments. ",
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+        "page_idx": 7
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+    {
+        "type": "text",
+        "text": "In the rest of the paper, we experiment with Mask R-CNN except the transfer experiments in Sec. 5.4. ",
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+    },
+    {
+        "type": "text",
+        "text": "5.1.3 EVALUATION METRICS ",
+        "text_level": 1,
+        "bbox": [
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+            416,
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "We adopt two metrics to evaluate the detection performance. The first one is a variation of the Intersection over Union proposed by Everingham et al. (2015). The IoU between a predicted box and the groundtruth bounding box is defined as $\\begin{array} { r } { \\mathsf { \\bar { I } } o U ( A , B ) = \\frac { A \\bigcap B } { A \\bigcup B } } \\end{array}$ . Since IoU was originally proposed to evaluate the results of multi-object detection, as opposed to the single vehicle detection in our context, we modify it to the following to better capture the vehicle of interest: $\\mathrm { m a x } _ { p \\in P } I o U ( p , G T )$ , where $P$ is the set of all detection proposals in an image. We average this quantity across all the test images and denote by mIoU the mean value. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Our second metric is precision at 0.5 or $\\mathrm { P @ 0 . 5 }$ . Everingham et al. (2015) set a 0.5 threshold for the detection IoU in the PASCAL VOC detection challenge to determine whether a detection is a hit or miss. We report the percentage of the hit detections out of all observations as our $\\mathrm { P @ 0 . 5 }$ . We also report the relative precision drop of the camouflage against the baseline colors whenever possible. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "5.1.4 BASELINES",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Our first baseline is when a vehicle is colored in popular real car colors. We select 6 basic car colors (red, black, silver, grey, blue, and white) which cover over $90 \\%$ of the car colors worldwide (Axalta). We obtain their RGB values according to the X11 Color Names. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "As the second baseline, we generate 800 random camouflages in different resolutions ranging in $\\{ 2 ^ { i } \\times 2 ^ { i } ; i \\in [ 1 . . 8 ] \\}$ . Since we find that camouflages with strong contrasts work better, we generate half of the camouflages using RGB values $\\in \\ [ 0 , 2 5 5 ]$ and the other half using RGB values $\\in \\ \\{ 0 , 2 5 5 \\}$ . After we obtain these camouflages and the corresponding detection scores, we use those with proper resolutions to initialize the training set for the clone network $V _ { \\theta } ( c , t )$ . ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The two baselines partially resolve the concern one might have that the learned camouflage successfully attacks the detector not because it exploits the CNN’s structural weakness, but because it takes advantage of the domain gap between the real data used to train the detector and our simulated data used to test the detector. Results show that the baselines could not fail the detectors under most test cases, indicating that the detectors are fairly resilient to the domain gap between the simulated imagery and the real data (at least for the vehicle detection task). ",
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+    {
+        "type": "text",
+        "text": "5.2 RESOLUTION OF THE CAMOUFLAGES ",
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+    {
+        "type": "text",
+        "text": "We first report the random camouflages’ performance on hiding the Camry from the Mast R-CNN detector in the DownTown environment. Fig. 7 shows the results. The first observation is that, although random camouflages are visually very different from conventional car paintings (cf. Fig. 8), the Mask R-CNN detector is still able to detect most of them. Another slightly counter-intuitive yet interesting observation is that the detector’s performance does not always decrease as the camouflages’ resolutions increase. This is probably because some fine-grained patterns displayed by the high-resolution camouflage become harder to observe from a distance. Since the high-resolution camouflage does not bring any additional benefits beyond the $1 6 \\times 1 6$ resolution, we use camouflages of size $1 6 \\times 1 6$ in the remaining experiments. ",
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+        "img_path": "images/11a4ab5dbefbbf5e29ba8a2952b686f6f3f99b009e05bd12095189207c954e4a.jpg",
+        "image_caption": [
+            "Figure 7: The mIoU and $\\mathrm { P @ 0 . 5 }$ of the 800 random camouflages in different resolutions on Camry in the DownTown environment. There are 100 camouflages per resolution. "
+        ],
+        "image_footnote": [],
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+        "img_path": "images/217a875298bd410a386c9f2e08143f17befd7b1540cd894602391b3b94dc891d.jpg",
+        "image_caption": [
+            "Figure 8: Visualization of three random camouflages of resolutions $4 \\times 4$ , $1 6 \\times 1 6$ , and $2 5 6 \\times 2 5 6$ , respectively, as well as the resulting images by the same camera. "
+        ],
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+    {
+        "type": "text",
+        "text": "5.3 CAMOUFLAGING TOYOTA CAMRY IN THE URBAN ENVIRONMENT ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Here we report the results on detecting the Camry in the urban environment. Table 1 summarizes the results for the Camry respectively with the baseline colors, random camouflages, and our learned camouflage. We can see from the table that the Mask R-CNN is surprisingly robust against different types of random camouflages. The random camouflages’ detection scores are close to the baseline colors’. Moreover, the standard deviation of the random camouflages’ scores is also very low, indicating that the difference in the random camouflages does not really change the detector’s performance. Note that we apply the camouflage to the body of the Camry, leaving tires, windows, grilles, etc. as informative visual cues to the detector. Despite that, our learned camouflage reduces the precision by around $3 0 \\%$ over baseline colors in both training and testing scenes in the urban environment. ",
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+    {
+        "type": "table",
+        "img_path": "images/d94b3582e439b337d6719f6fd752836aee1c56ce6d6ee5b8b124314fea11781b.jpg",
+        "table_caption": [
+            "Table 1: Mask R-CNN detection performance on the Camry in the urban environment. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Camouflages</td><td colspan=\"2\">Training Scenes</td><td colspan=\"2\">Testing Scenes</td></tr><tr><td>mIoU (%)</td><td>P@0.5 (%)</td><td>mIoU (%)</td><td>P@0.5 (%)</td></tr><tr><td>Baseline Colors</td><td>76.14</td><td>84.40</td><td>72.88</td><td>77.57</td></tr><tr><td>Random Camou</td><td>73.48± 0.80</td><td>82.17± 1.20</td><td>67.79± 0.79</td><td>71.42± 1.20</td></tr><tr><td>Ours</td><td>57.69</td><td>62.14</td><td>53.64</td><td>52.17</td></tr><tr><td>Relative Performance Drop</td><td>24.23%</td><td>26.37%</td><td>26.39%</td><td>32.74%</td></tr></table>",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/560406611012e0e930fce122aa5836b60b840c0cd2e08835bbd5c49a6437c156.jpg",
+        "table_caption": [
+            "Table 2: YOLOv3-SPP detection performance on the Camry in the urban environment. In addition to the camouflage inferred for YOLO, we also include the YOLO detection results on the camouflage learned for Mask R-CNN. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Camouflages</td><td colspan=\"2\">Training Scenes</td><td colspan=\"2\">Testing Scenes</td></tr><tr><td>mIoU (%)</td><td>P@0.5 (%)</td><td>mIoU (%)</td><td>P@0.5 (%)</td></tr><tr><td>Baseline colors</td><td>76.79</td><td>85.34</td><td>73.00</td><td>78.50</td></tr><tr><td>Random Camou</td><td>73.19±0.75</td><td>83.30±0.89</td><td>68.76±0.81</td><td>73.92±1.00</td></tr><tr><td>Ours (YOLO trained)</td><td>65.83</td><td>72.53</td><td>64.03</td><td>69.56</td></tr><tr><td>Ours (Mask R-CNN trained)</td><td>65.43</td><td>70.42</td><td>61.79</td><td>65.21</td></tr><tr><td>Relative Performance Drop</td><td>14.79%</td><td>17.48%</td><td>15.35%</td><td>16.92%</td></tr></table>",
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+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Virtual SUV. Appendix A presents the results on the virtual SUV. The learned camouflage reduces Mask R-CNN’s detection precision by around $40 \\%$ from the precision for the baseline colors. ",
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+    {
+        "type": "text",
+        "text": "5.4 TRANSFERABILITY EXPERIMENTS ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "We show that the camouflage learned to attack Mask R-CNN can actually also defeat YOLOv3 to a certain degree. The results are reported in Table 2. Similarly, appendices A to D report the transferabilities of the learned camouflage across different environments, vehicles, camera viewing angles, and distances from the camera to the object. ",
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+    {
+        "type": "text",
+        "text": "5.5 QUALITATIVE RESULTS ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "We present some of our detection results on the baseline colors, random camouflages, and the learned camouflages for the Camry in Fig. 11. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We can draw a lot of interesting observations from the qualitative results which were hidden by the quantitative results. We find that there are 3 types of successful attacks: (1) Camouflages lower the objectiveness of the car and the car region is not proposed or only partially proposed as a candidate for the classifier of the detector; (2) The car region is successfully proposed but misclassified (e.g., to kite, cake, truck, or potted plant as shown in the examples) or the classification score is too low to pass the threshold for the detection score; (3) The car region is successfully proposed and classified, but the camouflage results in an incorrect detection which largely overlaps with the car (cf. the 5th row where the regions covering the car are detected as a car and a boat, respectively). ",
+        "bbox": [
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+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "One can see that the context or background plays a vital role in object detection. Although some images capture the Camry by the same pose, the detector makes completely different predictions for them. Besides, these qualitative results imply that the detector works in a way different from human vision. In the Landscape environment, our learned camouflage has the strongest contrast to the background compared to other baseline patterns. However, the detector is still sometimes not able to detect the camouflaged car or SUV. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "6 CONCLUSION ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "In this paper, we investigate whether it is possible to physically camouflage 3D objects of complex shapes, i.e., vehicles, in order to hide them from state-of-the-art object detectors. We conduct extensive experimental studies with a photo-realistic simulation engine. We propose to use a clone network to mimic the simulator and the detector’s joint response to the 3D vehicles. Then, we infer a camouflage for a 3D vehicle by minimizing the output of the clone network. Our learned camouflage significantly reduces the detectability of a Toyota Camry and a SUV. Moreover, we find that the camouflage is transferable across different environments. For future work, We plan to look into possible ways to white-box the entire process so as to propose a more effective camouflage. ",
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+    {
+        "type": "text",
+        "text": "ACKNOWLEDGMENT ",
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+        "type": "text",
+        "text": "This work was in part supported by the NSF grants IIS-1212948, IIS-1566511, and a gift from Uber Technologies Inc. ",
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+        "bbox": [
+            174,
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+        "page_idx": 12
+    },
+    {
+        "type": "table",
+        "img_path": "images/e84352dde5e804ac5dd2e5bdc008624ee578d024ba28727d32c89c5f570f02c8.jpg",
+        "table_caption": [
+            "Table 3: Detection performance of camouflages on SUV in urban environment. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"3\">Camouflages</td><td colspan=\"2\">Training Scenes</td><td colspan=\"2\">Testing Scenes</td></tr><tr><td>mIoU (%)</td><td>P@0.5 (%)</td><td>mIoU (%)</td><td>P@0.5 (%)</td></tr><tr><td>Baseline Colors</td><td>82.35</td><td>91.07</td><td>81.06</td><td>89.22</td></tr><tr><td>Random Camou</td><td>83.53±3.26</td><td>93.21±3.48</td><td>78.02±2.53</td><td>84.79±2.81</td></tr><tr><td>Ours</td><td>53.27</td><td>55.79</td><td>48.91</td><td>50.36</td></tr><tr><td>Relative Performance Drop</td><td>35.31%</td><td>38.79%</td><td>39.66%</td><td>43.55%</td></tr></table>",
+        "bbox": [
+            192,
+            101,
+            805,
+            213
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "table",
+        "img_path": "images/10cc77eb1dd79d7cfec9133089eeabe353a3ab9354e732ce1c7b99022ca9bcc3.jpg",
+        "table_caption": [
+            "Table 4: Detection performance of camouflages on Camry in Landscape environment. Note that this camouflage is pretrained in urban environment and then transferred without any finetuning. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Camouflages</td><td colspan=\"2\">Testing Scenes</td></tr><tr><td>mIoU (%)</td><td>P@0.5 (%)</td></tr><tr><td>Baseline Colors</td><td>74.81</td><td>82.04</td></tr><tr><td>Random Camou</td><td>72.45±4.26</td><td>77.11±5.45</td></tr><tr><td>Ours - Transferred</td><td>40.39</td><td>43.26</td></tr><tr><td>Relative Performance Drop</td><td>46.00%</td><td>47.26%</td></tr></table>",
+        "bbox": [
+            299,
+            258,
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+            372
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "A VIRTUAL SUV IN URBAN AREA ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            443,
+            477,
+            459
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "We then report the camouflage performance on the newly modeled SUV in the urban environment in Table 3. ",
+        "bbox": [
+            171,
+            479,
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+            508
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "Judging by the results, it is clear that the Mask R-CNN is a very generalized detector. The SUV’s baseline color and random camouflage detection scores are even higher than the Camry correspondence although the detector has never seen it before. This might be because the SUV has much less polygon and is built to resemble the shape of a general SUV as shown in Fig. 6. ",
+        "bbox": [
+            174,
+            515,
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+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "However, the price for not seeing this vehicle during training is that Mask R-CNN is more likely to be affected by the camouflage. The standard deviation of the random camouflage mIoU/ precision is higher (3.26/3.48 vs. 0.8/1.2) than Camry. And our camouflage achieves lower detection precision despite both baseline colors and random camouflage’s detection scores are higher than Camry’s. The detectability is reduced by almost 1.5 times of Camry’s results in this case. This experiment shows that Mask R-CNN might well generalize to unseen vehicles, but it is easier to get attacked. ",
+        "bbox": [
+            174,
+            578,
+            825,
+            662
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "B TRANSFERABILITY ACROSS ENVIRONMENTS ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            691,
+            581,
+            708
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "Another important question is that what if we transfer the camouflage to a not only previously unseen but a totally different environment? To quantitatively answer this question, we build the Landscape environment (Fig. 5b) to test our camouflages trained in urban environment (Fig. 5a) using the Camry vehicle. The results are reported in Table. 4. Some qualitative results are shown in Fig. 11. ",
+        "bbox": [
+            174,
+            728,
+            825,
+            797
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "Given the barren landscape with few objects in sight, the detector detects the car better than it did in the urban environment for both baseline colors (82.04 vs. 77.57) and random camouflages (77.11 vs. 71.42) possibly due to the absence of distractions. However, our directly transferred camouflage is still able to beat both of them by more than $46 \\%$ regarding both detection mIoU and precision without any fine-tuning. ",
+        "bbox": [
+            174,
+            805,
+            825,
+            875
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "It is interesting to notice that the Camry with grey color looks almost identical to the background in this environment (Fig. 11). However, it still could be perfectly detected. Meanwhile, our leaned camouflage results in far better stealth despite it has a sharp contrast to the background. ",
+        "bbox": [
+            176,
+            882,
+            823,
+            924
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "table",
+        "img_path": "images/207830d460f97efc0bb2717cf94292a6f95cbf0561e25dfb8093a5d80326b127.jpg",
+        "table_caption": [
+            "Table 5: Camouflage transferability across vehicle reported in testing $\\mathrm { P @ 0 . 5 }$ in urban environment. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td></td><td colspan=\"2\">Test</td></tr><tr><td></td><td></td><td>SUV</td><td>Camry</td></tr><tr><td>TTeil</td><td>SUV</td><td>50.36</td><td>47.44</td></tr><tr><td></td><td>Camry</td><td>58.39</td><td>52.17</td></tr></table>",
+        "bbox": [
+            388,
+            102,
+            609,
+            172
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "table",
+        "img_path": "images/dcb576bd1e9028889955556c15030532b297490e561e4b31bbf970a987905c31.jpg",
+        "table_caption": [
+            "Table 6: Detection performance of pretrained camouflages on Camry with urban environment in 16 unseen cameras. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Camouflages</td><td colspan=\"2\">Testing Scenes</td></tr><tr><td>mIoU (%)</td><td>P@0.5 (%)</td></tr><tr><td>Baseline Colors</td><td>78.43</td><td>86.16</td></tr><tr><td>Random Camou</td><td>77.26±0.96</td><td>84.61±1.06</td></tr><tr><td>Ours - Transferred</td><td>67.74</td><td>73.14</td></tr><tr><td>Relative Performance Drop</td><td>13.62%</td><td>15.11%</td></tr></table>",
+        "bbox": [
+            299,
+            210,
+            697,
+            323
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "C TRANSFERABILITY ACROSS VEHICLES ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            386,
+            531,
+            401
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "It will be impractical to retrain a specific camouflage for each vehicle whenever we need it. Hence it would be interesting to look into the transferability between vehicles in this scenario. We swap the camouflages of SUV and Camry and see how they would perform in the urban environment. We present the testing precision after swapping in Table. 5. ",
+        "bbox": [
+            174,
+            416,
+            825,
+            473
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "First, both camouflages are definitely transferable. It is also interesting to see that the Camry learned camouflage is not as good as the SUV learned camouflage even when being applied on the Camry itself. This might be due to the fact that the SUV resembles a car with more generic features and hence learning camouflage on SUV is less likely to encounter local minima during optimization. ",
+        "bbox": [
+            174,
+            479,
+            825,
+            536
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "D TRANSFERABILITY ACROSS VIEWING POSITION ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            555,
+            607,
+            571
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "One of the possibly most concerning questions is whether the learned camouflage is robust to the change of the camera position. To answer this question, we set up another 16 new cameras, as shown in Fig. 3, surrounding the vehicle in different relative locations. We then test the learned camouflage’s performance on these new cameras. The results are shown in Table 6. ",
+        "bbox": [
+            174,
+            587,
+            825,
+            642
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "Our camouflage performance drop has a slightly decrease of $5 \\%$ from Table 1. This indicates that the change of the camera locations would impact the performance, but the performance drop is still way beyond the standard deviation of random camouflages’ scores. Given that the new camera views cover more perspectives as shown in Fig. 3, this result is reasonable. ",
+        "bbox": [
+            174,
+            650,
+            825,
+            705
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "E IMPACT OF CLONE NETWORK QUALITY ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            726,
+            539,
+            742
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "How does the clone network’s quality affect the camouflage’s performance? Is the alternative optimization necessary? We quantitatively show the first 300 simulation calls of our system in Fig. 9 and meanwhile evaluate the camouflages proposed by the clone network. Note that initially the clone network has already been trained with 800 random camouflages. However, the proposed camouflage’s score does not fall until the new camouflages from iteration scheme join the optimization. This suggests that without our iterative optimization mechanism, the clone network could only find camouflage with mIoU around $70 \\%$ , which is the same as the random camouflage. Those new samples serve as the hard samples. They gradually calibrate the clone network’s global minima to $V _ { t } ( )$ ’s and help it to generate better camouflages. Note that although the score descends quicker during the first 50 iterations, it does not find the global best camouflage until near the end (296th iteration). This graph also shows the classification score is a suitable choice to be minimized as it is highly correlated with mIoU. ",
+        "bbox": [
+            174,
+            757,
+            825,
+            922
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "Note that the system automatically re-initialize the clone network’s parameters to prevent it from falling into local minima during the optimization whenever we add a new sample to the training set $C$ . Hence, there are some spikes in the graph. ",
+        "bbox": [
+            174,
+            103,
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+            146
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "image",
+        "img_path": "images/e6cea3b0fef3f0adcba8636a06e8de8e20ff076673920721b5d123a99143cf71.jpg",
+        "image_caption": [
+            "Figure 9: Clone network’s learned camouflage’s classification score and mIoU vs. Simulation called. We can see how the new samples helped the clone network to find the minimal. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            173,
+            161,
+            825,
+            342
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "F DETECTION ATTENTION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            416,
+            408,
+            431
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "How exactly does our camouflage work against the detector? We partially answer this question by visualizing Mask-RCNN’s completely/partially successful detection attention on our grey and camouflaged Camry. Since our Mask-RCNN implementation does not explicitly yield failed detection’s prediction, we are unable to visualize the failed detection’s attention w.r.t. the input image if the failed detection does not exist. ",
+        "bbox": [
+            174,
+            450,
+            825,
+            520
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "There are two main visualization approaches: Grad-CAM (Selvaraju et al., 2017) and saliency (Simonyan et al., 2013). Approximately speaking, grad-CAM visualizes the gradient of output w.r.t. penultimate (pre-fully-connected layer) convolutional layer feature map output; Saliency visualizes the gradient of output w.r.t. initial input image. Grad-CAM is generally considered superior as the last convolutional layer’s feature map contains much more abstracted semantic information, leading to less noisy visualization. However, we find that it is hard to define the single “penultimate layer” in Mask-RCNN: It has multiple penultimate layers, tracing back to different stages of the network, prior to the ROI pooling layer. Each of those penultimate layers contains varying levels of information. We choose to use saliency in this case. ",
+        "bbox": [
+            174,
+            526,
+            825,
+            652
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "It is clear how to define the “attention” in the image classification scenario: It is the gradient heatmap of the classification score scalar w.r.t. the entire input image. On the other hand, an end-to-end detection neural network often yields multiple structure predictions. Each structure contains bounding box and classification score, etc. We choose to visualize the gradient of the best bounding-box’s classification score w.r.t. the input image. ",
+        "bbox": [
+            174,
+            659,
+            825,
+            728
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "Our visualizations are presented in Fig. 10. It is surprising that the window, roof and upper bodies are playing the predominant role in car detection. Upper body attention exists even when the upper body is not included in the detection bounding box (row 3). Given that the classification stage makes the classification decision based on the proposed feature map box region, such attention must have been already included in the detection proposal before the ROI layer, i.e. detection stage. This may also explain why it is easier to fail the front-viewing and the rear-view detectors: front-view (row 1) and the rear-view (row 5) detectors place their attention on the hood and trunk, where camouflage pattern is presented. A partially successful attack (row 4) was carried out by wiping out detector’s attention on the car hood. On the other hand, the side-view detector is harder to attack since the detector merely places any attention of the car body (row 2) where the camouflages are mainly located. However, our camouflages on the roof could still fail the side-view detector partially (row 3). ",
+        "bbox": [
+            174,
+            736,
+            825,
+            901
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "Since we only visualize the (partially) successful detections, there are still many cases to explore. ",
+        "bbox": [
+            171,
+            909,
+            807,
+            924
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "image",
+        "img_path": "images/b49fa4ebb626dc4aa9b44f1f8895d991d5d6a97915956a86c42489b7211c7c33.jpg",
+        "image_caption": [
+            "Figure 10: The best detections in each image and the gradient heatmap of their classification scores w.r.t. the input images. The detector places its attention predominantly on the upper car body, i.e., roof, hood, trunk, and windows. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            217,
+            102,
+            781,
+            661
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "text",
+        "text": "G SIMULATION SETUP ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            752,
+            377,
+            768
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "text",
+        "text": "G.1 SIMULATION IMPLEMENTATION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            792,
+            437,
+            808
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "text",
+        "text": "The iterative optimization framework works on two Nvidia GTX 1080 Ti in our experiment. We use one to run the detector and another one to run the simulation and training/ prediction of evaluation network. The simulation was implemented partially using AirSim by Shah et al. (2017) and UnrealEnginePython. All submodules are implemented asynchronously to run in parallel and are communicating with each other using RPC/ RPyC. All the camouflages and the baseline colors are implemented either using or based on the official Unreal Automotive Material. Each evaluation in the simulation, which is the most time-consuming part, takes around 15 to 20 second. ",
+        "bbox": [
+            173,
+            825,
+            825,
+            924
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "text",
+        "text": "G.2 SIMULATION ERROR ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            103,
+            361,
+            118
+        ],
+        "page_idx": 17
+    },
+    {
+        "type": "text",
+        "text": "Despite our best effort, we observe $V _ { t } ( c )$ come with a standard deviation of 0.008 due to the inherent and mostly necessary random processes in the rendering (i.e., Monte Carlo in path tracing, etc.). This unfortunately makes $V _ { t } ( c )$ a noisy function. We reduce this error by repeat sampling $\\bar { V } _ { t } ( c )$ 5 times whenever we use it. ",
+        "bbox": [
+            173,
+            128,
+            825,
+            185
+        ],
+        "page_idx": 17
+    },
+    {
+        "type": "text",
+        "text": "H NON-LINEARITY AND NON-CONVEXITY ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            205,
+            544,
+            223
+        ],
+        "page_idx": 17
+    },
+    {
+        "type": "text",
+        "text": "Since this is a blackbox optimization problem, it is important to examine some important features of the $\\textstyle \\mathbb { E } _ { t } V _ { t } ( \\cdot )$ . We first verify its convexity via the convexity definition. We test the convexity of $\\mathbb { E } _ { t } V _ { t } ( \\cdot )$ by testing the convexity of subsampled correspondence $\\begin{array} { r } { \\frac { 1 } { \\left| T _ { S } \\right| } \\sum _ { t \\in T _ { S } } V _ { t } ( \\cdot ) } \\end{array}$ via: ",
+        "bbox": [
+            173,
+            236,
+            826,
+            284
+        ],
+        "page_idx": 17
+    },
+    {
+        "type": "equation",
+        "img_path": "images/45993684d7564ba464b9774e2b3610f538ed82fee79369c832d73eff708a22b1.jpg",
+        "text": "$$\n\\forall c _ { 1 } , c _ { 2 } \\in C : \\quad \\frac { 1 } { | T _ { S } | } \\sum _ { t \\in T _ { S } } V _ { t } ( \\frac { c _ { 1 } + c _ { 2 } } { 2 } ) \\leq \\frac { 1 } { | T _ { S } | } \\sum _ { t \\in T _ { S } } V _ { t } \\frac { V _ { T _ { S } } ( c _ { 1 } ) + V _ { T _ { S } } ( c _ { 2 } ) } { 2 }\n$$",
+        "text_format": "latex",
+        "bbox": [
+            251,
+            295,
+            745,
+            337
+        ],
+        "page_idx": 17
+    },
+    {
+        "type": "text",
+        "text": "where $C$ is a set of camouflages. We sampled 1000 pairs of random camouflages from $C$ and half of them do not meet the equation. Hence $\\begin{array} { r } { \\frac { 1 } { | T _ { S } | } \\sum _ { t \\in T _ { S } } ^ { } { \\bar { V } } _ { t } ( \\cdot ) } \\end{array}$ is nonconvex. ",
+        "bbox": [
+            174,
+            345,
+            823,
+            377
+        ],
+        "page_idx": 17
+    },
+    {
+        "type": "text",
+        "text": "Besides, we find a simple linear MLP is insufficient to approximate $\\begin{array} { r } { \\frac { 1 } { \\left| T _ { S } \\right| } \\sum _ { t \\in T _ { S } } V _ { t } ( \\cdot ) } \\end{array}$ , which empirically shows it is nonlinear. ",
+        "bbox": [
+            173,
+            383,
+            820,
+            416
+        ],
+        "page_idx": 17
+    },
+    {
+        "type": "text",
+        "text": "I SUPPLEMENTAL FIGURES ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            436,
+            415,
+            453
+        ],
+        "page_idx": 17
+    },
+    {
+        "type": "text",
+        "text": "Algorithm 1: Iterative Object Camouflage Learning ",
+        "text_level": 1,
+        "bbox": [
+            173,
+            478,
+            517,
+            493
+        ],
+        "page_idx": 17
+    },
+    {
+        "type": "text",
+        "text": "Input : Clone network parameter $V _ { \\theta } ( \\cdot )$ ; Simulation and detection $V _ { T _ { S } } ( \\cdot )$ ; Transformation $T _ { S }$ which are parameterized as rendered background and foreground images; Regularization tradeoff $\\alpha$ ; Random camouflage set $C _ { R }$ . ",
+        "bbox": [
+            168,
+            496,
+            813,
+            539
+        ],
+        "page_idx": 17
+    },
+    {
+        "type": "text",
+        "text": "1 Initialize $V _ { \\theta }$ with random weights $\\theta$ ",
+        "bbox": [
+            163,
+            539,
+            410,
+            551
+        ],
+        "page_idx": 17
+    },
+    {
+        "type": "text",
+        "text": "2 Set score record $s ^ { * }  + \\infty$ ",
+        "bbox": [
+            161,
+            553,
+            357,
+            565
+        ],
+        "page_idx": 17
+    },
+    {
+        "type": "text",
+        "text": "5 F $\\begin{array} { r } { \\theta  \\arg \\operatorname* { m i n } _ { \\theta } \\ \\frac { 1 } { | C | | T _ { S } | } \\sum _ { c \\in C } \\sum _ { t \\in T _ { S } } H \\big [ s , V _ { \\theta } ( c , t ) \\big ] + \\lambda \\| \\theta \\| _ { 2 } } \\end{array}$   \n6 $\\begin{array} { r } { c ^ { \\prime } \\gets \\arg \\operatorname* { m i n } _ { c } \\frac { 1 } { | T | } \\sum _ { t \\in T _ { S } } H \\big [ 0 , V _ { \\theta } ( c , t ) \\big ] } \\end{array}$   \n7 s0 ← {Vt(c)|t ∈ T }   \n8 C ← C ∪ {c0}   \n9 if mea $1 ( s ^ { \\prime } ) < s ^ { * }$ then   \n10 s∗ ← mean(s0)   \n11 c ∗ ← c 0 ",
+        "bbox": [
+            158,
+            593,
+            601,
+            700
+        ],
+        "page_idx": 17
+    },
+    {
+        "type": "text",
+        "text": "12 until Reach maximum training steps output: Best learned camouflage $c ^ { * }$ ",
+        "bbox": [
+            155,
+            702,
+            415,
+            729
+        ],
+        "page_idx": 17
+    },
+    {
+        "type": "image",
+        "img_path": "images/e53c10bceacd153d333f31b7e0cdfa3d6e757e1bc35df9f0780558ccc6b33f10.jpg",
+        "image_caption": [
+            "Figure 11: Qualitative comparison of the Mask R-CNN detections results of the grey baseline color, random camouflages and our learned camouflages in different transformations. Zoom in for more details. 19 "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            202,
+            47,
+            790,
+            912
+        ],
+        "page_idx": 18
+    },
+    {
+        "type": "image",
+        "img_path": "images/b1188dd4fb2e6e0ce606158e83f009828d30947abde20b98c09f3a3ea6c18f4e.jpg",
+        "image_caption": [
+            "Figure 12: A fraction of different Toyota sedan appearances in MS COCO dataset. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            176,
+            376,
+            823,
+            618
+        ],
+        "page_idx": 19
+    }
+]

parse/train/SylR6n4tPS/SylR6n4tPS.md

@@ -0,0 +1,443 @@
+# LEARNING TO GENERATE GROUNDED VISUAL CAPTIONS WITHOUT LOCALIZATION SUPERVISION
+
+Anonymous authors Paper under double-blind review
+
+# ABSTRACT
+
+When automatically generating a sentence description for an image or video, it often remains unclear how well the generated caption is grounded, or if the model hallucinates based on priors in the dataset and/or the language model. The most common way of relating image regions with words in caption models is through an attention mechanism over the regions that are used as input to predict the next word. The model must therefore learn to predict the attentional weights without knowing the word it should localize. This is difficult to train without grounding supervision since recurrent models can propagate past information and there is no explicit signal to force the captioning model to properly ground the individual decoded words. In this work, we help the model to achieve this via a novel cyclical training regimen that forces the model to localize each word in the image after the sentence decoder generates it, and then reconstruct the sentence from the localized image region(s) to match the ground-truth. Our proposed framework only requires learning one extra fully-connected layer (the localizer), a layer that can be removed at test time. We show that our model significantly improves grounding accuracy without relying on grounding supervision or introducing extra computation during inference for both image and video captioning tasks.
+
+# 1 INTRODUCTION
+
+Vision and language tasks, such as visual captioning, combine linguistic descriptions with data from real-world scenes. Deep learning models for such tasks have achieved great success, driven in part by the development of attention mechanisms that focus on various objects in the scene while generating captions. The resulting models, however, are known to have poor grounding performance (Liu et al., 2017), leading to undesirable behaviors such as object hallucinations (Rohrbach et al., 2018), despite having high captioning accuracy. That is, they often do not correctly associate generated words with the appropriate image regions (e.g., objects) in the scene, resulting in models that lack interpretability.
+
+Several existing approaches have tried to improve the grounding of captioning models. One class of methods generate sentence templates with slot locations explicitly tied to specific image regions. These slots are then filled in by visual concepts identified by off-the-shelf object detectors (Lu et al., 2018). Other methods have developed specific grounding or attention modules that aim to attend to the correct region(s) for generating visually groundable word. Such methods, however, rely on explicit supervision for optimizing the grounding or attention modules (Liu et al., 2017; Zhou et al., 2019) and require bounding box annotations for each visually groundable word.
+
+In this work, we propose a novel cyclical training regimen that is able to significantly improve grounding performance without any grounding annotations. The key insight of our work is that current models use attention mechanisms conditioned on the hidden features of recurrent modules such as LSTMs, which leads to effective models with high accuracy but entangle grounding and decoding. Since LSTMs are effective at propagating information across the decoding process, the network does not necessarily need to associate particular decoded words with their corresponding image region(s). However, for a captioning model to be visually grounded, the model has to predict attentional weights without knowing the word to localize.
+
+Based on this insight, we develop a cyclical training regimen to force the network to ground individual decoded words: decoding localization reconstruction. Specifically, the model of the decoding stage can be any state-of-the-art captioning model; in this work, we follow GVD (Zhou et al.,
+
+![](images/0191d1b03fd8d68cefb4d470c6580cba03e8cbf57b16895815382e18d40d3f8d.jpg)  
+Figure 1: Visual captioning models are often not visually-grounded. As human, we perform localization to check whether the generated caption is visually-grounded. If the localized image region is incorrect, we update the model. However, without the ground-truth grounding annotation, how does the model know the localized region is incorrect? To overcome this issue, we propose to perform localization and reconstruction to regularize the captioning model to be visually-grounded without relying on the grounding annotations.
+
+2019) to extend the widely used Up-Down model (Anderson et al., 2018). At the localization stage, each word generated by the first decoding stage is localized through a localizer, and the resulting grounded image region(s) are then used to reconstruct the ground-truth caption in the final stage. Both decoding and reconstruction stages are trained using a standard cross-entropy loss. Key to our method, both stages share the same decoder, thereby causing the localization stage to guide the decoder to improve its attention mechanism. Our method is simple and only adds a fully-connected layer to perform localization. During inference, we only use the (shared) decoder, thus we do not add any computational cost.
+
+We benchmark our proposed method on the challenging Flickr30k Entities image captioning dataset (Plummer et al., 2015) and the ActivityNet-Entities video captioning dataset (Zhou et al., 2019) on both captioning and grounding performances. In addition to the existing grounding metric that calculate the grounding accuracy for each object class (Zhou et al., 2019), we further include a grounding metric that compute grounding accuracy for each generated sentence. This new metric on each sentence removes the stringency of the original evaluation metric (as we discuss in Sec. 4) and provides an alternative way of measuring the grounding performance.
+
+Despite the simplicity of our proposed method, we are able to significantly surpass prior unsupervised models quantitatively and qualitatively on both datasets. We achieve around $18 \%$ relative improvements in terms of bridging the gap between the unsupervised baseline and supervised methods on Flickr30k Entites and around $34 \%$ on ActivityNet-Entities. We further find that our method can even outperform the supervised method on infrequent words, owing to its self-supervised nature.
+
+Contributions summary. We propose object re-localization as a form of self-supervision for grounded visual captioning and present a cyclical training regimen that re-generates sentences after re-localizing the objects conditioned on each word, implicitly imposing grounding consistency. We evaluate our proposed approach on both image and video captioning tasks. We show that the proposed training regime can boost grounding accuracy over a state-of-the-art baseline, enabling grounded models to be trained without bounding box annotations, while retaining high captioning quality across two datasets and various experimental settings. Our code will be publicly released and can be found in supplemental.
+
+# 2 RELATED WORK
+
+Visual captioning. Neural models for visual captioning have received significant attention recently (Anderson et al., 2018; Ma et al., 2018; Lu et al., 2018; Donahue et al., 2015; Venugopalan et al., 2015; Rohrbach et al., 2017b; Venugopalan et al., 2017; Rohrbach et al., 2017a; Shetty et al., 2017; Park et al., 2019). Most current state-of-the-art models contain attention mechanisms, allowing the process to focus on subsets of the image when generating the next word. These attention mechanisms can be defined over spatial locations (Vinyals et al., 2015), semantic metadata (Li et al., 2018; Yao et al., 2017; You et al., 2016; Zhou et al., 2017) or a predefined set of regions extracted via a region proposal network (Ma et al., 2018; Zanfir et al., 2016; Anderson et al., 2018; Lu et al., 2018; Das et al., 2013; Kulkarni et al., 2013). In the latter case, off-the-shelf object detectors are first used to extract object proposals (Ren et al., 2015; He et al., 2017) and the captioning model then learns to dynamically attend over them when generating the caption.
+
+Visual grounding. Although attention mechanisms are generally shown to improve captioning quality and metrics, it has also been shown that they don’t really focus on the same regions as a human would (Das et al., 2017). This make models less trustworthy and interpretable, and therefore creating grounded image captioning models, i.e., models that accurately link generated words or phrases to specific regions of the image, has recently been an active research area. A number of approaches have been proposed, e.g., for grounding phrases or objects from image descriptions (Rohrbach et al., 2016; Hu et al., 2016; Xiao et al., 2017; Deng et al., 2018; Zhou et al., 2019; Zhang et al., 2019), grounding visual explanations (Hendricks et al., 2018), visual co-reference resolution for actors in video (Rohrbach et al., 2017a), or improving grounding via human supervision (Selvaraju et al., 2019). Recently, Zhou et al. (2019) presented a model with self-attention based context encoding and direct grounding supervision that achieves state-of-the-art results in both the image and video tasks. They exploit ground-truth bounding box annotations to significantly improve the visual grounding accuracy. In contrast, we focus on reinforcing the visual grounding capability of the existing captioning model via a cyclical training regimen without using bounding box annotations and present a method that can increase grounding accuracy while maintaining comparable captioning performance with state of the arts.
+
+Cyclical training. Cycle consistency (Wang et al., 2013; Zhu et al., 2017; He et al., 2016; Chen & Lawrence Zitnick, 2015) has been used recently in a wide range of domains, including machine translation (He et al., 2016), unpaired image-to-image translation (Zhu et al., 2017), visual question answering (Shah et al., 2019), question answering (Tang et al., 2018), image captioning (Chen & Lawrence Zitnick, 2015), video captioning (Wang et al., 2018; Duan et al., 2018), captioning and drawing (Huang et al., 2018) as well as domain adaptation (Hosseini-Asl et al., 2019). While the cyclical training regime has been explored vastly in both vision and language domains, it has not yet been used for enforcing the visual grounding capability of a captioning model.
+
+# 3 METHOD
+
+Notation. For a visual captioning task, we denote the input image as $I$ (or input video as $V$ ) and the target sentence as $S$ . Each image (or video) is represented by spatial feature map(s) extracted by a ResNet-101 model and a bag of regions obtained from Faster-RCNN (Ren et al., 2015) as $\pmb { \dot { R } } = [ \pmb { r } _ { 1 } , \pmb { r } _ { 2 } , . . . , \pmb { r } _ { N } ] \in \mathbb { R } ^ { d \times N }$ . The target sentence is represented as a sequence of one-hot vectors $\pmb { y } _ { t } ^ { * } \in \mathbb { R } ^ { s }$ , where $T$ is the sentence length, $t \in { 1 , 2 , . . . , T }$ , and $s$ is the dictionary size.
+
+# 3.1 BASELINE
+
+We reimplemented the model used in GVD (Zhou et al., 2019) without self-attention for region feature encoding (Ma et al., 2018; Vaswani et al., 2017) as our baseline. It is an extension of the state-of-the-art Up-Down (Anderson et al., 2018) model with the grounding-aware region encoding (see Appendix A.5). Specifically, our baseline model uses two LSTM modules: Attention LSTM and Language LSTM. The Attention LSTM identifies which visual representation in the image is needed for the Language LSTM to generate the next word. It encodes the global image feature $v _ { g }$ , previous hidden state output of the Language LSTM $h _ { t - 1 } ^ { L }$ , and the previous word embedding $e _ { t - 1 }$ into the hidden state $h _ { t } ^ { A }$ .
+
+$$
+\pmb { h } _ { t } ^ { A } = L S T M _ { A t t n } ( [ \pmb { v } _ { g } ; \pmb { h } _ { t - 1 } ^ { L } ; \pmb { e } _ { t - 1 } ] ) , \quad \pmb { e } _ { t - 1 } = W _ { e } \pmb { y } _ { t - 1 } ,
+$$
+
+where $[ ; ]$ denotes concatenation, and $W _ { e }$ are learned parameters. We omit the Attention LSTM input hidden and cell states to avoid notational clutter in the exposition.
+
+The Language LSTM uses the hidden state $h _ { t } ^ { A }$ from the Attention LSTM to dynamically attend on the bag of regions $\pmb { R }$ for obtaining visual representations of the image $\hat { \mathbf { } } _ { { t } }$ to generate a word $y _ { t }$ .
+
+$$
+z _ { t , n } = W _ { a a } t a n h ( W _ { a } h _ { t } ^ { A } + r _ { n } ) , ~ \alpha _ { t } = \mathrm { s o f t m a x } ( z _ { t } ) , ~ \hat { r } _ { t } = R \alpha ,
+$$
+
+![](images/e6f974376d1216e7c1a2b7b83d291ab4ffae737cb4291bf01166aaf379e38a26.jpg)  
+Figure 2: Proposed cyclical training regimen: decoding localization reconstruction. The decoder attends to the image regions and sequentially generate each of the output words. The localizer then uses the generated words as input to locate the image regions. Finally, the shared decoder during reconstruction stage uses the localized image regions to regenerate a sentence that matches with the ground-truth sentence.
+
+where $W _ { a a }$ and $W _ { a }$ are learned parameters. The conditional probability distribution over possible output words ${ \mathbf { } } _ { \mathbf { } } \mathbf { \psi } _ { \mathbf { } } \mathbf { _ { } } \mathbf { \psi } _ { \mathbf { } } \mathbf { _ { } } \mathbf { \psi } _ { \mathbf { } } \mathbf { _ { } } \mathbf { \psi } _ { \mathbf { } } \mathbf { _ { } } \mathbf { \psi } _ { \mathbf { } } \mathbf { _ { } } \mathbf { \psi } _ { \mathbf { } } \mathbf { _ { } } \mathbf { \psi } _ { \mathbf { } \psi } \mathbf { _ { } } \textbf { } \psi _ { } \psi _ { } \left. \textbf { } \psi _ { } \mathbf { } \psi _ { } \textbf { } \right.$ is computed as:
+
+$$
+\begin{array} { r } { \boldsymbol { h } _ { t } ^ { L } = L S T M _ { L a n g } ( [ \hat { \boldsymbol { r } } _ { t } , \boldsymbol { h } _ { t } ^ { A } ] ) , \quad p ( \boldsymbol { y } _ { t } | \boldsymbol { y } _ { 1 : t - 1 } ) = \mathrm { s o f t m a x } ( \boldsymbol { W } _ { o } \boldsymbol { h } _ { t } ^ { L } ) , } \end{array}
+$$
+
+where $\mathbf { \delta } _ { y _ { 1 } : t - 1 }$ is a sequence of outputs $( \pmb { y } _ { 1 } , . . . , \pmb { y } _ { t - 1 } )$ . We refer the Language LSTM and the output logit layer as the complete language decoder.
+
+# 3.2 OVERVIEW
+
+Our goal is to enforce the generated caption to be visually grounded, i.e., attended image regions correspond specifically to individual words being generated, without ground-truth grounding supervision. Towards this end, we propose a novel cyclical training regimen that is comprised of decoding, localization, and reconstruction stages, as illustrated in Figure 2.
+
+The intuition of our method is that the baseline network is not forced to generate a correct correspondence between the attended objects and generated words, since the LSTMs can learn priors in the data instead of looking at the image or propagate information forward which can subsequently be used to generate corresponding words in future time steps. The proposed cyclical training regimen, in contrast, aims at enforcing visual grounding to the model by requiring the language decoder (Eq. 3) to rely on the localized image regions $\hat { r } _ { t } ^ { l }$ to reconstruct the ground-truth sentence, where the localization is conditioned only on the generated word from the decoding stage. Our cyclical method can therefore be done without using any annotations of the grounding itself.
+
+Specifically, let $\pmb { y } _ { t } ^ { d } = \mathcal { D } ^ { d } ( \hat { \pmb { r } } _ { t } ; \theta _ { d } )$ be the initial language decoder with parameters $\theta _ { d }$ (Eq. 3), trained to sequentially generate words $\mathbf { \Delta } _ { \mathbf { \mathcal { Y } } _ { t } ^ { d } } ^ { d }$ . Let $\mathcal { G } ( \boldsymbol { y } _ { t } ^ { d } ; \boldsymbol { \theta } _ { g } )$ define a localizer unit with parameters $\theta _ { g }$ , that learns to map (ground) each generated word to region(s) in the image, i.e., $\hat { { \pmb r } } _ { t } ^ { l } = \mathcal { G } ( { \pmb y } _ { t } ^ { d } , R ; \theta _ { g } )$ . Finally, let $\pmb { y } _ { t } ^ { l } = \mathcal { D } ^ { l } ( \hat { \pmb { r } } _ { t } ^ { l } ; \theta _ { l } )$ be a second decoder, that is required to reconstruct the ground-truth caption using the localized region(s), instead of the attention computed by the decoder itself. We define the cycle:
+
+$$
+\begin{array} { r } { \pmb { y } _ { t } ^ { l } = \mathcal { D } ^ { r } ( \mathcal { G } ( \mathcal { D } ^ { d } ( \hat { \pmb { r } } _ { t } ; \theta _ { d } ) , \pmb { R } ; \theta _ { g } ) ; \theta _ { l } ) , \theta _ { d } = \theta _ { l } , } \end{array}
+$$
+
+where $\mathcal { D } ^ { d }$ and $\mathcal { D } ^ { l }$ share parameters. Although parameters are shared, the inputs for the two language decoders differ, leading to unique LSTM hidden state values during a run. Note that the Attention LSTMs and logit layers in the two stages also share parameters, though they are omitted for clarity.
+
+Through cyclical joint training, both $\mathcal { D } ^ { d }$ and $\mathcal { D } ^ { l }$ are required to generate the same ground-truth sentence. They are both optimized to maximize the likelihood of the correct caption:
+
+$$
+\boldsymbol { \theta } ^ { * } = \underset { \boldsymbol { \theta } _ { d } } { \arg \operatorname* { m a x } } \sum \log p ( \boldsymbol { y } _ { t } ^ { d } ; \boldsymbol { \theta } _ { d } ) + \underset { \boldsymbol { \theta } _ { l } } { \arg \operatorname* { m a x } } \sum \log p ( \boldsymbol { y } _ { t } ^ { l } ; \boldsymbol { \theta } _ { l } ) ,
+$$
+
+During training, the localizer regularizes the region attention of the reconstructor and the effect is further propagated to the baseline network in the decoding stage, since the parameters of Attention
+
+![](images/8790be4151f698138db485497d12f1252598f256ee240cd7126eec08ab26422a.jpg)  
+Figure 3: Proposed model architecture (left) and how the model operates during decoding, localization, and reconstruction stages (right). During the decoding stage, the soft-attention module uses the hidden state of the Attention LSTM to compute attention weights on image regions. During the localization and reconstruction stage, the soft-attention module instead uses the generated word from decoding stage to compute attention weights on image regions.
+
+LSTM and Language LSTM are shared for both decoding and reconstruction stages. Note that the gradient from reconstruction loss will not backprop to the decoder $\mathcal { D } ^ { d }$ in the decoding stage since the generated words used as input to the localizer are leafs in the computational graph. The network is implicitly regularized to update its attention mechanism to match with the localized image regions $\hat { r } _ { t } \stackrel { \cdot } { \mapsto } \hat { r } _ { t } ^ { l }$ . In Sec. 4.3, we demonstrate that the localized image regions $\hat { r } _ { t } ^ { l }$ indeed have higher attention accuracy than $\hat { \mathbf { } r } _ { t }$ when using ground-truth words as inputs for the localizer.
+
+# 3.3 CYCLICAL TRAINING
+
+We now describe each stage of our cyclical model in detail, as illustrated in Figure 3.
+
+Decoding. We first use the baseline model presented in Sec. 3.1 to generate a sequence of words $\pmb { y } = [ \pmb { y } _ { 1 } ^ { d } , \pmb { y } _ { 2 } ^ { d } , . . . , \pmb { y } _ { T } ^ { d } ]$ , where $T$ is the ground-truth sentence length.
+
+Localization. Following the decoding process, a localizer $\mathcal { G }$ is then learned to localize the image regions from each generated word ${ \mathbf { } } _ { \pmb { y } _ { t } }$ .
+
+$$
+\begin{array} { r } { \boldsymbol { e } _ { t } = W _ { e } \boldsymbol { y } _ { t } ^ { d } , \quad \boldsymbol { z } _ { t , n } ^ { l } = ( W _ { l } \boldsymbol { e } _ { t } ) ^ { \top } \boldsymbol { r } _ { n } \quad \mathrm { a n d } \quad \beta _ { t } = \mathrm { s o f t m a x } ( z _ { t } ^ { l } ) , } \end{array}
+$$
+
+where $e _ { t }$ is the embedding for the word generated during decoding stage at step $t$ , $\boldsymbol { r } _ { n }$ is the image representation of a region proposal, and $W _ { e }$ and $W _ { l }$ are the learned parameters. Based on the localized weights $\beta _ { t }$ , the localized region representation can be obtained by $\hat { \mathbf { } r } _ { t } ^ { l } = R \boldsymbol { \beta }$ .
+
+Reconstruction. Finally, the shared language decoder $\mathcal { D } ^ { l }$ relies on the localized region representation $\hat { r } _ { t } ^ { l }$ to generate the next word. The probability over possible output words is:
+
+$$
+\begin{array} { r } { \pmb { h } _ { t } ^ { L } = L S T M _ { L a n g } ( [ \hat { \pmb r } _ { t } ^ { l } ; \pmb { h } _ { t } ^ { A } ] ) , p ( \pmb y _ { t } ^ { l } | \pmb { y } _ { 1 : t - 1 } ^ { l } ) = \mathrm { s o f t m a x } ( \pmb { W } _ { o } \pmb h _ { t } ^ { L } ) , } \end{array}
+$$
+
+Given the target ground truth caption $\pmb { y } _ { 1 : T } ^ { * }$ and our proposed captioning model parameterized with $\theta$ , we minimize the following cross-entropy losses:
+
+$$
+\mathcal { L } _ { C E } ( \theta ) = - \lambda _ { 1 } \sum _ { t = 1 } ^ { T } l o g ( p _ { \theta } ( y _ { t } ^ { * } | y _ { 1 : t - 1 } ^ { * } ) ) \mathbb { 1 } _ { ( y _ { t } ^ { * } = y _ { t } ^ { d } ) } - \lambda _ { 2 } \sum _ { t = 1 } ^ { T } l o g ( p _ { \theta } ( y _ { t } ^ { * } | y _ { 1 : t - 1 } ^ { * } ) ) \mathbb { 1 } _ { ( y _ { t } ^ { * } = y _ { t } ^ { l } ) } .
+$$
+
+where $\lambda _ { 1 }$ and $\lambda _ { 2 }$ are weighting coefficient selected on the validation split.
+
+# 4 EXPERIMENTS
+
+Datasets. We use the Flickr30k Entities image dataset (Plummer et al., 2015) and the ActivityNetEntities video dataset (Zhou et al., 2019) for evaluating our proposed approach. Flickr30k Entities contains $2 7 5 \mathrm { k }$ annotated bounding boxes from 31k images associated with natural language phrases. Each image is annotated with 5 crowdsourced captions. ActivityNet-Entities contains 15k videos with 158k spatially annotated bounding boxes from 52k video segments.
+
+Captioning evaluation metrics. We measure captioning performance using four language metrics, including BLEU (Papineni et al., 2002), METEOR (Banerjee & Lavie, 2005), CIDEr (Vedantam et al., 2015), and SPICE (Anderson et al., 2016).
+
+Grounding evaluation metrics. Following the grounding evaluation from GVD (Zhou et al., 2019), we measure the attention accuracy on generated sentences, denoted by $\mathrm { F } 1 _ { \mathrm { a l l } }$ and $\mathrm { F l } _ { \mathrm { l o c } }$ . In $\mathrm { F } 1 _ { \mathrm { a l l } }$ , a region prediction is considered correct if the object word1 is correctly predicted and also correctly localized. We also compute $\mathrm { F l } _ { \mathrm { l o c } }$ , which only considers correctly-predicted object words. Please see illustration of the grounding metrics in Appendix A.1.
+
+In the original formulation, the precision and recall for the two F1 metrics are computed for each object class, and it is set to zero if an object class has never been predicted. The scores are computed for each object class and averaged by the total number of classes. Such metrics are extremely stringent as captioning models are generally biased toward certain words in the vocabulary, given the long-tailed distribution of words. In fact, both the baseline and proposed method generate about $45 \%$ of the annotated object words within the val set in Flickr30k Entities. The grounding accuracy of the other $55 \%$ of the classes are therefore zero, making the averaged grounding accuracy seemingly low.
+
+Measuring grounding per generated sentence. Instead of evaluating grounding on each object class (which might be less intuitive), we include a new grounding evaluation metric per sentence to directly reflect the grounding measurement of each generated sentence. The metrics are computed against a pool of object words and their ground-truth bounding boxes (GT bbox) collected across five GT captions on Flickr30k Entities (and one GT caption on ActivityNet-Entities). We use the same $\mathrm { P r e c } _ { \mathrm { a l l } }$ , $\mathrm { R e c } _ { \mathrm { a l l } }$ , $\mathrm { P r e c } _ { \mathrm { l o c } }$ , and $\scriptstyle { \mathrm { R e c } } _ { \mathrm { l o c } }$ as defined previously, but their scores are averaged on each of the generated sentence. As a result, the $\mathrm { F 1 } _ { \mathrm { l o c \_ p e r \_ s e n t } }$ measures the F1 score only on the generated words. The model will not be punished if some object words are not generated, but it also needs to maintain diversity to achieve high captioning performance.
+
+# 4.1 IMPLEMENTATION AND TRAINING DETAILS
+
+Region proposal and spatial features. Following GVD (Zhou et al., 2019), we extracted 100 region proposals from each image (video frame) and encode them via the grounding-aware region encoding. Please refer to Appendix A.5 for more implementation details.
+
+Training. We train the model with ADAM optimizer (Kingma & Ba, 2015). The initial learning rate is set to $1 e - 4$ . Learning rates automatically drop by 10x when the CIDEr score is saturated. The batch size is 32 for Flickr30k Entities and 96 for ActivityNet-Entities. We learn the word embedding layer from scratch for fair comparisons with existing work (Zhou et al., 2019).
+
+# 4.2 CAPTIONING AND GROUNDING PERFORMANCE COMPARISON
+
+Flickr30k Entities. We first compare the proposed method with our baseline with or without grounding supervision on the Flickr30k Entities test set (see Table 1). To train the supervised baseline, we train the attention mechanism as well as add the region classification task using the ground-truth grounding annotation, similar to GVD (Zhou et al., 2019). We train the proposed baselines and our method on the training set and choose the best performing checkpoints based on their CIDEr score on the val set. Our experimental results are reported by averaging across five runs on the test set. We report only the mean of the five runs to keep the table uncluttered. When compared to the existing state of the arts, our proposed baselines achieve comparable captioning evaluation performances and grounding accuracy. Using the resulting supervised baseline as the upper bound, our proposed method with cyclical training statistically achieves around 20 to $2 5 \%$ relative grounding accuracy improvements for both $F 1 _ { \mathrm { a l l } }$ and $F 1 _ { \mathrm { l o c } }$ and 10 to $15 \%$ for $F 1 _ { \mathrm { a l l \_ p e r \_ s e n t } }$ and $F 1 _ { \mathrm { l o c } }$ per sent without utilizing any grounding annotations or additional computation during inference.
+
+ActivityNet-Entities. We adapt our proposed baselines and method to the ActivityNet-Entities video dataset (see Table 2). We can see that our proposed method significantly improved the grounding accuracy around $2 5 \%$ to $30 \%$ relative grounding accuracy improvements for both $F 1 _ { \mathrm { a l l } }$ and $F 1 _ { \mathrm { l o c } }$ and around $40 \%$ for $F 1 _ { \mathrm { a l l \_ p e r \_ s e n t } }$ and $F 1 _ { \mathrm { l o c } }$ per sent.
+
+Table 1: Performance comparison on the Flickr30k Entities test set: ATT-FCN (You et al., 2016), NBT (Lu et al., 2018), Up-Down (Anderson et al., 2018), GVD (Zhou et al., 2019), and Baseline is our reimplementation of GVD. \*: our results are averaged across five runs. Only numbers reported by multiple runs are considered to be bolded.   
+
+<table><tr><td rowspan="2">Method</td><td rowspan="2">Grounding supervision</td><td colspan="5">Captioning Evaluation</td><td colspan="4">Grounding Evaluation</td></tr><tr><td>B@1</td><td>B@4</td><td>M</td><td>C</td><td>S</td><td>Flall</td><td>F1loc</td><td>Flall_per_sent</td><td>Flloc_per_sent</td></tr><tr><td>ATT-FCN</td><td></td><td>64.7</td><td>19.9</td><td>18.5</td><td>-</td><td>-</td><td>-</td><td>-</td><td>=</td><td>-</td></tr><tr><td>NBT</td><td></td><td>69.0</td><td>27.1</td><td>21.7</td><td>57.5</td><td>15.6</td><td>-</td><td>-</td><td></td><td></td></tr><tr><td>Up-Down</td><td></td><td>69.4</td><td>27.3</td><td>21.7</td><td>56.6</td><td>16.0</td><td>4.14</td><td>12.3</td><td></td><td></td></tr><tr><td>GVD (w/o SelfAttn)</td><td></td><td>69.2</td><td>26.9</td><td>22.1</td><td>60.1</td><td>16.1</td><td>3.97</td><td>11.6</td><td></td><td></td></tr><tr><td>GVD</td><td>√</td><td>69.9</td><td>27.3</td><td>22.5</td><td>62.3</td><td>16.5</td><td>7.77</td><td>22.2</td><td></td><td>-</td></tr><tr><td>Baseline*</td><td>√</td><td>69.0</td><td>26.8</td><td>22.4</td><td>61.1</td><td>16.8</td><td>8.44 (+100%)</td><td>22.78 (+100%)</td><td>27.37 (+100%)</td><td>63.19 (+100%)</td></tr><tr><td>Baseline*</td><td></td><td>69.1</td><td>26.0</td><td>22.1</td><td>59.6</td><td>16.3</td><td>4.08 (+0%)</td><td>11.83 (+0%)</td><td>13.20 (+0%)</td><td>31.83 (+0%)</td></tr><tr><td>Cyclical*</td><td></td><td>69.4</td><td>26.9</td><td>22.3</td><td>60.8</td><td>16.6</td><td>5.11 (+24%)</td><td>14.15 (+21%)</td><td>15.15 (+14%)</td><td>35.56 (+12%)</td></tr></table>
+
+Table 2: Performance comparison on the ActivityNet-Entities val set: GVD (Zhou et al., 2019) and Baseline is our reimplementation of GVD. \*: our results are averaged across five runs. Only numbers reported by multiple runs are considered to be bolded.   
+
+<table><tr><td rowspan="2">Method</td><td rowspan="2">Grounding supervision</td><td colspan="5">Captioning Evaluation</td><td colspan="4">Grounding Evaluation</td></tr><tr><td>B@1</td><td>B@4</td><td>M</td><td>C</td><td>S</td><td>Flall</td><td>Floc</td><td>Flallper_sent</td><td>Fl1oc_per_sent</td></tr><tr><td>GVD</td><td></td><td>23.0</td><td>2.27</td><td>10.7</td><td>44.6</td><td>13.8</td><td>0.28</td><td>1.13</td><td>=</td><td>-</td></tr><tr><td>GVD (w/o SelfAttn)</td><td></td><td>23.2</td><td>2.28</td><td>10.9</td><td>45.6</td><td>15.0</td><td>3.70</td><td>12.7</td><td></td><td></td></tr><tr><td>GVD</td><td>√</td><td>23.9</td><td>2.59</td><td>11.2</td><td>47.5</td><td>15.1</td><td>7.11</td><td>24.1</td><td></td><td></td></tr><tr><td>Baseline*</td><td>√</td><td>23.1</td><td>2.13</td><td>10.7</td><td>45.0</td><td>14.6</td><td>7.30 (+100%)</td><td>25.02 (+100%)</td><td>17.88 (+100%)</td><td>60.23 (+100%)</td></tr><tr><td>Baseline*</td><td></td><td>23.2</td><td>2.22</td><td>10.8</td><td>45.9</td><td>15.1</td><td>3.75 (+0%)</td><td>12.00 (+0%)</td><td>9.41 (+0%)</td><td>31.68 (+0%)</td></tr><tr><td>Cyclical*</td><td></td><td>23.7</td><td>2.45</td><td>11.1</td><td>46.4</td><td>14.8</td><td>4.68 (+26%)</td><td>15.84 (+29%)</td><td>12.60 (+38%)</td><td>44.04 (+43%)</td></tr></table>
+
+# 4.3 ANALYSIS
+
+Are localized image regions better than attended image regions during training? Given our intuition described in Sec. 3, we expect the decoder to be regularized to update its attention mechanism to match with the localized image regions $\hat { r } _ { t } \mapsto \hat { r } _ { t } ^ { l }$ . This indicates that the localized image regions should be more accurate than the attended image regions by the decoder during training. To verify this, we compute the attention accuracy for both decoder and localizer over ground-truth sentences following (Rohrbach et al., 2016; Zhou et al., 2018). The attention accuracy for localizer is $2 0 . 4 \%$ and is higher than the $1 9 . 3 \%$ from the decoder at the end of training, which confirms our hypothesis.
+
+Grounding performance when using a better object detector. In Table 1 and 2 we showed that our proposed method significantly improved the grounding accuracy for both image and video captioning. These experimental settings follow the widely used procedure for visual captioning systems: extract regional proposal features and generate visual captions by attending to those extracted visual features.
+
+Table 3: Grounding performance when using better object detector on the Flickr30k Entities test set (see Table 4 for complete version).   
+
+<table><tr><td rowspan="2">#</td><td rowspan="2">Grounding supervision</td><td colspan="3">Captioning Eval.</td><td colspan="3">Grounding Eval.</td></tr><tr><td>M</td><td>C</td><td>S</td><td>F1all</td><td>F1oc</td><td>Flloc_per_sent</td></tr><tr><td colspan="9">Unrealistically perfect object detector</td></tr><tr><td>Baseline</td><td>√</td><td>25.3</td><td>76.5</td><td>22.3</td><td>23.19</td><td>52.83</td><td>90.76</td></tr><tr><td>Baseline</td><td></td><td>25.2</td><td>76.3</td><td>22.0</td><td>20.82</td><td>48.74</td><td>77.81</td></tr><tr><td>Cyclical</td><td></td><td>25.8</td><td>80.2</td><td>22.7</td><td>25.27</td><td>54.54</td><td>81.56</td></tr><tr><td colspan="8">Grounding-biased object detector</td></tr><tr><td>Baseline</td><td>√</td><td>21.3</td><td>53.3</td><td>15.5</td><td>8.23</td><td>23.95</td><td>66.96</td></tr><tr><td>Baseline</td><td></td><td>21.2</td><td>52.4</td><td>15.4</td><td>5.95</td><td>17.51</td><td>42.84</td></tr><tr><td>Cyclical</td><td></td><td>21.2</td><td>52.0</td><td>15.4</td><td>6.87</td><td>19.65</td><td>50.25</td></tr></table>
+
+![](images/0dfa0b5e7f4acb611c38fd6a8629254e1898ce452fc88fe563566c76e7a0e1f2.jpg)  
+Figure 4: Average $\mathrm { F } 1 _ { a l l }$ -score per class as a function of class frequency.
+
+![](images/6cd95fab48e48ba089f10aaffbd7cbee9b74a7169ca5a4ab7879b8be5a84590b.jpg)  
+Figure 5: Generated captions and corresponding visual grounding regions with comparison between baseline (left) and proposed approach (right). Our proposed method is able to generate more descriptive sentences while selecting the correct regions for generating the corresponding words.
+
+One might ask, what if we have a better object detector that can extract robust visual representation that are better aligned with the word embeddings? Will visual grounding still an issue for captioning?
+
+To answer this, we ran two sets of experiments (Table 3): (1) Perfect object detector: we replace the ROIs by ground-truth bbox and represent the new ROIs by learning embedding features directly from ground-truth object words associated with each ground-truth bbox. This experiment gives an estimate of the captioning and grounding performance if we have (almost) perfect ROI representations (though unrealistic). We can see that the fully-supervised method achieves an $\mathrm { F } 1 _ { \mathrm { a l l } }$ of only $23 \%$ , which further confirms the difficulty of the metric and the necessity of our grounding metric on a per sentence level (note that $\mathrm { F 1 } _ { \mathrm { l o c \_ p e r \_ s e n t } }$ shows $90 \%$ ). We can also see that baseline (unsup.) still leaves room for improvement on grounding performance. Surprisingly, our method improved both captioning and grounding accuracy and surpasses the fully-supervised baseline except on the $\mathrm { F 1 } _ { \mathrm { l o c \_ p e r \_ s e n t } }$ . We find that it is because the baseline (sup.) overfits to the training set, while ours is regularized from the cyclical training. Also, our generated object words are more diverse, which is critical for $\mathrm { F } 1 _ { \mathrm { a l l } }$ and $\mathrm { F l } _ { \mathrm { l o c } }$ . (2) Grounding-biased object detector: we extract ROI features from an object detector pre-trained on Flick $- 3 0 \mathrm { k }$ . Thus, the ROI features and their associated object predictions are biased toward the annotated object words but do not generalize to predict diverse captions compared to the original object detector trained from Visual Genome, resulting in lower captioning performance. We can see that our proposed method still successfully improves grounding and maintains captioning performance in this experiment setting as well.
+
+How does the number of annotations affect grounding performance? In Figure 4, we present the average F1-score on the Flickr30k Entities val set when grouping classes according to their frequency of appearance in the training set3. We see that, unsurprisingly, the largest difference in grounding accuracy between the supervised and our proposed cyclical training is for the 50 most frequently appearing object classes, where enough training data exists. As the number of annotated boxes decreases, however, the difference in performance diminishes, and cyclical training appears to be more robust. Overall, we see that the supervised method is biased towards frequently appearing objects, while grounding performance for the proposed approach is more balanced among classes.
+
+Qualitative analysis. We additionally conduct qualitative analysis for comparing the baseline (Unsup.) and the proposed method in Figure 5. Each highlighted word has a corresponding image region annotated on the original image. The image regions are selected based on the region with the maximum attention weight in $\alpha _ { t }$ . We can see that our proposed method significantly outperformed the baseline (Unsup.) in terms of both the quality of the generated sentence and grounding accuracy. In addition, we also discuss a number of correct and incorrect examples of our proposed method in Figure 8 in the Appendix. Please refer to the Appendix A.4 for further discussions on the qualitative results and the complete sequence of attended image regions of examples in Figure 5.
+
+# 5 CONCLUSION
+
+Working from the intuition that typical attentional mechanisms in the visual captioning task are not forced to ground generated words since recurrent models can propagate past information, we devise a novel cyclical training regime to explicitly force the model to ground each word without grounding annotations. Our method only adds a fully-connected layer during training, which can be removed during inference, and we show thorough quantitative and qualitative results demonstrating around $20 \%$ or $30 \%$ relative improvements in visual grounding accuracy over existing methods for image and video captioning tasks.
+
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+Luowei Zhou, Nathan Louis, and Jason J Corso. Weakly-supervised video object grounding from text by loss weighting and object interaction. In British Machine Vision Conference (BMVC), 2018.
+
+Luowei Zhou, Yannis Kalantidis, Xinlei Chen, Jason J. Corso, and Marcus Rohrbach. Grounded video description. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2019.
+
+Jun-Yan Zhu, Taesung Park, Phillip Isola, and Alexei A Efros. Unpaired image-to-image translation using cycle-consistent adversarial networks. In Proceedings of the IEEE International Conference on Computer Vision (ICCV), pp. 2223–2232, 2017.
+
+<table><tr><td rowspan="2">Method</td><td rowspan="2">Grounding supervision</td><td colspan="5">Captioning Evaluation</td><td colspan="4">Grounding Evaluation</td></tr><tr><td>B@1</td><td>B@4</td><td>M</td><td>C</td><td>S</td><td>Flall</td><td>Flloc</td><td>Flall_per_sent</td><td>F1loc_per_sent</td></tr><tr><td colspan="9">Unrealistically perfect object detector</td><td></td></tr><tr><td>Baseline</td><td>√</td><td>75.6</td><td>32.0</td><td>25.3</td><td>75.6</td><td>22.3</td><td>23.19 (+100%)</td><td>52.83 (+100%)</td><td>51.43 (+100%)</td><td>90.76 (+100%)</td></tr><tr><td>Baseline</td><td></td><td>75.1</td><td>32.1</td><td>25.2</td><td>76.3</td><td>22.0</td><td>20.82 (+0%)</td><td>48.74(+0%)</td><td>43.21(+0%)</td><td>77.81(+0%)</td></tr><tr><td>Cyclical</td><td></td><td>76.7</td><td>32.8</td><td>25.8</td><td>80.2</td><td>22.7</td><td>25.27 (+188%)</td><td>54.54 (+142%)</td><td>46.98 (+46%)</td><td>81.56 (+29%)</td></tr><tr><td colspan="9">Grounding-biased object detector</td><td></td><td></td></tr><tr><td>Baseline</td><td>√</td><td>65.9</td><td>23.4</td><td>21.3</td><td>53.3</td><td>15.5</td><td>8.23 (+100%)</td><td>23.95 (+100%)</td><td>28.06(+100%)</td><td>66.96(+100%)</td></tr><tr><td>Baseline</td><td></td><td>66.1</td><td>23.5</td><td>21.2</td><td>52.4</td><td>15.4</td><td>5.95(+0%)</td><td>17.51 (+0%)</td><td>18.11 (+0%)</td><td>42.84 (+0%)</td></tr><tr><td>Cyclical</td><td></td><td>65.5</td><td>23.3</td><td>21.2</td><td>52.0</td><td>15.4</td><td>6.87 (+40%)</td><td>19.65 (+33%)</td><td>20.82 (+27%)</td><td>50.25 (+31%)</td></tr></table>
+
+Table 4: Grounding performance when using better object detector on the Flickr30k Entities test set (results are averaged three runs). Fully-supervised method (Sup.) is used as upper bound, thus its numbers are not bolded.
+
+![](images/19e408b0397c3d31a3ee7770bbff16e8b31bbf784ff30d985b91e5b4abfd47ad.jpg)
+
+Predicted:
+
+# Ground-truth:
+
+A man is hiking while holding a water bottle.   
+A man wearing a hat and hiking shoes is hiking.
+
+A man wearing a hat is hiking with a dog.
+
+Object words: {man, bottle, hat, shoes}
+
+![](images/7d9ecda2775be4b602c980e9bef3e8efad4c970518b6b277896618355c1b01f7.jpg)
+
+Object words: {man, hat, dog}
+
+A: {man, hat, dog}   
+B: {man, bottle, hat, shoes}   
+C: {man, hat}   
+D: {man, hat}   
+E: {man} (IoU $> 0 . 5 \AA$ )
+
+![](images/b5fec40c2fe1bf9f049e5223e507a718a331abcb474a64db3e2b46cdde06c513.jpg)  
+Figure 6: Illustration of Grounding metrics.
+
+# A APPENDIX
+
+# A.1 GROUNDING EVALUATION METRICS ILLUSTRATED
+
+To help better understand the grounding evaluation metrics used in this work, we illustrated the grounding evaluation metrics in Figure 6.
+
+We define the number of object words in the generated sentences as A, the number of object words in the GT sentences as B, the number of correctly predicted object words in the generated sentences as C and the counterpart in the GT sentences as D, and the number of correctly predicted and localized words as $\mathrm { E }$ (see illustration of the grounding metrics in Appendix A.1). A region prediction is considered correct if the object word is correctly predicted and also correctly localized (i.e., IoU with GT box $> 0 . 5$ ). We then compute two version of the precision and recall as $\mathrm { P r e c } _ { \mathrm { a l l } } = { \frac { E } { A } }$ $\operatorname { R e c } _ { \mathrm { a l l } } = { \frac { E } { B } }$ , ${ \mathrm { P r e c } } _ { \mathrm { l o c } } = { \frac { E } { C } }$ , $\operatorname { R e c } _ { \mathrm { l o c } } = { \frac { E } { D } }$
+
+The original grounding evaluation metric proposed in GVD (Zhou et al., 2019) average the grounding for each object class. We additionally calculate the grounding accuracy for each generated sentence as demonstrated in the figure. From this example, we can see that while $P r e c i s i o n _ { a l l }$ counts dog as a wrong prediction for the dog object class, the $P r e c i s i o n _ { l o c }$ only cares if man and hat are predicted and correctly localizer $\mathrm { ( I o U > 0 . 5 ) }$ ).
+
+Table 5: Model ablation study on the Flickr30k Entities val set.   
+
+<table><tr><td rowspan="2"></td><td colspan="3">Captioning Eval.</td><td colspan="2">Grounding Eval.</td></tr><tr><td>M</td><td>C</td><td>S</td><td>Flall</td><td>F11oc</td></tr><tr><td>Baseline (Unsup.)</td><td>22.3</td><td>62.1</td><td>16.0</td><td>4.18</td><td>11.9</td></tr><tr><td>Cyclical</td><td>22.2</td><td>62.2</td><td>16.2</td><td>5.63</td><td>14.6</td></tr><tr><td>- Attention consistency</td><td>22.3</td><td>61.8</td><td>16.2</td><td>4.19</td><td>11.3</td></tr><tr><td>- Localizer using h A</td><td>22.2</td><td>61.8</td><td>16.1</td><td>4.58</td><td>11.3</td></tr></table>
+
+<table><tr><td rowspan="2">Method</td><td colspan="5">Captioning Evaluation</td><td colspan="4">Grounding Evaluation</td></tr><tr><td>B@1</td><td>B@4</td><td>M</td><td>C</td><td>S</td><td>Flall</td><td>Floc</td><td>Flall_per_sent</td><td>F1loc_per_sent</td></tr><tr><td>Baseline</td><td>69.1</td><td>26.0</td><td>22.1</td><td>59.6</td><td>16.3</td><td>4.08</td><td>11.83</td><td>13.20</td><td>31.83</td></tr><tr><td>Cyclical</td><td>69.4</td><td>26.9</td><td>22.3</td><td>60.8</td><td>16.6</td><td>5.11</td><td>14.15</td><td>15.15</td><td>35.56</td></tr><tr><td>Cyclical (1)</td><td>69.7</td><td>27.0</td><td>22.2</td><td>60.1</td><td>16.5</td><td>5.14</td><td>14.32</td><td>15.36</td><td>36.33</td></tr><tr><td>Cyclical (2)</td><td>69.9</td><td>27.5</td><td>22.4</td><td>62.0</td><td>16.6</td><td>5.13</td><td>13.99</td><td>16.30</td><td>38.45</td></tr></table>
+
+Table 6: Performance comparison on the Flickr30k Entities test set. All results are averaged across five runs.
+
+# A.2 ADDITIONAL ANALYSIS
+
+Should we explicitly make attended image regions to be similar to localized image regions? One possible way to regularize the attention mechanism of the decoder is to explicitly optimize $\hat { r } _ { t } \mapsto \hat { r } _ { t } ^ { l }$ via KL divergence over two soft-attention weights $\pmb { \alpha } _ { t }$ and $\beta _ { t }$ . The experimental results are shown in Table 5 (Attention consistency). We use a single run unsupervised baseline with a fix random seed as baseline model for ablation study. We can see that when explicitly forcing the attended regions to be similar to the localized regions, both the captioning performance and the grounding accuracy remain similar to the baseline (unsup.). We conjecture that this is due to the noisy localized regions at the initial training stage. When forcing the attended regions to be similar to noisy localized regions, the Language LSTM will eventually learn to not rely on the attended region at each step for generating sequence of words. To verify, we increase the weight for attention consistency loss and observed that it has lower grounding accuracy $\mathrm { F } 1 _ { \mathrm { a l l } } = 3 . 2 $ ), but the captioning will reach similar performance while taking $1 . 5 \mathrm { x }$ longer to reach convergence.
+
+Is using only the generated word for localization necessarily? Our proposed localizer (Eq. 6 and Figure 3) relies on purely the word embedding representation to locate the image regions. This forces the localizer to rely only on the word embedding without biasing it with the memorized information from the Attention LSTM. As shown in the Table 5 (localizer using $\boldsymbol { h } ^ { A }$ ), although this achieves comparable captioning performance, it has lower grounding accuracy improvement compared to our proposed method.
+
+Can words that are not visually-groundable handled differently? In the proposed method, all the words are handled the same regardless of whether they are visually-groundable or not. Yet, typically words that are nouns or verbs are more likely to be grounded, and words like ”a”, ”the”, etc, are not visually-groundable.
+
+We explored a few method variants to handle nouns and verbs differently. Mainly, we explored with two variants. Cyclical (1): the reconstruction loss is only computed when the target word is either nouns or verbs. Cyclical (2): the localized region representation will be invalid (set to zero) if the target word is neither nouns nor verbs.
+
+The experimental results are shown in Table 6, 7, and 8. For the first variant, Cyclical (1), we observed that the captioning performance stays the same while grounding accuracy has a small improvement. On the other hand, for the second variant, Cyclical (2), we can see that all captioning scores are improved over baseline with CIDEr improved 2.4. We can also see that grounding accuracy on per sentence basis further improved as well. We then conducted further experiments on both ActivityNet-Entities and Flickr30k Entities with unrealistically perfect object detector, but the improvements however are not consistent. In summary: on the Flickr30k Entities test set, we observed that CIDEr is better and grounding per sentence better, on the ActivityNet-Entities val set, the captioning performances are about the same but grounding accuracy became worse, and on the Flickr30k Entities test set with unrealistically perfect object detector, captioning performances are slightly worse but grounding accuracy improved.
+
+Table 7: Performance comparison on the ActivityNet-Entities val set. All results are averaged across five runs.   
+
+<table><tr><td></td><td colspan="5">Captioning Evaluation</td><td colspan="4">Grounding Evaluation</td></tr><tr><td>Method</td><td>B@1</td><td>B@4</td><td>M</td><td>C</td><td>S</td><td>F1all</td><td>F1loc</td><td>Flall_per_sent</td><td>F1loc_per_sent</td></tr><tr><td>Baseline</td><td>23.2</td><td>2.22</td><td>10.8</td><td>45.9</td><td>15.1</td><td>3.75</td><td>12.00</td><td>9.41</td><td>31.68</td></tr><tr><td>Cyclical</td><td>23.7</td><td>2.45</td><td>11.1</td><td>46.4</td><td>14.8</td><td>4.68</td><td>15.84</td><td>12.60</td><td>44.04</td></tr><tr><td>Cyclical (2)</td><td>23.9</td><td>2.58</td><td>11.2</td><td>46.6</td><td>14.8</td><td>4.48</td><td>15.01</td><td>11.53</td><td>40.30</td></tr></table>
+
+<table><tr><td></td><td colspan="5">Captioning Evaluation</td><td colspan="4">Grounding Evaluation</td></tr><tr><td>Method</td><td>B@1</td><td>B@4</td><td>M</td><td>C</td><td>S</td><td>Flall</td><td>F11oc</td><td>Flall_per_sent</td><td>F1loc_per_sent</td></tr><tr><td colspan="10">Unrealistically perfect object detector</td></tr><tr><td>Baseline</td><td>75.1</td><td>32.1</td><td>25.2</td><td>76.3</td><td>22.0</td><td>20.82</td><td>48.74</td><td>43.21</td><td>77.81</td></tr><tr><td>Cyclical</td><td>76.7</td><td>32.8</td><td>25.8</td><td>80.2</td><td>22.7</td><td>25.27</td><td>54.54</td><td>46.98</td><td>81.56</td></tr><tr><td>Cyclical (2)</td><td>75.8</td><td>32.2</td><td>25.6</td><td>79.0</td><td>22.4</td><td>25.65</td><td>55.81</td><td>48.99</td><td>85.99</td></tr></table>
+
+Table 8: Grounding performance when using better object detector on the Flickr30k Entities test set (results are averaged three runs).
+
+# A.3 HUMAN EVALUATION ON GROUNDING
+
+We conduct a human evaluation on the perceptual quality of the grounding. We asked 10 human subjects to pick the best among two grounded regions (by baseline and Cyclical) for each word. The subjects have three options to choose from: 1) grounded region A is better, 2) grounded region B is better, and 3) they are about the same (see Figure 7 for example). Authors or other colleagues familiar with the proposed method were excluded from the study. Each of the human subjects were given 25 images, each with a varying number of groundable words. Each image was presented to two different human subjects in order to be able to measure inter-rater agreement. To avoid being biased towards the object words defined in the dataset for automatic grounding evaluation, for the study we define a word to be groundable if it is either a noun or verb. The order of approaches was randomized for each sentence.
+
+Our experiment on the Flickr30k Entities val set showed that: $2 8 . 1 \%$ of words are more grounded by Cyclical, $2 4 . 8 \%$ of words are more grounded by baseline, and $4 7 . 1 \%$ of words are similarly grounded.
+
+We also measured inter-rater agreement between each pair of human subjects: $7 2 . 7 \%$ of ratings are the same, $4 . 9 \%$ of ratings are the opposite, and $2 2 . 4 \%$ of ratings could be ambiguous (e.g., one chose A is better, the other chose they are about the same).
+
+We would also like to make a note that the grounded words judged to be similar largely consisted of very easy or impossible cases. For example, words like mountain, water, street, etc, are typically rated to be ”about the same” since they usually have many possible boxes and is very easy for both models to ground the words correctly. On the other hand, for visually ungroundable cases, e.g., stand appears a lot and the subject would choose about the same since the image does not cover the fact that the person’s feet are on the ground.
+
+We see that the human study results follow the grounding results presented in the paper and show an improvement in grounding accuracy for the proposed method over a strong baseline. The improvement is achieved without grounding annotations or extra computation at test time.
+
+![](images/9ce94f801d13c3bc6cae41c70440b7fbaba97b35bebcd6a2a5472832eb913703.jpg)  
+Figure 7: Demonstration of our human evaluation study on grounding. Each human subject is required to rate which method (A or B) has a better grounding on each highlighted word.
+
+![](images/509ab9ea43e60ad5b4802cefde85fe4af9a9eaa9786f312fc7ddf9353ab1de47.jpg)  
+A man in a red shirt is standing on a wooden platform.
+
+![](images/0cf21cacc3d45487732e83d189590b32bb2d0df2318299f22f5e1ac2baaa056c.jpg)  
+A man in a yellow jacket and blue helmet riding a bike.
+
+![](images/35900f4c9771d02469a75b66274836b21c5a941ae065a6b896b043fcb898e0d6.jpg)  
+A man in an orange shirt and a hat is standing next to a blue wall.
+
+![](images/253e01e731364121f62789199add05bd71193b07d828b2adec3d0a82767d16c8.jpg)  
+A man sits on a chair in front of a lake.
+
+![](images/7a65ed2ed3f1a9ea1ad9ae28b3df6efb0ed28bce0e9bd5a139196392ab59062d.jpg)  
+A girl in a purple sweater is jumping on rocks.
+
+![](images/445dea1b6542684dbbbde2ce087394bb064e12088de57a2590a1c83199c22b75.jpg)  
+A young girl in a pink shirt and jeans is walking down a brick wall.
+
+![](images/561a0dcc10585d341663c6767abc6bc36859a507d8d25d66fc1ce16a5703017d.jpg)  
+An Asian woman is holding a red umbrella and walking down the sidewalk.
+
+![](images/e41aa7e8097cc4e002cdba8b5559fb99eb7126f40d828b3ec66d52fe2ed29028.jpg)  
+A man in a black shirt is holding up a flag.
+
+Figure 8: Correct (top) examples and examples with errors (bottom) from the proposed method.
+
+A.4 ADDITIONAL QUALITATIVE RESULTS
+
+In Figure 8, we show a number of correct and incorrect examples of our proposed method. We observe that while the model is able to generate grounded captions for the images, it may sometimes overlook the semantic meaning of the generated sentences, for example, ”A young girl [...] walking down a brick wall”. Similarly, the model can overlook the spatial relationship between the objects, for instance, ”A man [...] is holding up a flag”. While a flag is present in the scene and was able to be successfully located with the corresponding word, the man in a black shirt is spatially far from the flag.
+
+In Figure 9, 10, 11, 12, 13, 14, 15, and 16, we illustrated the sequence of attended image region when generating each word for a complete image description. At each step, only the top-1 attended image region is shown. This is the same as how the grounding accuracy is measured. Please see the description for Figure 9 - 16 for further discussions on the qualitative results.
+
+# A.5 ADDITIONAL IMPLEMENTATION DETAILS
+
+Region proposal features. We use a Faster-RCNN model (Ren et al., 2015) pre-trained on Visual Genome (Krishna et al., 2017) for region proposal and feature extraction. In practice, besides the region proposal features, we also use the Conv features (conv4) extracted from an ImageNet pretrained ResNet-101. Following GVD (Zhou et al., 2019), the region proposals are represented using the grounding-aware region encoding, which is the concatenation of i) region feature, ii) region-class similarity matrix, and iii) location embedding.
+
+For region-class similarity matrix, we define a set of object classifiers as $W _ { c }$ , and the region-class similarity matrix can be computed as $M _ { s } = \operatorname { s o f t m a x } ( W _ { c } ^ { \top } R )$ , which captures the similarity between regions and object classes. We omit the ReLU and Dropout layer after the linear embedding layer for clarity. We initialize $W _ { c }$ using the weight from the last linear layer of an object classifiers pre-trained on the Visual Genome dataset (Krishna et al., 2017).
+
+For location embedding, we use 4 values for the normalized spatial location. The 4-D feature is then projected to a $d _ { s } = 3 0 0 \mathrm { - D }$ location embedding for all the regions.
+
+Software and hardware configuration. Our code is implemented in PyTorch. All experiments were ran on the 1080Ti, 2080Ti, and Titan Xp GPUs.
+
+Network architecture. The embedding dimension for encoding the sentences is 512. We use a dropout layer with ratio 0.5 after the embedding layer. The hidden state size of the Attention and Language LSTM are 1024. The dimension of other learnable matrices are: $W _ { e } \in \mathbb { R } ^ { d _ { v } \times 5 1 2 }$ , $W _ { a } \in \mathbb { R } ^ { \breve { 1 } 0 2 \breve { 4 } \times 5 1 2 }$ , $W _ { a a } \in \mathbb { R } ^ { 5 1 2 \times 1 }$ , $W _ { o } \in \mathbb { R } ^ { 1 0 2 4 \times d _ { v } }$ , $W _ { l } \in \mathbb { R } ^ { 5 1 2 \times 5 1 2 }$ , where the vocabulary size $d _ { v }$ is 8639 for Flickr30k Entities and 4905 for ActivityNet-Entities.
+
+# A.5.1 TRAINING DETAILS.
+
+The hyper-parameters $\lambda _ { 1 }$ and $\lambda _ { 2 }$ are set to 0.5 after hyper-parameter search between 0 and 1.
+
+Flickr30k Entities. Images are randomly cropped to $5 1 2 \times 5 1 2$ during training, and resized to $5 1 2 \times 5 1 2$ during inference. Before entering the proposed cyclical training regimen, the decoder was pre-trained for about 35 epochs. The total training epoch with the cyclical training regimen is around 80 epochs. The total training time takes about 1 day.
+
+ActivityNet-Entities. Before entering the proposed cyclical training regimen, the decoder was pretrained for about 50 epochs. The total training epoch with the cyclical training regimen is around 75 epochs. The total training time takes about 1 day.
+
+![](images/03bbf2e6fd079ee3d7c55bbf92334493825b6ffd6cf2cee40704aaf75553b345.jpg)  
+Figure 9: A group of men in white uniforms are standing in a field with a crowd watching. We can see that our proposed method attends to the sensible image regions for generating visually-groundable words, e.g., man, uniforms, field, and crowd. Interestingly, when generating standing, the model pays its attention on the image region with a foot on the ground.
+
+![](images/a094defa104483478da79d88e347c6bdf16e35f6bc69da201c8d335233d034d0.jpg)  
+Figure 10: A young girl wearing a winter hat and a purple coat is smiling at the camera. The proposed method is able to select the corresponding image regions to generate girl, hat, and coat correctly. We have also observed that the model tends to localize the person’s face when generating camera.
+
+![](images/54069882361162d512b85e6ff541586c2bb270ebd739b9333326c5b0fd9c2224.jpg)  
+Figure 11: A white horse with a rider in a blue helmet and white shirt jumping over a hurdle. While the model is able to correctly locate objects such as horse, rider, helmet, shirt, and hurdle, it mistakenly describes the rider as wearing a blue helmet, while it’s actually black, and with white shirt while it’s blue.
+
+![](images/c774a8ab60eb3ce0389e8b772a34d47b7728eb5b80f9ed9da5ae7c38322551cd.jpg)  
+Figure 12: A man in a red shirt is standing on a wooden platform. Our method correctly attends on the correct regions for generating man, shirt, and platform.
+
+![](images/dbcd47c60ba25d3c8bf726e2159ec209d6ff2c219e432438a82e4a8062548d0e.jpg)  
+Figure 13: A man in a yellow jacket and blue helmet riding a bike. The proposed method correctly generates a descriptive sentence while precisely attending to the image regions for each visuallygroundable words: man, jacket, helmet, and bike.
+
+![](images/f89de42ed7af5a97e11a0cd3800a1348a530031d4ed6fadb3ba8ef9662e05d44.jpg)  
+Figure 14: A man in an orange shirt and a hat is standing next to a blue wall. While our method is able to ground the generated sentence on the objects like: man, shirt, hat, and wall , it completely ignores the person standing next to the man in the orange cloth.
+
+![](images/0776ed2f2f010e289a9bd7b834cddb236f744fa4fa4fc53d90d09278915f0ac4.jpg)  
+Figure 15: A girl in a white shirt and black pants is jumping on a red couch. Our method is able to ground the generated descriptive sentence with the correct grounding on: girl, shirt, pants, and couch.
+
+![](images/63b50dba644737d8ded418d574be8f9d95f21a52ddb3d0a26c4fed812b999e52.jpg)  
+Figure 16: A man in a blue robe walks down a cobblestone street. Our method grounds the visuallyrelevant words like: man, robe, and street. We can also see that it is able to locate the foot on ground for walks.

parse/train/x5hh6N9bUUb/x5hh6N9bUUb.md

@@ -0,0 +1,252 @@
+# Stochastic Solutions for Linear Inverse Problems using the Prior Implicit in a Denoiser
+
+Eero P. Simoncelli
+
+Zahra Kadkhodaie Center for Data Science, New York University zk388@nyu.edu
+
+Center for Neural Science, and Courant Inst. of Mathematical Sciences, New York University Flatiron Institute, Simons Foundation eero.simoncelli@nyu.edu
+
+# Abstract
+
+Deep neural networks have provided state-of-the-art solutions for problems such as image denoising, which implicitly rely on a prior probability model of natural images. Two recent lines of work – Denoising Score Matching and Plug-and-Play – propose methodologies for drawing samples from this implicit prior and using it to solve inverse problems, respectively. Here, we develop a parsimonious and robust generalization of these ideas. We rely on a classic statistical result that shows the least-squares solution for removing additive Gaussian noise can be written directly in terms of the gradient of the log of the noisy signal density. We use this to derive a stochastic coarse-to-fine gradient ascent procedure for drawing high-probability samples from the implicit prior embedded within a CNN trained to perform blind denoising. A generalization of this algorithm to constrained sampling provides a method for using the implicit prior to solve any deterministic linear inverse problem, with no additional training, thus extending the power of supervised learning for denoising to a much broader set of problems. The algorithm relies on minimal assumptions and exhibits robust convergence over a wide range of parameter choices. To demonstrate the generality of our method, we use it to obtain state-of-the-art levels of unsupervised performance for deblurring, super-resolution, and compressive sensing.
+
+# 1 Introduction
+
+Many problems in image processing and computer vision rely, explicitly or implicitly, on prior probability models. Describing the full density of natural images is a daunting problem, given the high dimensionality of the signal space. Traditionally, models have been developed by combining assumed symmetry properties (e.g., translation-invariance, dilation-invariance), with simple parametric forms (e.g., Gaussian, exponential, Gaussian mixtures), often within pre-specified transformed coordinate systems (e.g., Fourier transform, multi-scale wavelets). While these models have led to steady advances in problems such as denoising (e.g., [1–7]), they are too simplistic to generate complex features that occur in our visual world, or to solve more demanding statistical inference problems.
+
+In recent years, nearly all problems in image processing and computer vision have been revolutionalized by the use of deep Convolutional Neural Networks (CNNs). These networks are generally optimized in supervised fashion to obtain a direct input-output mapping for a specific task. This approach does not explicitly rely on a known prior, and offers performance far superior to prior-based methods. The downside, however, is that the learned mappings are intertwined with the task for which they are optimized, and in most cases require training a separate network for each new application. In contrast, a prior probability model can provide a universal substrate for solving inference problems. The superior performance of CNNs suggests that they embed, implicitly, sophisticated prior knowledge of images. These implicit priors arise from a combination of the distribution of the training data, the architecture of the network [8], regularization terms included in the optimization objective, and the optimization algorithm.
+
+Here, our goal is to extract the implicit prior from a network trained for denoising and use it to solve other inverse problems without further training. We choose denoising not because it is of particular importance or interest, but because we can make the relationship between mapping of a denoiser and a prior explicit. We combine the advantages of prior-based and mapping-based approaches, deriving a general algorithm for solving linear inverse problems using the prior implicit in a trained denoiser. We start with a result from classical statistics $[ [ 9 $ that states that a denoiser that aims to minimize squared error of images corrupted by additive Gaussian noise may be interpreted as computing the gradient of the log of the density of noisy images. This result is related to Score Matching [10], but provides a more direct relationship between least-squares optimal denoising and the embedded prior [11, 12]. We develop a stochastic ascent algorithm that uses this denoiser-estimated gradient to draw high-probability samples from the embedded prior. Importantly, we use a blind denoiser that can handle noise contamination of unknown amplitude, which provides a means of adaptively controlling the gradient step sizes and the amplitude of injected noise, enabling robust and efficient convergence. We then modify the algorithm to incorporate constraints arising from any deterministic linear measurement of an image. The resulting procedure generates high-probability samples from the prior conditioned on the measurements, thus providing a general stochastic solution for any deterministic linear inverse problem. We demonstrate that our method produces visually high-quality results in recovering missing pixels, and state-of-the-art levels of unsupervised performance on superresolution, deblurring and compressive sensing.1 Earlier versions of this work were presented in [13].
+
+This work is closely related to two lines of research. Nearly a decade ago, a strategy known as Plug-and-Play (P&P) was proposed for using a denoiser as a regularizer in solving other inverse problems $\dot { \lVert 1 4 \rVert }$ , and a number of recent extensions have used this concept to develop MAP solutions for linear inverse problems [15–22, 12]. Generally, the objective is decoupled into data fidelity and regularization terms, introducing a slack variable for use in a proximal optimization algorithm (e.g., ADMM). The proximal operator of the regularization term is interpreted as the MAP solution of a denoising problem, and is replaced by a denoiser. Of particular relevance to our work, recent publications have proven convergence of such algorithms when used in conjunction with MMSE denoisers [23, 24]. A parallel line of research has focused on the use of generative models based on Score Matching [25–30]. The connection between Score Matching $\mathbb { \ m }$ and denoising autoencoders [31] was first shown in [32], by proving that the training criterion of a denoising autoencoder is equivalent to matching the score of the model and a Parzan density estimate of the data. Most recently, this idea has been used as the basis for an MCMC algorithm for sampling from the prior implicit in a CNN denoiser [29]. In Section 4 we elaborate on how these methods are related to our results.
+
+# 1.1 Image priors, manifolds, and noisy observations
+
+Digital photographic images lie in a high-dimensional space $\mathbb { R } ^ { N }$ , where $N$ is the number of pixels), and simple thought experiments suggest that they are concentrated on or near low-dimensional manifolds whose local coordinates represent continuous deformations and intensity variations. In contrast, images generated with random pixels are almost always feature and content free, and thus not considered to be part of this manifold. We can associate with this manifold a prior probability model, $p ( x )$ , by assuming that images within the manifold have constant or slowly-varying probability, while unnatural or distorted images (which lie off the manifold) have low or zero probability. Suppose we make a noisy observation of an image, $y = x + z$ , where $\boldsymbol { x } \in R ^ { N }$ is the original image drawn from $p ( x )$ , and $z \sim \mathcal { N } ( 0 , \sigma ^ { 2 } I _ { N } )$ is a sample of Gaussian white noise. The observation density $p ( y )$ is related to the prior $p ( x )$ via marginalization:
+
+$$
+p ( y ) = \int p ( y | x ) p ( x ) d x = \int g ( y - x ) p ( x ) d x ,
+$$
+
+where $g ( z )$ is the Gaussian noise distribution. Equation $\mathbb { \oplus }$ is in the form of a convolution, and thus $p ( y )$ is a Gaussian-blurred version of the signal prior, $p \overline { { ( x ) } }$ . Moreover, the family of observation
+
+densities over different noise variances, $p _ { \sigma } ( y )$ , forms a Gaussian scale-space representation of the prior $\pm \pm \pm \pm$ , analogous to the temporal evolution of a diffusion process.
+
+# 1.2 Least squares denoising and CNNs
+
+Given a noisy observation, $y$ , the minimum mean squared error (MMSE) estimate of the true signal is well known to be the conditional mean of the posterior density:
+
+$$
+\hat { x } ( y ) = \int x p ( x | y ) d x = \int x \frac { p ( y | x ) p ( x ) } { p ( y ) } d x
+$$
+
+The structure of the equation mirrors the traditional approach to the problem: one chooses a prior probability model, $p ( x )$ , combines it with a likelihood function describing the noisy measurement process, $p ( y | x )$ , and solves. Modern denoising solutions, on the other hand, are often based on supervised learning of a direct mapping from noisy to denoised images. One expresses the estimation function (as opposed to the prior) in parametric form, and sets the parameters by minimizing the denoising MSE over a large training set of example signals and their noise-corrupted counterparts $\pmb { \mathbb { B 5 } }$ $\textcircled { 3 8 } \textcircled { 1 }$ . Current state-of-the-art denoising results using CNNs obtained with this supervised approach are far superior to results of previous methods [39–41]. Recent analysis of these networks demonstrates that when they are trained to handle a broad range of noise levels, they perform an approximate projection onto a low-dimensional subspace [42]. In our context, we interpret this subspace as a tangent hyperplane of the image manifold.
+
+# 1.3 Exposing the implicit prior through Empirical Bayes estimation
+
+Trained CNN denoisers contain detailed prior knowledge of image structure, but Eq. $\textcircled{2}$ suggests that it is embedded within a high-dimensional integral. How can we make use of this implicit prior? Recent results have derived relationships between Score Matching density estimates and denoising, and have used these relationships to make use of implicit prior information [43, 44, 29, 45]. Here, we exploit a more direct but less-known result from the literature on Empirical Bayesian estimation. The idea was introduced in $\boxed { \boxplus 6 }$ , extended to the case of Gaussian additive noise in $\pmb { \bigtriangledown }$ (see also $\mathbb { I } 1 2 \mathbb { I } )$ ), and generalized to many other measurement models $\mathbb { m }$ . In the case of additive Gaussian noise, one can rewrite the estimator of Eq. (2) as:
+
+$$
+\begin{array} { r } { \hat { x } ( y ) = y + \sigma ^ { 2 } \nabla _ { y } \log p ( y ) . } \end{array}
+$$
+
+The proof is relatively straightforward. The gradient of the observation density of Eq. $\mathbb { \underline { { \left( 1 \right) } } }$ is:
+
+$$
+\nabla _ { y } p ( y ) = \frac { 1 } { \sigma ^ { 2 } } \int ( x - y ) g ( y - x ) p ( x ) d x = \frac { 1 } { \sigma ^ { 2 } } \int ( x - y ) p ( y , x ) d x .
+$$
+
+Multiplying both sides by $\sigma ^ { 2 } / p ( y )$ and separating the right side into two terms gives:
+
+$$
+\sigma ^ { 2 } \frac { \nabla _ { y } p ( y ) } { p ( y ) } = \int x p ( x | y ) d x - \int y p ( x | y ) d x = \hat { x } ( y ) - y .
+$$
+
+Rearranging terms and using the chain rule to compute the gradient of the log gives Eq. $\textcircled{3}$ . This remarkable result re-expresses the integral over the prior and likelihood of Eq. $( 2 )$ in terms of a gradient. Note that 1) the relevant density is not the prior, $p ( x )$ , but the noisy observation density, $p ( y ) ; 2 )$ the gradient is computed on the log density (the associated “energy function”); and 3) the gradient adjustment is not iterative - the estimate is achieved in a single step, and holds for any noise level, $\sigma$ .
+
+# 2 Drawing high-probability samples from the implicit prior
+
+Suppose we wish to draw a sample from the prior implicit in a denoiser. Equation $\textcircled{3}$ allows us to generate an image proportional to the gradient of $\log p ( y )$ by computing the denoiser residual, $f ( \bar { y } ) = \hat { x } ( y ) - y$ . Song and Ermon $\mathbb { \left. 2 9 \right. }$ developed a Markov chain Monte Carlo (MCMC) scheme, combining gradient steps derived from Score Matching and injected noise in a Langevin sampling algorithm to draw samples from a sequence of densities $p _ { \sigma } ( y )$ , while reducing $\sigma$ in a sequence of discrete steps, each associated with an appropriately trained denoiser. In contrast, starting from a random initialization, $y _ { 0 }$ , we aim to find a high-probability image (i.e., an image from the manifold) using a more direct and efficient stochastic gradient ascent procedure.
+
+# 2.1 Unconstrained sampling algorithm
+
+We compute gradients using the residual of a universal blind CNN denoiser, which automatically estimates and adapts to each noise level. On each iteration, the algorithm takes a small step in the direction specified by the denoiser, moving toward the image manifold and thereby reducing the amplitude of the effective noise. Under the interpretation that the denoiser performs a projection onto the current approximation of the image manifold, this noise reduction occurs in the subspace orthogonal to that manifold, and noise components parallel to the manifold are retained. As the effective noise decreases, the observable dimensionality of the image manifold increases $\pm 2 \|$ , enabling the synthesis of detailed image content. Since the family of observation densities, $p _ { \sigma } ( y )$ forms a scale-space representation of $p ( x )$ , the algorithm may be viewed as a form of coarse-to-fine optimization $\pm \infty \vert \sqrt { 4 7 } \vert - \vert 5 0 \vert$ . Assuming the step sizes are adequately controlled, the procedure will converge to a local optimum of the implicit prior - i.e., a point on the manifold. Figure 7 provides a visualization of this process in two dimensions.
+
+Each iteration operates by taking a deterministic step in the direction of the gradient (as obtained from the denoising function) and injecting some additional noise:
+
+$$
+y _ { t } = y _ { t - 1 } + h _ { t } f ( y _ { t - 1 } ) + \gamma _ { t } z _ { t } ,
+$$
+
+where $f ( y ) = { \hat { x } } ( y ) - y$ is the residual of the denoising function, which is proportional to the gradient of $\log p ( y )$ , from Eq. $\textcircled { 3 }$ . The parameter $h _ { t } \in [ 0 , 1 ]$ controls the fraction of the denoising correction that is taken, and $\gamma _ { t }$ controls the amplitude of a sample of white Gaussian noise, $z _ { t } \sim \mathcal { N } ( 0 , I )$ . The purpose of injecting noise is two-fold. First, from an optimization perspective, it allows the method to avoid getting stuck in local maxima. Second, it allows stochastic exploration of the manifold, yielding a more diverse (higher entropy) family of solutions. The effective noise variance of image $y _ { t }$ is:
+
+$$
+\sigma _ { t } ^ { 2 } = ( 1 - h _ { t } ) ^ { 2 } \sigma _ { t - 1 } ^ { 2 } + \gamma _ { t } ^ { 2 } ,
+$$
+
+where the first term is the variance of the noise remaining after the denoiser correction (assuming the denoiser is perfect), and the second term is the variance arising from the injected noise. The assumption of perfect denoising is an idealization, but we show empirically (Fig. $\mathbf { \bar { \rho } } _ { 1 ) } ^ { 1 ) }$ that the algorithm converges reliably, with error levels falling as predicted by Eq. $( 5 )$ or faster, across different settings of $\beta$ and $h _ { 0 }$ .
+
+To ensure convergence, we require the effective noise variance on each time step to be reduced, despite the injection of additional noise. For this purpose, we introduce a parameter $\beta \in [ 0 , 1 ]$ to control the proportion of injected noise ( $\beta = 1$ indicates no noise), and enforce the convergence by requiring that:
+
+$$
+\sigma _ { t } ^ { 2 } = ( 1 - \beta h _ { t } ) ^ { 2 } \sigma _ { t - 1 } ^ { 2 } .
+$$
+
+Combining this with Eq. $( 5 )$ yields an expression for $\gamma _ { t }$ in terms of $h _ { t }$ :
+
+$$
+\gamma _ { t } ^ { 2 } = \left[ ( 1 - \beta h _ { t } ) ^ { 2 } - ( 1 - h _ { t } ) ^ { 2 } \right] \sigma _ { t - 1 } ^ { 2 } = \left[ ( 1 - \beta h _ { t } ) ^ { 2 } - ( 1 - h _ { t } ) ^ { 2 } \right] \left. f ( y _ { t - 1 } ) \right. ^ { 2 } / N ,
+$$
+
+where the second equation assumes that the magnitude of the denoising residual provides a good estimate of the effective noise standard deviation, as was found in $\pm 2 \|$ . This allows the denoiser to adaptively control the gradient ascent step sizes, reducing them as the $y _ { t }$ approaches the manifold (see Fig. $\dot { \bigtriangledown } \dot { \bigtriangledown } \dot { \bigtriangledown }$ . This automatic adjustment results in efficient and reliable convergence, as demonstrated empirically in Fig. 1. Our initial implementation with a small constant fractional step size $h _ { t } = h _ { 0 }$ produced high quality results, but required many iterations. Intuitively, step sizes that are a fixed proportion of the distance to the manifold lead to exponential decay - a form of Zeno’s paradox. To accelerate convergence, we introduced a schedule for increasing the step size proportion, starting from $h _ { 0 } \in [ 0 , 1 ]$ . The sampling process is summarized in Algorithm $\bigstar \bigstar$ and is provided as a block diagram in Fig. 6.
+
+![](images/11572b019770ba01444407a637b37fc09068d37759e4287c64753e8f8a63e465.jpg)  
+Figure 1: Convergence of sampling algorithm, quantified in terms of the effective noise standard deviation $\begin{array} { r } { \sigma = { \frac { | | d _ { t } | | } { \sqrt { N } } } } \end{array}$ for three different values of $\beta$ and two valus of $h _ { 0 }$ . Left. Convergence of single examples (solid curves) is well-behaved and efficient in all cases. Dashed curves indicate the convergence predicted from the formulation of the algorithm: $\sigma _ { t } = ( 1 - \beta h _ { t } ) \sigma _ { t - 1 }$ . For $\beta = 1$ (no injected noise), the empirical convergence closely approximates the prediction. For larger amounts of injected noise (smaller $\beta$ ), convergence is slower, but faster than predicted. Right. Distribution of number of iterations before convergence to a criterion level of $\sigma = 0 . 0 1$ for 50 images. Red symbols indicate average values for each $\beta$ and $h _ { 0 }$ .
+
+<table><tr><td>Algorithm 1: Coarse-to-fine stochastic ascent method for sampling from the implicit prior of adenoiser, using denoiser residual f(y)=x(y)- y.</td></tr><tr><td>parameters:σo,σL,ho,β initialization: t =1, draw yo~ N(0.5,σ²I)</td></tr><tr><td>while Ot-1 ≥σL do hot</td></tr><tr><td>ht=1+h(t-1）； dt=f(yt-1);</td></tr><tr><td>²=；</td></tr><tr><td>γ²=(1-βht）²-(1-ht）²)²; N</td></tr><tr><td>Draw zt ~ N(0, I); yt←yt-1+htdt+Yt2t;</td></tr></table>
+
+# 2.2 Image synthesis examples
+
+For the denoiser, we used BF-CNN $\lVert \rVert 2 \rVert$ , a bias-free variant of DnCNN $\mathbb { \lVert 3 9 \rVert }$ . We obtained similar results (not shown) using other CNN architectures described in $\lVert \overline { { 4 2 } } \rVert$ , including Recurrent-CNN, Dense-Net, and truncated U-Net. We trained this network on three different datasets: $4 0 \times 4 0$ patches cropped from Berkeley segmentation training set $\pmb { \Vert 5 \bot }$ , in color and grayscale, and MNIST dataset $\pmb { \mathbb { E 2 } }$ (see Appendix $\mathbf { A }$ for further details). We chose parameters $\sigma _ { 0 } = 1 , \sigma _ { L } = 0 . 0 1$ , and $h _ { 0 } = 0 . 0 1$ . Figure $2$ provides visualization of two example trajectories, and diversity of samples. Additional visual examples, obtained with different levels of $\beta$ , are shown in Appendix D.
+
+![](images/043a82f4daa5d07e966ff34402bc57e887839726f96a71a7659a71050786fcdb.jpg)  
+Figure 2: Left. Visualization of sampling algorithm trajectories. Each row shows a sequence of images, $y _ { t } , t = 1 , 9 , 1 7 , 2 5 , . . . ,$ from the iterative sampling procedure, with different initializations, $y _ { 0 }$ , and no added noise $( \beta = 1 )$ ), demonstrating the way that the algorithm amplifies and "hallucinates" structure found in the initial (noise) images. Right. Sampling diversity. Inpainting examples generated using two BF-CNN denoisers. First column: original images. Second column: partially measured images, with missing block . Right three columns: Restored examples.
+
+# 3 Solving deterministic linear inverse problems using the implicit prior
+
+Many applications in signal processing can be expressed as deterministic linear inverse problems - deblurring, super-resolution, estimating missing pixels (e.g., inpainting), and compressive sensing are all examples. Given a set of linear measurements of an image, $\mathbf { \bar { \Psi } } \mathbf { x } ^ { c } = \mathbf { \Psi } \mathbf { M } ^ { T } \mathbf { \Psi } \mathbf { \bar { x } }$ , where $M$ is a low-rank measurement matrix, one attempts to recover the original image. In Section 2, we developed a stochastic gradient-ascent algorithm for obtaining a high-probability sample from $p ( x )$ . Here, we generalize this algorithm to solve for a high-probability sample from the conditional density $p ( x \vert M ^ { T } x = x ^ { c } )$ . Geometrically, constrained sampling corresponds to drawing points which sit at the intersection of the image manifold and the constrained hyperplane (see Fig. 11). Note that for these problems, the injection of noise $\begin{array} { r } { \beta < 1 \ ' } \end{array}$ ) is particularly important, because points on the intersection are not necessarily the closest points to the initial image.
+
+# 3.1 Constrained sampling algorithm
+
+Consider the distribution of a noisy image, $y$ , conditioned on the linear measurements, $x ^ { c } = M ^ { T } x$ . Without loss of generality, we assume the columns of the matrix M are orthogonal unit vectors $\bigstar$ We project $y$ onto two complementary subspaces spanned by the measurement matrix and its orthogonal complement $\bar { M }$ . We write the conditional density of the noisy image conditioned on the linear measurement as
+
+$$
+p ( y | x ^ { c } ) = p ( y ^ { c } , y ^ { u } | x ^ { c } ) = p ( y ^ { u } | y ^ { c } , x ^ { c } ) p ( y ^ { c } | x ^ { c } ) = p ( y ^ { u } | x ^ { c } ) p ( y ^ { c } | x ^ { c } )
+$$
+
+where $\boldsymbol { y } ^ { c } = \boldsymbol { M } ^ { T } \boldsymbol { y }$ , $y ^ { u } = { \bar { M } } ^ { T } y$ . The last equality is obtained by considering that $y ^ { c }$ is equal to $x ^ { c }$ plus independent Gaussian noise. So given $x ^ { c }$ , $y ^ { c }$ does not provide any additional information about $y ^ { u }$ . That is, $y ^ { u }$ is independent of $y ^ { c }$ when conditioned on $x ^ { c }$ . As with the algorithm of Section $2 ,$ we wish to obtain a local maximum of this function using stochastic coarse-to-fine gradient ascent. Applying the operator $\sigma ^ { 2 } \nabla \log ( \cdot )$ yields
+
+$$
+\sigma ^ { 2 } \nabla _ { y } \log p ( y | x ^ { c } ) = \sigma ^ { 2 } \nabla _ { y } \log p ( y ^ { u } | x ^ { c } ) + \sigma ^ { 2 } \nabla _ { y } \log p ( y ^ { c } | x ^ { c } )
+$$
+
+The second term is the gradient of the log of the observation noise distribution that lies within the measurement subspace (column space of M). For Gaussian noise with variance $\sigma ^ { 2 }$ , it reduces to $M ( y ^ { c } - x ^ { c } )$ . The first term is the gradient of log of the noisy image distribution in the subspace orthogonal to the measurement subspace, conditioned on the measurements. This can be computed by projecting the measurement subspace out of the full gradient given by the denoiser residual. Specifically, we project $f ( y )$ onto the orthogonal complement of $M$ using the matrix $I - M M ^ { T }$ . Combining these gives:
+
+$$
+\begin{array} { c } { { \sigma ^ { 2 } \nabla _ { y } \log p ( y ) = ( I - M M ^ { T } ) \sigma ^ { 2 } \nabla _ { y } \log p ( y ) + M ( x ^ { c } - y ^ { c } ) } } \\ { { = ( I - M M ^ { T } ) f ( y ) + M ( x ^ { c } - M ^ { T } y ) . } } \end{array}
+$$
+
+Thus, we see that the gradient of the conditional density is partitioned into two orthogonal components, capturing the gradient of the (log) noisy density, and the deviation from the constraints, respectively.
+
+![](images/2ec59d9377115c8f5c81bf6ad9110de40d068d19b01cb339b1cca01358abce04.jpg)  
+Figure 3: Spatial super-resolution. First column shows cropped portion of original images from Set14 (face: $2 7 2 \times 2 7 2$ and, Barbara: $7 2 0 \times 5 7 6$ ). The algorithm can be applied to images of any resolution - we show cropped portions to facilitate visual inspection. Second column shows cropped portion with resolution reduced by averaging over $4 \mathbf { x } 4$ blocks (dimensionality reduction to $6 . 2 5 \%$ ). Next three columns show reconstruction results obtained using DIP $\textcircled { 8 }$ , DeepRED $\left[ \left[ 2 0 \right] \right]$ , and our method. In all cases, our method produces an image that is sharper with less noticeable artifacts (e.g., note blocking/aliasing artifacts along diagonal contours of lower image). The last column shows an average over 10 samples obtained by our method.
+
+To draw a high-probability sample from $p ( x | x ^ { c } )$ , we use the same algorithm described in Section 2, substituting Eq. $\overset { \cdot } { ( 7 ) }$ for the deterministic update vector, $d _ { t }$ (see Algorithm 2 in Appendix). Note that without any measurements (i.e., $M = 0$ ) Algorithm $2$ reduces to Algorithm 1.
+
+# 3.2 Linear inverse examples
+
+We evaluate our method on three linear inverse problems (and provide two additional problems in Appendix $\boxed { \mathrm { E } }$ . The same algorithm and parameters are used on all problems - only the measurement matrix $M$ and measured values $M ^ { T } x$ are altered. In particular, as in section $\boxed { 2 . 2 }$ we used BF-CNN $\lVert \rVert 2 \rVert$ , and chose parameters $\sigma _ { 0 } = 1 , \sigma _ { L } = 0 . 0 1 , h _ { 0 } = 0 . 0 1 , \beta = 0 . 0 1$ . For each example, we show original images $( x )$ , the direct least-squares reconstruction $( M M ^ { T } x )$ , and restored images. Subjective assessment of perceptual quality is particularly important in cases where the measurement matrix is of very low rank, and the distribution of solutions is diverse (the synthesis examples of the previous section correspond to the limiting case, with measurements of rank zero). We also provide numerical comparisons with other unsupervised methods, in terms of both PSNR and SSIM (an approximate measure of perceptual quality). Since our method is stochastic, we provide standard deviations of these performance values across 10 realizations.
+
+Spatial super-resolution. Here, one aims to reconstruct a high resolution image from a low resolution (i.e. downsampled) image. Downsampling is typically performed after lowpass filtering, and the downsampling factor and filter kernel determine the measurement model, $M$ . Here, we use a $4 \times 4$ constant filter, and $4 \times 4$ downsampling (i.e., measurements are averages over non-overlapping blocks). We compare to two recent unsupervised methods Deep image Prior (DIP) $\pmb { \Vert 8 \Vert }$ and DeepRED [20] DIP chooses a random input vector, and adjusts the weights of a CNN to minimize the mean square error between the output and the corrupted image. Regularization by denoising (RED) is a recent successful method closely related to P&P $\pmb { \mathbb { D } } \bar { \sf S } \bar { \sf I }$ . DeepRED $\left[ \left[ 2 0 \right] \right]$ combines DIP and RED, obtaining better performance than either method alone.
+
+Inspection of results on two example images demonstrates that our method produces results that are sharper with less noticeable artifacts (Fig. 3). Despite this, the PSNR and SSIM values are slightly worse than both DIP and DeepRED (Table 1). These can be improved by averaging over realizations (last column of Table 1), producing superior PSNR and SSIM values at the expense of some blurring (last column of Fig. 3). This is expected: the algorithm produces high-probability samples of the prior subject to the measurement constraint, but the least-squares optimal solution is the mean of the posterior distribution. If the samples are drawn from a curved manifold, their average (a convex combination of those points) will lie off the manifold. Finally, note that our method is more than two orders of magnitude faster than either DIP or DeepRED (bottom row, Table 1)
+
+Table 1: Spatial super-resolution performance over Set5 (top 2 rows) and Set14 (second 2 rows). Values indicate YCbCr-PSNR (SSIM). Last row shows average Set14 runtime on a DGX GPU.   
+
+<table><tr><td></td><td>MMTx</td><td>DIP </td><td>DeepRED[ [20]</td><td>Ours±std</td><td>Ours:avg</td></tr><tr><td>4:1</td><td>26.35 (0.826)</td><td>30.04 (0.902)</td><td>30.22 (0.904)</td><td>29.47±0.09 (0.894±0.001)</td><td>31.20 (0.913)</td></tr><tr><td>8:1</td><td>23.02 (0.673)</td><td>24.98 (0.760)</td><td>24.95 (0.760)</td><td>25.07±0.13 (0.767±0.003)</td><td>25.64 (0.792)</td></tr><tr><td>4:1</td><td>24.65 (0.765)</td><td>26.88 (0.815)</td><td>27.01 (0.817)</td><td>26.56±0.09 (0.808±0.001)</td><td>27.14 (0.826)</td></tr><tr><td>8:1</td><td>22.06 (0.628)</td><td>23.33 (0.685)</td><td>23.34 (0.685)</td><td>23.32±0.11 (0.681±0.002)</td><td>23.78 (0.703)</td></tr><tr><td colspan="2">runtime (sec):</td><td>1,190</td><td>1,584</td><td>9</td><td>10×9</td></tr></table>
+
+![](images/43d9657aff1589508287aa0f3a9445d6f1d0793a97bb2a37db727c14f428c2fb.jpg)  
+Figure 4: Deblurring (spectral super-resolution). Measurements correspond to $5 \%$ of low frequencies. Original images are from Set5 (butterfly of size $2 5 6 \times 2 5 6$ and woman of size $2 2 4 \times 3 3 6$ ).
+
+Deblurring (spectral super-resolution). The applications described above (and in Appendix $\boxed { \mathrm { E } }$ are based on partial measurements in the pixel domain. Here, we consider a blurring operator that retains a set of low-frequency coefficient in the Fourier domain, discarding the rest. This is equivalent to convolving the image with a sinc kernel. In this case, $M$ consists of the preserved low-frequency columns of the discrete Fourier transform, and $M M ^ { T } x$ is the blurred version of $x$ . Example images are shown in Fig. $\nsupseteq$ and numerical comparisons are shown in Table $\bigtriangledown$ Our method produces strong results, both perceptually and numerically.
+
+Compressive sensing. Compressive sensing $\mathbb { B 6 } \mathbb { B 7 }$ aims to recover signals from a small number of (typically, random) linear measurements. In brief, one acquires measurements with a sensing matrix containing a set of $n < < N$ random orthogonal axes, and solves the inverse problem by assuming a sparse prior. Photographic images are not truly sparse in any fixed linear basis, but they can be reasonably approximated by low-dimensional subsets of Fourier or wavelet basis functions, and compressive sensing results are typically demonstrated using one of these. The manifold prior embedded within our CNN denoiser corresponds to a nonlinear form of sparsity, and our stochastic coarse-to-fine ascent algorithm can be used to recover an image from the measured linear projections onto the random basis. We compare to four other methods. TVAL3 $\mathbb { \left. \boldsymbol { \bar { 5 3 } } \right. }$ is an optimization algorithm using total variation regularization, ISTA-Net $\textcircled { | 5 4 | }$ is a block-based supervised CNN method trained to reconstruct images from measurements obtained from a single pre-specified measurement matrix. BNN $\mathbb { \lVert } \mathbb { 5 } \mathbb { 5 } \mathbb { I }$ is an unsupervised Bayesian method for solving compressive sensing problems. DIP $\pmb { \mathbb { B } } \|$ was previously described. Fig. $\dot { 5 }$ shows results for two example images, and Table $3$ summarizes numerical performance. All values are taken from $\lVert 5 5 \rVert$ except for ISTA-Net which were obtained by running the open-source code. Our method generally outperforms all other methods, even those that are specialized for Compressive Sensing (ISTA-NET, BNN).
+
+Table 2: Spectral super-resolution (deblurring) performance over Set5, in YCbCr-PSNR (SSIM).   
+
+<table><tr><td>Ratio</td><td>MMTx</td><td>DIP 图</td><td>DeepRED 四</td><td>Ours±std</td><td>Ours:avg</td></tr><tr><td>10%</td><td>30.2 (0.91)</td><td>32.54 (0.93)</td><td>32.63 (0.93)</td><td>31.82±0.08 (0.93±0.001)</td><td>32.78 (0.94)</td></tr><tr><td>5%</td><td>27.77 (0.85)</td><td>29.88 (0.89)</td><td>29.91 (0.89)</td><td>29.22±0.14(0.89±0.002)</td><td>30.07 (0.90)</td></tr></table>
+
+Table 3: Compressive sensing performance over Set68 [51]. Values indicate PSNR (SSIM).   
+
+<table><tr><td>Ratio</td><td>TVAL3 </td><td>ISTA-Net[ 54</td><td>DIP 图</td><td>BNN 55</td><td>Ours±std</td><td>Ours:avg</td></tr><tr><td>25%</td><td>26.48 (0.77)</td><td>29.07 (0.84)</td><td>27.78 (0.80)</td><td>28.63 (0.84)</td><td>29.16±0.033 (0.88±0.001)</td><td>29.74(0.89)</td></tr><tr><td>10%</td><td>22.49 (0.58)</td><td>25.23 (0.69)</td><td>24.82 (0.69)</td><td>25.24 (0.71)</td><td>25.47±0.03 (0.78±0.001)</td><td>25.84 (0.80)</td></tr><tr><td>4%</td><td>19.10 (0.42)</td><td>22.02 (0.54)</td><td>22.51 (0.58)</td><td>22.52 (0.58)</td><td>22.07±0.05 (0.68±0.002)</td><td>22.29 (0.69)</td></tr></table>
+
+![](images/3129f1ba9229c172ff0f854859868b7251f861df15e24d94382ee83e181527b9.jpg)  
+Figure 5: Compressive sensing. Measurement matrix $M$ contains random orthogonal unit vectors, whose number is equal to $1 0 \%$ of the number of image pixels $( 3 0 0 \times 3 0 0 )$ . Third column: images recovered using ISTA-Net (trained with supervision for a particular measurement matrix). Fourth column: Our method, which again is seen to exhibit fewer artifacts.
+
+# 4 Related work
+
+Our method is conceptually similar to P&P[14] in that it uses a denoiser to solve linear inverse problems. But it differs in a number of important ways: (1) direct relationship between prior and denoiser mapping. The rationale for using a denoiser as a regularizer in P&P frameworks arises from interpreting the proximal operator of the regularizer as a MAP solution of a denoising problem, providing an indirect connection to prior; We derive our method from Miyasawa’s relationship between an MMSE denoiser and the prior, which is exact and explicit, and makes the algorithm interpretable. This connection has also been made in $\pm \pm \pm \pm \pm \pm$ . (2) sampling vs. MAP estimation. We obtain a high probability image from the implicit prior that is consistent with a linear constraint. Our solution is stochastic, and does not minimize MSE, but has high perceptual quality. RED and other P&P methods are derived as MAP solutions, and although this is not equivalent to minimizing MSE (maximizing PSNR), the results generally have better PSNR than our sampling results, but are visually more blurred (see Figs. $3$ and $\textcircled{4}$ ; (3) automatic step-size selection and convergence. P&P, which uses ADMM for optimization, relies on hyper-parameter selection that are critical for convergence (as discussed extensively in $\mathbb { L } \Sigma \mathbb { I } .$ ). Our algorithm adjusts step-size automatically using the blind denoiser, with only two primary hyper-parameters ( $h _ { 0 }$ and $\beta$ ), and convergence is robust to choices of these (Fig. 1).
+
+Our method is also closely related to recent work that uses Score Matching $\mathbb { m }$ to draw samples from an implicit prior. This line of work is rooted in the connection between Denoising Autoencoders and Score Matching, first described in $\pmb { \mathbb { B 2 } }$ . Denoising autoencoders learn the gradient of log density, and their connection to an underlying data manifold has been explored in $\boxed { 2 5 } \boxed { 4 3 } \boxed { 3 1 }$ . More recently, Refs. [44, $\textcircled { 2 6 }$ trained a neural network to directly estimate energy (the negative log prior) and interpreted its gradient as the Score of the data. Finally, in a breakthrough paper that partially inspired our approach, Song and Ermon $\pmb { \mathbb { Z } } 9 \|$ trained a sequence of denoisers with decreasing levels of noise and used Langevin dynamics to sample from the underlying probability distributions in succession. Our work differs from these in several important ways: (1) Direct derivation. Our method is based on Miyasawa’s explicit relationship between the denoiser mapping and implicit density $\pmb { \mathbb { Q } } \mathbf { \| }$ , which can be proven with a few lines of math (Section $1 . 3 )$ . The relationship of this result to Score Matching [11, 12], and the relationship between Score Matching and Denoising Autoencoders $\pmb { \Vert 3 2 \Vert }$ are both significantly more nuanced and complex. (2) Automatic stepsize adjustment and efficiency. The algorithm presented in $\mathbb { \left| \left[ 2 9 \right] \right| }$ uses a discrete sequence of denoisers, each trained for a single noise level, and embedding a distribution of noisy images with that specific noise level. Langevin dynamics are used to sample from each of these distributions in succession. Langevin sampling guarantees (asymptotically) convergence to each successive distribution, although these intermediate samples are used only for initialization of the subsequent stage. In addition to the Langevin sampling itself, the method requires choices of the schedule of noise levels (standard deviations, and number of iterations used at each level).
+
+In contrast, our formulation relies on a single universal blind denoiser which implicitly embeds an infinite family of distributions of noisy images (corresponding to a continuous range of noise levels). The gradient provided by the denoiser is not used for sampling, but for coarse-to-fine ascent of the noisy distribution, removing a fraction of the noise at each step. The universal denoiser adapts to this updated implicit noisy density, both in terms of gradient direction and magnitude. We use the denoiser magnitude as an estimate of the implicit noise level $\bigtriangledown ,$ and this is used to control the amplitude of injected noise. Note that this differs markedly from the control of noise injection in the Langevin method, which is of constant magnitude in each stage. Under assumptions about the denoiser (which hold empirically), our method converges rapidly to a mode of the prior and is robust to parameter choices $\mathbb { L }$ The continuous maximization of probability results in substantial gains in efficiency. For comparison, Song&Ermon $\pmb { \mathbb { Z } } 9 \|$ report 1000 iteration to synthesize a $3 2 \times 3 2$ image, whereas we synthesize $4 0 \times 4 0$ images in roughly 35 iteration (for $\beta = 1$ ). (3) Image synthesis vs. linear inverse problems. Finally, we’ve focused the use of our method as a universal solver for linear inverse problems, whereas Score Matching methods have generally been focused on unconditional image synthesis.
+
+# 5 Discussion
+
+We’ve described a framework for using the prior embedded in a denoiser to solve inverse problems. Specifically, we developed a stochastic coarse-to-fine gradient ascent algorithm that uses the denoiser to draw high-probability samples from its implicit prior, and a constrained variant that can be used to solve any deterministic linear inverse problem. To demonstrate the generality of our algorithm, we showed solving five inverse problems using the same algorithm and parameters, without any additional training. The derivation is based on a simple and direct expression relating denoising to priors, and a few basic empirical facts about universal CNN denoisers. Finally, we empirically demonstrated its efficiency in Fig. 1 and Table 1. It is worth noting that the assumed use of Gaussian additive noise and MSE objective in training the denoiser is necessary only to justify the use of Miyasawa’s expression (Eq. 3), but does not impose any such restrictions on use of the trained denoiser for sampling from the implicit prior or solving inverse problems. Denoisers can be trained supervised on unlimited amounts of unlabeled data, and as such, our method extends the power of supervised learning to a much broader set of problems, with no additional training.
+
+As discussed following Eq. $\textcircled{5}$ , the control of step sizes and noise injection in our algorithm is chosen by assuming that the denoiser residual exactly cancels the noise. We showed empirically (Fig. 1) that this idealization does not disrupt convergence for BF-CNN, but we cannot guarantee this would hold for all other denoisers. More generally, although the method can be used with any universal least-squares denoiser designed or trained to remove Gaussian noise, the complexity of the embedded prior, and thus the quality of our linear inverse results, relies heavily on the expressive power of the denoiser (BF-CNN in our case), as well as the diversity of the training set. Finally, the current algorithm is designed to solve deterministic linear inverse problems. We are currently exploring extensions to inverse problems based on stochastic or nonlinear measurements.
+
+# Acknowledgments and Disclosure of Funding
+
+We gratefully acknowledge financial support from the Simons Foundation, the Howard Hughes Medical Institute, and NSF NRT HDR Award 1922658 to the Center for Data Science at NYU. High performance computing resources were provided by the NYU HPC center and the Flatiron Institute of the Simons Foundation.
+
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+        "text": "Stochastic Solutions for Linear Inverse Problems using the Prior Implicit in a Denoiser ",
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+        "text": "Eero P. Simoncelli ",
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+        "text": "Zahra Kadkhodaie Center for Data Science, New York University zk388@nyu.edu ",
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+        "text": "Center for Neural Science, and Courant Inst. of Mathematical Sciences, New York University Flatiron Institute, Simons Foundation eero.simoncelli@nyu.edu ",
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+        "text": "Abstract ",
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+        "text": "Deep neural networks have provided state-of-the-art solutions for problems such as image denoising, which implicitly rely on a prior probability model of natural images. Two recent lines of work – Denoising Score Matching and Plug-and-Play – propose methodologies for drawing samples from this implicit prior and using it to solve inverse problems, respectively. Here, we develop a parsimonious and robust generalization of these ideas. We rely on a classic statistical result that shows the least-squares solution for removing additive Gaussian noise can be written directly in terms of the gradient of the log of the noisy signal density. We use this to derive a stochastic coarse-to-fine gradient ascent procedure for drawing high-probability samples from the implicit prior embedded within a CNN trained to perform blind denoising. A generalization of this algorithm to constrained sampling provides a method for using the implicit prior to solve any deterministic linear inverse problem, with no additional training, thus extending the power of supervised learning for denoising to a much broader set of problems. The algorithm relies on minimal assumptions and exhibits robust convergence over a wide range of parameter choices. To demonstrate the generality of our method, we use it to obtain state-of-the-art levels of unsupervised performance for deblurring, super-resolution, and compressive sensing. ",
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+        "text": "1 Introduction ",
+        "text_level": 1,
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+        "text": "Many problems in image processing and computer vision rely, explicitly or implicitly, on prior probability models. Describing the full density of natural images is a daunting problem, given the high dimensionality of the signal space. Traditionally, models have been developed by combining assumed symmetry properties (e.g., translation-invariance, dilation-invariance), with simple parametric forms (e.g., Gaussian, exponential, Gaussian mixtures), often within pre-specified transformed coordinate systems (e.g., Fourier transform, multi-scale wavelets). While these models have led to steady advances in problems such as denoising (e.g., [1–7]), they are too simplistic to generate complex features that occur in our visual world, or to solve more demanding statistical inference problems. ",
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+        "text": "In recent years, nearly all problems in image processing and computer vision have been revolutionalized by the use of deep Convolutional Neural Networks (CNNs). These networks are generally optimized in supervised fashion to obtain a direct input-output mapping for a specific task. This approach does not explicitly rely on a known prior, and offers performance far superior to prior-based methods. The downside, however, is that the learned mappings are intertwined with the task for which they are optimized, and in most cases require training a separate network for each new application. In contrast, a prior probability model can provide a universal substrate for solving inference problems. The superior performance of CNNs suggests that they embed, implicitly, sophisticated prior knowledge of images. These implicit priors arise from a combination of the distribution of the training data, the architecture of the network [8], regularization terms included in the optimization objective, and the optimization algorithm. ",
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+        "text": "Here, our goal is to extract the implicit prior from a network trained for denoising and use it to solve other inverse problems without further training. We choose denoising not because it is of particular importance or interest, but because we can make the relationship between mapping of a denoiser and a prior explicit. We combine the advantages of prior-based and mapping-based approaches, deriving a general algorithm for solving linear inverse problems using the prior implicit in a trained denoiser. We start with a result from classical statistics $[ [ 9 $ that states that a denoiser that aims to minimize squared error of images corrupted by additive Gaussian noise may be interpreted as computing the gradient of the log of the density of noisy images. This result is related to Score Matching [10], but provides a more direct relationship between least-squares optimal denoising and the embedded prior [11, 12]. We develop a stochastic ascent algorithm that uses this denoiser-estimated gradient to draw high-probability samples from the embedded prior. Importantly, we use a blind denoiser that can handle noise contamination of unknown amplitude, which provides a means of adaptively controlling the gradient step sizes and the amplitude of injected noise, enabling robust and efficient convergence. We then modify the algorithm to incorporate constraints arising from any deterministic linear measurement of an image. The resulting procedure generates high-probability samples from the prior conditioned on the measurements, thus providing a general stochastic solution for any deterministic linear inverse problem. We demonstrate that our method produces visually high-quality results in recovering missing pixels, and state-of-the-art levels of unsupervised performance on superresolution, deblurring and compressive sensing.1 Earlier versions of this work were presented in [13]. ",
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+        "type": "text",
+        "text": "This work is closely related to two lines of research. Nearly a decade ago, a strategy known as Plug-and-Play (P&P) was proposed for using a denoiser as a regularizer in solving other inverse problems $\\dot { \\lVert 1 4 \\rVert }$ , and a number of recent extensions have used this concept to develop MAP solutions for linear inverse problems [15–22, 12]. Generally, the objective is decoupled into data fidelity and regularization terms, introducing a slack variable for use in a proximal optimization algorithm (e.g., ADMM). The proximal operator of the regularization term is interpreted as the MAP solution of a denoising problem, and is replaced by a denoiser. Of particular relevance to our work, recent publications have proven convergence of such algorithms when used in conjunction with MMSE denoisers [23, 24]. A parallel line of research has focused on the use of generative models based on Score Matching [25–30]. The connection between Score Matching $\\mathbb { \\ m }$ and denoising autoencoders [31] was first shown in [32], by proving that the training criterion of a denoising autoencoder is equivalent to matching the score of the model and a Parzan density estimate of the data. Most recently, this idea has been used as the basis for an MCMC algorithm for sampling from the prior implicit in a CNN denoiser [29]. In Section 4 we elaborate on how these methods are related to our results. ",
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+        "text": "1.1 Image priors, manifolds, and noisy observations ",
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+        "text": "Digital photographic images lie in a high-dimensional space $\\mathbb { R } ^ { N }$ , where $N$ is the number of pixels), and simple thought experiments suggest that they are concentrated on or near low-dimensional manifolds whose local coordinates represent continuous deformations and intensity variations. In contrast, images generated with random pixels are almost always feature and content free, and thus not considered to be part of this manifold. We can associate with this manifold a prior probability model, $p ( x )$ , by assuming that images within the manifold have constant or slowly-varying probability, while unnatural or distorted images (which lie off the manifold) have low or zero probability. Suppose we make a noisy observation of an image, $y = x + z$ , where $\\boldsymbol { x } \\in R ^ { N }$ is the original image drawn from $p ( x )$ , and $z \\sim \\mathcal { N } ( 0 , \\sigma ^ { 2 } I _ { N } )$ is a sample of Gaussian white noise. The observation density $p ( y )$ is related to the prior $p ( x )$ via marginalization: ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "equation",
+        "img_path": "images/c577cea2d187f7d29dc88a9bdfcbaeb5176e580d757fe717d900e77f9b2616cb.jpg",
+        "text": "$$\np ( y ) = \\int p ( y | x ) p ( x ) d x = \\int g ( y - x ) p ( x ) d x ,\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "where $g ( z )$ is the Gaussian noise distribution. Equation $\\mathbb { \\oplus }$ is in the form of a convolution, and thus $p ( y )$ is a Gaussian-blurred version of the signal prior, $p \\overline { { ( x ) } }$ . Moreover, the family of observation ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "densities over different noise variances, $p _ { \\sigma } ( y )$ , forms a Gaussian scale-space representation of the prior $\\pm \\pm \\pm \\pm$ , analogous to the temporal evolution of a diffusion process. ",
+        "bbox": [
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "1.2 Least squares denoising and CNNs ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Given a noisy observation, $y$ , the minimum mean squared error (MMSE) estimate of the true signal is well known to be the conditional mean of the posterior density: ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/b9c48926d93c756db47ad0762a195a18a92a6f88a901475cb846cc30c948a19f.jpg",
+        "text": "$$\n\\hat { x } ( y ) = \\int x p ( x | y ) d x = \\int x \\frac { p ( y | x ) p ( x ) } { p ( y ) } d x\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The structure of the equation mirrors the traditional approach to the problem: one chooses a prior probability model, $p ( x )$ , combines it with a likelihood function describing the noisy measurement process, $p ( y | x )$ , and solves. Modern denoising solutions, on the other hand, are often based on supervised learning of a direct mapping from noisy to denoised images. One expresses the estimation function (as opposed to the prior) in parametric form, and sets the parameters by minimizing the denoising MSE over a large training set of example signals and their noise-corrupted counterparts $\\pmb { \\mathbb { B 5 } }$ $\\textcircled { 3 8 } \\textcircled { 1 }$ . Current state-of-the-art denoising results using CNNs obtained with this supervised approach are far superior to results of previous methods [39–41]. Recent analysis of these networks demonstrates that when they are trained to handle a broad range of noise levels, they perform an approximate projection onto a low-dimensional subspace [42]. In our context, we interpret this subspace as a tangent hyperplane of the image manifold. ",
+        "bbox": [
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "1.3 Exposing the implicit prior through Empirical Bayes estimation ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Trained CNN denoisers contain detailed prior knowledge of image structure, but Eq. $\\textcircled{2}$ suggests that it is embedded within a high-dimensional integral. How can we make use of this implicit prior? Recent results have derived relationships between Score Matching density estimates and denoising, and have used these relationships to make use of implicit prior information [43, 44, 29, 45]. Here, we exploit a more direct but less-known result from the literature on Empirical Bayesian estimation. The idea was introduced in $\\boxed { \\boxplus 6 }$ , extended to the case of Gaussian additive noise in $\\pmb { \\bigtriangledown }$ (see also $\\mathbb { I } 1 2 \\mathbb { I } )$ ), and generalized to many other measurement models $\\mathbb { m }$ . In the case of additive Gaussian noise, one can rewrite the estimator of Eq. (2) as: ",
+        "bbox": [
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+        "page_idx": 2
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+    {
+        "type": "equation",
+        "img_path": "images/c4ee88f5adf1dd313f201ad4c2769e9db475f81c03c61f78a154a479f8092cae.jpg",
+        "text": "$$\n\\begin{array} { r } { \\hat { x } ( y ) = y + \\sigma ^ { 2 } \\nabla _ { y } \\log p ( y ) . } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The proof is relatively straightforward. The gradient of the observation density of Eq. $\\mathbb { \\underline { { \\left( 1 \\right) } } }$ is: ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/fb61d5912de545c9324642586b688fc0dd153a1e2a7f5357cef2b12301066c6a.jpg",
+        "text": "$$\n\\nabla _ { y } p ( y ) = \\frac { 1 } { \\sigma ^ { 2 } } \\int ( x - y ) g ( y - x ) p ( x ) d x = \\frac { 1 } { \\sigma ^ { 2 } } \\int ( x - y ) p ( y , x ) d x .\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Multiplying both sides by $\\sigma ^ { 2 } / p ( y )$ and separating the right side into two terms gives: ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/01e387c25f7a2d5d3907fbf25785bd4c8ebe394a8260e86950393cca3e3c81dd.jpg",
+        "text": "$$\n\\sigma ^ { 2 } \\frac { \\nabla _ { y } p ( y ) } { p ( y ) } = \\int x p ( x | y ) d x - \\int y p ( x | y ) d x = \\hat { x } ( y ) - y .\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Rearranging terms and using the chain rule to compute the gradient of the log gives Eq. $\\textcircled{3}$ . This remarkable result re-expresses the integral over the prior and likelihood of Eq. $( 2 )$ in terms of a gradient. Note that 1) the relevant density is not the prior, $p ( x )$ , but the noisy observation density, $p ( y ) ; 2 )$ the gradient is computed on the log density (the associated “energy function”); and 3) the gradient adjustment is not iterative - the estimate is achieved in a single step, and holds for any noise level, $\\sigma$ . ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2 Drawing high-probability samples from the implicit prior ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Suppose we wish to draw a sample from the prior implicit in a denoiser. Equation $\\textcircled{3}$ allows us to generate an image proportional to the gradient of $\\log p ( y )$ by computing the denoiser residual, $f ( \\bar { y } ) = \\hat { x } ( y ) - y$ . Song and Ermon $\\mathbb { \\left. 2 9 \\right. }$ developed a Markov chain Monte Carlo (MCMC) scheme, combining gradient steps derived from Score Matching and injected noise in a Langevin sampling algorithm to draw samples from a sequence of densities $p _ { \\sigma } ( y )$ , while reducing $\\sigma$ in a sequence of discrete steps, each associated with an appropriately trained denoiser. In contrast, starting from a random initialization, $y _ { 0 }$ , we aim to find a high-probability image (i.e., an image from the manifold) using a more direct and efficient stochastic gradient ascent procedure. ",
+        "bbox": [
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "2.1 Unconstrained sampling algorithm ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We compute gradients using the residual of a universal blind CNN denoiser, which automatically estimates and adapts to each noise level. On each iteration, the algorithm takes a small step in the direction specified by the denoiser, moving toward the image manifold and thereby reducing the amplitude of the effective noise. Under the interpretation that the denoiser performs a projection onto the current approximation of the image manifold, this noise reduction occurs in the subspace orthogonal to that manifold, and noise components parallel to the manifold are retained. As the effective noise decreases, the observable dimensionality of the image manifold increases $\\pm 2 \\|$ , enabling the synthesis of detailed image content. Since the family of observation densities, $p _ { \\sigma } ( y )$ forms a scale-space representation of $p ( x )$ , the algorithm may be viewed as a form of coarse-to-fine optimization $\\pm \\infty \\vert \\sqrt { 4 7 } \\vert - \\vert 5 0 \\vert$ . Assuming the step sizes are adequately controlled, the procedure will converge to a local optimum of the implicit prior - i.e., a point on the manifold. Figure 7 provides a visualization of this process in two dimensions. ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Each iteration operates by taking a deterministic step in the direction of the gradient (as obtained from the denoising function) and injecting some additional noise: ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/6e068ef7bc0415b7ed083bb67ad8b706ccc906a908932639c847e29c856dae7f.jpg",
+        "text": "$$\ny _ { t } = y _ { t - 1 } + h _ { t } f ( y _ { t - 1 } ) + \\gamma _ { t } z _ { t } ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            393,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where $f ( y ) = { \\hat { x } } ( y ) - y$ is the residual of the denoising function, which is proportional to the gradient of $\\log p ( y )$ , from Eq. $\\textcircled { 3 }$ . The parameter $h _ { t } \\in [ 0 , 1 ]$ controls the fraction of the denoising correction that is taken, and $\\gamma _ { t }$ controls the amplitude of a sample of white Gaussian noise, $z _ { t } \\sim \\mathcal { N } ( 0 , I )$ . The purpose of injecting noise is two-fold. First, from an optimization perspective, it allows the method to avoid getting stuck in local maxima. Second, it allows stochastic exploration of the manifold, yielding a more diverse (higher entropy) family of solutions. The effective noise variance of image $y _ { t }$ is: ",
+        "bbox": [
+            173,
+            380,
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/5973f6f7855ee880bc7a3ee14f24f56af469614426ef72ff2b83d6ef221d5541.jpg",
+        "text": "$$\n\\sigma _ { t } ^ { 2 } = ( 1 - h _ { t } ) ^ { 2 } \\sigma _ { t - 1 } ^ { 2 } + \\gamma _ { t } ^ { 2 } ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            408,
+            494,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where the first term is the variance of the noise remaining after the denoiser correction (assuming the denoiser is perfect), and the second term is the variance arising from the injected noise. The assumption of perfect denoising is an idealization, but we show empirically (Fig. $\\mathbf { \\bar { \\rho } } _ { 1 ) } ^ { 1 ) }$ that the algorithm converges reliably, with error levels falling as predicted by Eq. $( 5 )$ or faster, across different settings of $\\beta$ and $h _ { 0 }$ . ",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "To ensure convergence, we require the effective noise variance on each time step to be reduced, despite the injection of additional noise. For this purpose, we introduce a parameter $\\beta \\in [ 0 , 1 ]$ to control the proportion of injected noise ( $\\beta = 1$ indicates no noise), and enforce the convergence by requiring that: ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/7e32b8610d1fff2d4b280e458c97292b9884bfacb5ef1b3c9d785076bcbb11d3.jpg",
+        "text": "$$\n\\sigma _ { t } ^ { 2 } = ( 1 - \\beta h _ { t } ) ^ { 2 } \\sigma _ { t - 1 } ^ { 2 } .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            423,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Combining this with Eq. $( 5 )$ yields an expression for $\\gamma _ { t }$ in terms of $h _ { t }$ : ",
+        "bbox": [
+            173,
+            726,
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/7e30824f0f99e2e90cd774ae762516f6c768ac9a02dab68a1b98a030efb3323e.jpg",
+        "text": "$$\n\\gamma _ { t } ^ { 2 } = \\left[ ( 1 - \\beta h _ { t } ) ^ { 2 } - ( 1 - h _ { t } ) ^ { 2 } \\right] \\sigma _ { t - 1 } ^ { 2 } = \\left[ ( 1 - \\beta h _ { t } ) ^ { 2 } - ( 1 - h _ { t } ) ^ { 2 } \\right] \\left. f ( y _ { t - 1 } ) \\right. ^ { 2 } / N ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            209,
+            761,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where the second equation assumes that the magnitude of the denoising residual provides a good estimate of the effective noise standard deviation, as was found in $\\pm 2 \\|$ . This allows the denoiser to adaptively control the gradient ascent step sizes, reducing them as the $y _ { t }$ approaches the manifold (see Fig. $\\dot { \\bigtriangledown } \\dot { \\bigtriangledown } \\dot { \\bigtriangledown }$ . This automatic adjustment results in efficient and reliable convergence, as demonstrated empirically in Fig. 1. Our initial implementation with a small constant fractional step size $h _ { t } = h _ { 0 }$ produced high quality results, but required many iterations. Intuitively, step sizes that are a fixed proportion of the distance to the manifold lead to exponential decay - a form of Zeno’s paradox. To accelerate convergence, we introduced a schedule for increasing the step size proportion, starting from $h _ { 0 } \\in [ 0 , 1 ]$ . The sampling process is summarized in Algorithm $\\bigstar \\bigstar$ and is provided as a block diagram in Fig. 6. ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/11572b019770ba01444407a637b37fc09068d37759e4287c64753e8f8a63e465.jpg",
+        "image_caption": [
+            "Figure 1: Convergence of sampling algorithm, quantified in terms of the effective noise standard deviation $\\begin{array} { r } { \\sigma = { \\frac { | | d _ { t } | | } { \\sqrt { N } } } } \\end{array}$ for three different values of $\\beta$ and two valus of $h _ { 0 }$ . Left. Convergence of single examples (solid curves) is well-behaved and efficient in all cases. Dashed curves indicate the convergence predicted from the formulation of the algorithm: $\\sigma _ { t } = ( 1 - \\beta h _ { t } ) \\sigma _ { t - 1 }$ . For $\\beta = 1$ (no injected noise), the empirical convergence closely approximates the prediction. For larger amounts of injected noise (smaller $\\beta$ ), convergence is slower, but faster than predicted. Right. Distribution of number of iterations before convergence to a criterion level of $\\sigma = 0 . 0 1$ for 50 images. Red symbols indicate average values for each $\\beta$ and $h _ { 0 }$ . "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 4
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+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+    {
+        "type": "table",
+        "img_path": "images/06b7fd2d35ec78cd26073a6b38cd15004b406ebdba7ba193ea28447365a598c2.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Algorithm 1: Coarse-to-fine stochastic ascent method for sampling from the implicit prior of adenoiser, using denoiser residual f(y)=x(y)- y.</td></tr><tr><td>parameters:σo,σL,ho,β initialization: t =1, draw yo~ N(0.5,σ²I)</td></tr><tr><td>while Ot-1 ≥σL do hot</td></tr><tr><td>ht=1+h(t-1）； dt=f(yt-1);</td></tr><tr><td>²=；</td></tr><tr><td>γ²=(1-βht）²-(1-ht）²)²; N</td></tr><tr><td>Draw zt ~ N(0, I); yt←yt-1+htdt+Yt2t;</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "2.2 Image synthesis examples ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            785,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "For the denoiser, we used BF-CNN $\\lVert \\rVert 2 \\rVert$ , a bias-free variant of DnCNN $\\mathbb { \\lVert 3 9 \\rVert }$ . We obtained similar results (not shown) using other CNN architectures described in $\\lVert \\overline { { 4 2 } } \\rVert$ , including Recurrent-CNN, Dense-Net, and truncated U-Net. We trained this network on three different datasets: $4 0 \\times 4 0$ patches cropped from Berkeley segmentation training set $\\pmb { \\Vert 5 \\bot }$ , in color and grayscale, and MNIST dataset $\\pmb { \\mathbb { E 2 } }$ (see Appendix $\\mathbf { A }$ for further details). We chose parameters $\\sigma _ { 0 } = 1 , \\sigma _ { L } = 0 . 0 1$ , and $h _ { 0 } = 0 . 0 1$ . Figure $2$ provides visualization of two example trajectories, and diversity of samples. Additional visual examples, obtained with different levels of $\\beta$ , are shown in Appendix D. ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/043a82f4daa5d07e966ff34402bc57e887839726f96a71a7659a71050786fcdb.jpg",
+        "image_caption": [
+            "Figure 2: Left. Visualization of sampling algorithm trajectories. Each row shows a sequence of images, $y _ { t } , t = 1 , 9 , 1 7 , 2 5 , . . . ,$ from the iterative sampling procedure, with different initializations, $y _ { 0 }$ , and no added noise $( \\beta = 1 )$ ), demonstrating the way that the algorithm amplifies and \"hallucinates\" structure found in the initial (noise) images. Right. Sampling diversity. Inpainting examples generated using two BF-CNN denoisers. First column: original images. Second column: partially measured images, with missing block . Right three columns: Restored examples. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "3 Solving deterministic linear inverse problems using the implicit prior ",
+        "text_level": 1,
+        "bbox": [
+            173,
+            291,
+            779,
+            309
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Many applications in signal processing can be expressed as deterministic linear inverse problems - deblurring, super-resolution, estimating missing pixels (e.g., inpainting), and compressive sensing are all examples. Given a set of linear measurements of an image, $\\mathbf { \\bar { \\Psi } } \\mathbf { x } ^ { c } = \\mathbf { \\Psi } \\mathbf { M } ^ { T } \\mathbf { \\Psi } \\mathbf { \\bar { x } }$ , where $M$ is a low-rank measurement matrix, one attempts to recover the original image. In Section 2, we developed a stochastic gradient-ascent algorithm for obtaining a high-probability sample from $p ( x )$ . Here, we generalize this algorithm to solve for a high-probability sample from the conditional density $p ( x \\vert M ^ { T } x = x ^ { c } )$ . Geometrically, constrained sampling corresponds to drawing points which sit at the intersection of the image manifold and the constrained hyperplane (see Fig. 11). Note that for these problems, the injection of noise $\\begin{array} { r } { \\beta < 1 \\ ' } \\end{array}$ ) is particularly important, because points on the intersection are not necessarily the closest points to the initial image. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "3.1 Constrained sampling algorithm ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Consider the distribution of a noisy image, $y$ , conditioned on the linear measurements, $x ^ { c } = M ^ { T } x$ . Without loss of generality, we assume the columns of the matrix M are orthogonal unit vectors $\\bigstar$ We project $y$ onto two complementary subspaces spanned by the measurement matrix and its orthogonal complement $\\bar { M }$ . We write the conditional density of the noisy image conditioned on the linear measurement as ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "img_path": "images/b610bccabe5b679739de211628d79e1a0b49e5bdca0d3c89ee31ac9620409116.jpg",
+        "text": "$$\np ( y | x ^ { c } ) = p ( y ^ { c } , y ^ { u } | x ^ { c } ) = p ( y ^ { u } | y ^ { c } , x ^ { c } ) p ( y ^ { c } | x ^ { c } ) = p ( y ^ { u } | x ^ { c } ) p ( y ^ { c } | x ^ { c } )\n$$",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "where $\\boldsymbol { y } ^ { c } = \\boldsymbol { M } ^ { T } \\boldsymbol { y }$ , $y ^ { u } = { \\bar { M } } ^ { T } y$ . The last equality is obtained by considering that $y ^ { c }$ is equal to $x ^ { c }$ plus independent Gaussian noise. So given $x ^ { c }$ , $y ^ { c }$ does not provide any additional information about $y ^ { u }$ . That is, $y ^ { u }$ is independent of $y ^ { c }$ when conditioned on $x ^ { c }$ . As with the algorithm of Section $2 ,$ we wish to obtain a local maximum of this function using stochastic coarse-to-fine gradient ascent. Applying the operator $\\sigma ^ { 2 } \\nabla \\log ( \\cdot )$ yields ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "img_path": "images/6cc30a0f363346023f09da7863154ab70627b4badad63d8153bcd816077226a9.jpg",
+        "text": "$$\n\\sigma ^ { 2 } \\nabla _ { y } \\log p ( y | x ^ { c } ) = \\sigma ^ { 2 } \\nabla _ { y } \\log p ( y ^ { u } | x ^ { c } ) + \\sigma ^ { 2 } \\nabla _ { y } \\log p ( y ^ { c } | x ^ { c } )\n$$",
+        "text_format": "latex",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The second term is the gradient of the log of the observation noise distribution that lies within the measurement subspace (column space of M). For Gaussian noise with variance $\\sigma ^ { 2 }$ , it reduces to $M ( y ^ { c } - x ^ { c } )$ . The first term is the gradient of log of the noisy image distribution in the subspace orthogonal to the measurement subspace, conditioned on the measurements. This can be computed by projecting the measurement subspace out of the full gradient given by the denoiser residual. Specifically, we project $f ( y )$ onto the orthogonal complement of $M$ using the matrix $I - M M ^ { T }$ . Combining these gives: ",
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+    {
+        "type": "equation",
+        "img_path": "images/c10a34bff4feb66ac333aef398be9df73d97a73b399363da069a1f2686dc0eb2.jpg",
+        "text": "$$\n\\begin{array} { c } { { \\sigma ^ { 2 } \\nabla _ { y } \\log p ( y ) = ( I - M M ^ { T } ) \\sigma ^ { 2 } \\nabla _ { y } \\log p ( y ) + M ( x ^ { c } - y ^ { c } ) } } \\\\ { { = ( I - M M ^ { T } ) f ( y ) + M ( x ^ { c } - M ^ { T } y ) . } } \\end{array}\n$$",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "Thus, we see that the gradient of the conditional density is partitioned into two orthogonal components, capturing the gradient of the (log) noisy density, and the deviation from the constraints, respectively. ",
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+    },
+    {
+        "type": "image",
+        "img_path": "images/2ec59d9377115c8f5c81bf6ad9110de40d068d19b01cb339b1cca01358abce04.jpg",
+        "image_caption": [
+            "Figure 3: Spatial super-resolution. First column shows cropped portion of original images from Set14 (face: $2 7 2 \\times 2 7 2$ and, Barbara: $7 2 0 \\times 5 7 6$ ). The algorithm can be applied to images of any resolution - we show cropped portions to facilitate visual inspection. Second column shows cropped portion with resolution reduced by averaging over $4 \\mathbf { x } 4$ blocks (dimensionality reduction to $6 . 2 5 \\%$ ). Next three columns show reconstruction results obtained using DIP $\\textcircled { 8 }$ , DeepRED $\\left[ \\left[ 2 0 \\right] \\right]$ , and our method. In all cases, our method produces an image that is sharper with less noticeable artifacts (e.g., note blocking/aliasing artifacts along diagonal contours of lower image). The last column shows an average over 10 samples obtained by our method. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "To draw a high-probability sample from $p ( x | x ^ { c } )$ , we use the same algorithm described in Section 2, substituting Eq. $\\overset { \\cdot } { ( 7 ) }$ for the deterministic update vector, $d _ { t }$ (see Algorithm 2 in Appendix). Note that without any measurements (i.e., $M = 0$ ) Algorithm $2$ reduces to Algorithm 1. ",
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+    {
+        "type": "text",
+        "text": "3.2 Linear inverse examples ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "We evaluate our method on three linear inverse problems (and provide two additional problems in Appendix $\\boxed { \\mathrm { E } }$ . The same algorithm and parameters are used on all problems - only the measurement matrix $M$ and measured values $M ^ { T } x$ are altered. In particular, as in section $\\boxed { 2 . 2 }$ we used BF-CNN $\\lVert \\rVert 2 \\rVert$ , and chose parameters $\\sigma _ { 0 } = 1 , \\sigma _ { L } = 0 . 0 1 , h _ { 0 } = 0 . 0 1 , \\beta = 0 . 0 1$ . For each example, we show original images $( x )$ , the direct least-squares reconstruction $( M M ^ { T } x )$ , and restored images. Subjective assessment of perceptual quality is particularly important in cases where the measurement matrix is of very low rank, and the distribution of solutions is diverse (the synthesis examples of the previous section correspond to the limiting case, with measurements of rank zero). We also provide numerical comparisons with other unsupervised methods, in terms of both PSNR and SSIM (an approximate measure of perceptual quality). Since our method is stochastic, we provide standard deviations of these performance values across 10 realizations. ",
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+    {
+        "type": "text",
+        "text": "Spatial super-resolution. Here, one aims to reconstruct a high resolution image from a low resolution (i.e. downsampled) image. Downsampling is typically performed after lowpass filtering, and the downsampling factor and filter kernel determine the measurement model, $M$ . Here, we use a $4 \\times 4$ constant filter, and $4 \\times 4$ downsampling (i.e., measurements are averages over non-overlapping blocks). We compare to two recent unsupervised methods Deep image Prior (DIP) $\\pmb { \\Vert 8 \\Vert }$ and DeepRED [20] DIP chooses a random input vector, and adjusts the weights of a CNN to minimize the mean square error between the output and the corrupted image. Regularization by denoising (RED) is a recent successful method closely related to P&P $\\pmb { \\mathbb { D } } \\bar { \\sf S } \\bar { \\sf I }$ . DeepRED $\\left[ \\left[ 2 0 \\right] \\right]$ combines DIP and RED, obtaining better performance than either method alone. ",
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+    },
+    {
+        "type": "text",
+        "text": "Inspection of results on two example images demonstrates that our method produces results that are sharper with less noticeable artifacts (Fig. 3). Despite this, the PSNR and SSIM values are slightly worse than both DIP and DeepRED (Table 1). These can be improved by averaging over realizations (last column of Table 1), producing superior PSNR and SSIM values at the expense of some blurring (last column of Fig. 3). This is expected: the algorithm produces high-probability samples of the prior subject to the measurement constraint, but the least-squares optimal solution is the mean of the posterior distribution. If the samples are drawn from a curved manifold, their average (a convex combination of those points) will lie off the manifold. Finally, note that our method is more than two orders of magnitude faster than either DIP or DeepRED (bottom row, Table 1) ",
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+    {
+        "type": "table",
+        "img_path": "images/85ea7a7d6c1b80a2cbdea5416e3a135bfe1a6b4b8f28971b887e42f13f4198d9.jpg",
+        "table_caption": [
+            "Table 1: Spatial super-resolution performance over Set5 (top 2 rows) and Set14 (second 2 rows). Values indicate YCbCr-PSNR (SSIM). Last row shows average Set14 runtime on a DGX GPU. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>MMTx</td><td>DIP </td><td>DeepRED[ [20]</td><td>Ours±std</td><td>Ours:avg</td></tr><tr><td>4:1</td><td>26.35 (0.826)</td><td>30.04 (0.902)</td><td>30.22 (0.904)</td><td>29.47±0.09 (0.894±0.001)</td><td>31.20 (0.913)</td></tr><tr><td>8:1</td><td>23.02 (0.673)</td><td>24.98 (0.760)</td><td>24.95 (0.760)</td><td>25.07±0.13 (0.767±0.003)</td><td>25.64 (0.792)</td></tr><tr><td>4:1</td><td>24.65 (0.765)</td><td>26.88 (0.815)</td><td>27.01 (0.817)</td><td>26.56±0.09 (0.808±0.001)</td><td>27.14 (0.826)</td></tr><tr><td>8:1</td><td>22.06 (0.628)</td><td>23.33 (0.685)</td><td>23.34 (0.685)</td><td>23.32±0.11 (0.681±0.002)</td><td>23.78 (0.703)</td></tr><tr><td colspan=\"2\">runtime (sec):</td><td>1,190</td><td>1,584</td><td>9</td><td>10×9</td></tr></table>",
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+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/43d9657aff1589508287aa0f3a9445d6f1d0793a97bb2a37db727c14f428c2fb.jpg",
+        "image_caption": [
+            "Figure 4: Deblurring (spectral super-resolution). Measurements correspond to $5 \\%$ of low frequencies. Original images are from Set5 (butterfly of size $2 5 6 \\times 2 5 6$ and woman of size $2 2 4 \\times 3 3 6$ ). "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Deblurring (spectral super-resolution). The applications described above (and in Appendix $\\boxed { \\mathrm { E } }$ are based on partial measurements in the pixel domain. Here, we consider a blurring operator that retains a set of low-frequency coefficient in the Fourier domain, discarding the rest. This is equivalent to convolving the image with a sinc kernel. In this case, $M$ consists of the preserved low-frequency columns of the discrete Fourier transform, and $M M ^ { T } x$ is the blurred version of $x$ . Example images are shown in Fig. $\\nsupseteq$ and numerical comparisons are shown in Table $\\bigtriangledown$ Our method produces strong results, both perceptually and numerically. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Compressive sensing. Compressive sensing $\\mathbb { B 6 } \\mathbb { B 7 }$ aims to recover signals from a small number of (typically, random) linear measurements. In brief, one acquires measurements with a sensing matrix containing a set of $n < < N$ random orthogonal axes, and solves the inverse problem by assuming a sparse prior. Photographic images are not truly sparse in any fixed linear basis, but they can be reasonably approximated by low-dimensional subsets of Fourier or wavelet basis functions, and compressive sensing results are typically demonstrated using one of these. The manifold prior embedded within our CNN denoiser corresponds to a nonlinear form of sparsity, and our stochastic coarse-to-fine ascent algorithm can be used to recover an image from the measured linear projections onto the random basis. We compare to four other methods. TVAL3 $\\mathbb { \\left. \\boldsymbol { \\bar { 5 3 } } \\right. }$ is an optimization algorithm using total variation regularization, ISTA-Net $\\textcircled { | 5 4 | }$ is a block-based supervised CNN method trained to reconstruct images from measurements obtained from a single pre-specified measurement matrix. BNN $\\mathbb { \\lVert } \\mathbb { 5 } \\mathbb { 5 } \\mathbb { I }$ is an unsupervised Bayesian method for solving compressive sensing problems. DIP $\\pmb { \\mathbb { B } } \\|$ was previously described. Fig. $\\dot { 5 }$ shows results for two example images, and Table $3$ summarizes numerical performance. All values are taken from $\\lVert 5 5 \\rVert$ except for ISTA-Net which were obtained by running the open-source code. Our method generally outperforms all other methods, even those that are specialized for Compressive Sensing (ISTA-NET, BNN). ",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/f328d21f6146c01244b6b0911b10e58983baff5a60e97fbc8fa959acbb54fbc9.jpg",
+        "table_caption": [
+            "Table 2: Spectral super-resolution (deblurring) performance over Set5, in YCbCr-PSNR (SSIM). "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Ratio</td><td>MMTx</td><td>DIP 图</td><td>DeepRED 四</td><td>Ours±std</td><td>Ours:avg</td></tr><tr><td>10%</td><td>30.2 (0.91)</td><td>32.54 (0.93)</td><td>32.63 (0.93)</td><td>31.82±0.08 (0.93±0.001)</td><td>32.78 (0.94)</td></tr><tr><td>5%</td><td>27.77 (0.85)</td><td>29.88 (0.89)</td><td>29.91 (0.89)</td><td>29.22±0.14(0.89±0.002)</td><td>30.07 (0.90)</td></tr></table>",
+        "bbox": [
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+            854,
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+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/db2173fafffd7ca5a3da5fc32ee722f6e96463d2d2f8fc0a46a92754194b9c47.jpg",
+        "table_caption": [
+            "Table 3: Compressive sensing performance over Set68 [51]. Values indicate PSNR (SSIM). "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Ratio</td><td>TVAL3 </td><td>ISTA-Net[ 54</td><td>DIP 图</td><td>BNN 55</td><td>Ours±std</td><td>Ours:avg</td></tr><tr><td>25%</td><td>26.48 (0.77)</td><td>29.07 (0.84)</td><td>27.78 (0.80)</td><td>28.63 (0.84)</td><td>29.16±0.033 (0.88±0.001)</td><td>29.74(0.89)</td></tr><tr><td>10%</td><td>22.49 (0.58)</td><td>25.23 (0.69)</td><td>24.82 (0.69)</td><td>25.24 (0.71)</td><td>25.47±0.03 (0.78±0.001)</td><td>25.84 (0.80)</td></tr><tr><td>4%</td><td>19.10 (0.42)</td><td>22.02 (0.54)</td><td>22.51 (0.58)</td><td>22.52 (0.58)</td><td>22.07±0.05 (0.68±0.002)</td><td>22.29 (0.69)</td></tr></table>",
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+        "page_idx": 8
+    },
+    {
+        "type": "image",
+        "img_path": "images/3129f1ba9229c172ff0f854859868b7251f861df15e24d94382ee83e181527b9.jpg",
+        "image_caption": [
+            "Figure 5: Compressive sensing. Measurement matrix $M$ contains random orthogonal unit vectors, whose number is equal to $1 0 \\%$ of the number of image pixels $( 3 0 0 \\times 3 0 0 )$ . Third column: images recovered using ISTA-Net (trained with supervision for a particular measurement matrix). Fourth column: Our method, which again is seen to exhibit fewer artifacts. "
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "4 Related work ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Our method is conceptually similar to P&P[14] in that it uses a denoiser to solve linear inverse problems. But it differs in a number of important ways: (1) direct relationship between prior and denoiser mapping. The rationale for using a denoiser as a regularizer in P&P frameworks arises from interpreting the proximal operator of the regularizer as a MAP solution of a denoising problem, providing an indirect connection to prior; We derive our method from Miyasawa’s relationship between an MMSE denoiser and the prior, which is exact and explicit, and makes the algorithm interpretable. This connection has also been made in $\\pm \\pm \\pm \\pm \\pm \\pm$ . (2) sampling vs. MAP estimation. We obtain a high probability image from the implicit prior that is consistent with a linear constraint. Our solution is stochastic, and does not minimize MSE, but has high perceptual quality. RED and other P&P methods are derived as MAP solutions, and although this is not equivalent to minimizing MSE (maximizing PSNR), the results generally have better PSNR than our sampling results, but are visually more blurred (see Figs. $3$ and $\\textcircled{4}$ ; (3) automatic step-size selection and convergence. P&P, which uses ADMM for optimization, relies on hyper-parameter selection that are critical for convergence (as discussed extensively in $\\mathbb { L } \\Sigma \\mathbb { I } .$ ). Our algorithm adjusts step-size automatically using the blind denoiser, with only two primary hyper-parameters ( $h _ { 0 }$ and $\\beta$ ), and convergence is robust to choices of these (Fig. 1). ",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Our method is also closely related to recent work that uses Score Matching $\\mathbb { m }$ to draw samples from an implicit prior. This line of work is rooted in the connection between Denoising Autoencoders and Score Matching, first described in $\\pmb { \\mathbb { B 2 } }$ . Denoising autoencoders learn the gradient of log density, and their connection to an underlying data manifold has been explored in $\\boxed { 2 5 } \\boxed { 4 3 } \\boxed { 3 1 }$ . More recently, Refs. [44, $\\textcircled { 2 6 }$ trained a neural network to directly estimate energy (the negative log prior) and interpreted its gradient as the Score of the data. Finally, in a breakthrough paper that partially inspired our approach, Song and Ermon $\\pmb { \\mathbb { Z } } 9 \\|$ trained a sequence of denoisers with decreasing levels of noise and used Langevin dynamics to sample from the underlying probability distributions in succession. Our work differs from these in several important ways: (1) Direct derivation. Our method is based on Miyasawa’s explicit relationship between the denoiser mapping and implicit density $\\pmb { \\mathbb { Q } } \\mathbf { \\| }$ , which can be proven with a few lines of math (Section $1 . 3 )$ . The relationship of this result to Score Matching [11, 12], and the relationship between Score Matching and Denoising Autoencoders $\\pmb { \\Vert 3 2 \\Vert }$ are both significantly more nuanced and complex. (2) Automatic stepsize adjustment and efficiency. The algorithm presented in $\\mathbb { \\left| \\left[ 2 9 \\right] \\right| }$ uses a discrete sequence of denoisers, each trained for a single noise level, and embedding a distribution of noisy images with that specific noise level. Langevin dynamics are used to sample from each of these distributions in succession. Langevin sampling guarantees (asymptotically) convergence to each successive distribution, although these intermediate samples are used only for initialization of the subsequent stage. In addition to the Langevin sampling itself, the method requires choices of the schedule of noise levels (standard deviations, and number of iterations used at each level). ",
+        "bbox": [
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+        "page_idx": 8
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+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "In contrast, our formulation relies on a single universal blind denoiser which implicitly embeds an infinite family of distributions of noisy images (corresponding to a continuous range of noise levels). The gradient provided by the denoiser is not used for sampling, but for coarse-to-fine ascent of the noisy distribution, removing a fraction of the noise at each step. The universal denoiser adapts to this updated implicit noisy density, both in terms of gradient direction and magnitude. We use the denoiser magnitude as an estimate of the implicit noise level $\\bigtriangledown ,$ and this is used to control the amplitude of injected noise. Note that this differs markedly from the control of noise injection in the Langevin method, which is of constant magnitude in each stage. Under assumptions about the denoiser (which hold empirically), our method converges rapidly to a mode of the prior and is robust to parameter choices $\\mathbb { L }$ The continuous maximization of probability results in substantial gains in efficiency. For comparison, Song&Ermon $\\pmb { \\mathbb { Z } } 9 \\|$ report 1000 iteration to synthesize a $3 2 \\times 3 2$ image, whereas we synthesize $4 0 \\times 4 0$ images in roughly 35 iteration (for $\\beta = 1$ ). (3) Image synthesis vs. linear inverse problems. Finally, we’ve focused the use of our method as a universal solver for linear inverse problems, whereas Score Matching methods have generally been focused on unconditional image synthesis. ",
+        "bbox": [
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+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "5 Discussion ",
+        "text_level": 1,
+        "bbox": [
+            174,
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+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "We’ve described a framework for using the prior embedded in a denoiser to solve inverse problems. Specifically, we developed a stochastic coarse-to-fine gradient ascent algorithm that uses the denoiser to draw high-probability samples from its implicit prior, and a constrained variant that can be used to solve any deterministic linear inverse problem. To demonstrate the generality of our algorithm, we showed solving five inverse problems using the same algorithm and parameters, without any additional training. The derivation is based on a simple and direct expression relating denoising to priors, and a few basic empirical facts about universal CNN denoisers. Finally, we empirically demonstrated its efficiency in Fig. 1 and Table 1. It is worth noting that the assumed use of Gaussian additive noise and MSE objective in training the denoiser is necessary only to justify the use of Miyasawa’s expression (Eq. 3), but does not impose any such restrictions on use of the trained denoiser for sampling from the implicit prior or solving inverse problems. Denoisers can be trained supervised on unlimited amounts of unlabeled data, and as such, our method extends the power of supervised learning to a much broader set of problems, with no additional training. ",
+        "bbox": [
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+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "As discussed following Eq. $\\textcircled{5}$ , the control of step sizes and noise injection in our algorithm is chosen by assuming that the denoiser residual exactly cancels the noise. We showed empirically (Fig. 1) that this idealization does not disrupt convergence for BF-CNN, but we cannot guarantee this would hold for all other denoisers. More generally, although the method can be used with any universal least-squares denoiser designed or trained to remove Gaussian noise, the complexity of the embedded prior, and thus the quality of our linear inverse results, relies heavily on the expressive power of the denoiser (BF-CNN in our case), as well as the diversity of the training set. Finally, the current algorithm is designed to solve deterministic linear inverse problems. We are currently exploring extensions to inverse problems based on stochastic or nonlinear measurements. ",
+        "bbox": [
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+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Acknowledgments and Disclosure of Funding ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            824,
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+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "We gratefully acknowledge financial support from the Simons Foundation, the Howard Hughes Medical Institute, and NSF NRT HDR Award 1922658 to the Center for Data Science at NYU. High performance computing resources were provided by the NYU HPC center and the Flatiron Institute of the Simons Foundation. ",
+        "bbox": [
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+        "page_idx": 9
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+    {
+        "type": "text",
+        "text": "References   \n[1] D Donoho. Denoising by soft-thresholding. IEEE Trans Info Theory, 43:613–627, 1995.   \n[2] E P Simoncelli and E H Adelson. Noise removal via Bayesian wavelet coring. In Proc 3rd IEEE Int’l. Conf. on Image Processing (ICIP), pages 379–382, 1996.   \n[3] P Moulin and J Liu. Analysis of multiresolution image denoising schemes using a generalized Gaussian and complexity priors. IEEE Trans Info Theory, 45:909–919, 1999.   \n[4] Hyvärinen. Sparse code shrinkage: Denoising of nonGaussian data by maximum likelihood estimation. Neural Computation, 11(7):1739–1768, 1999.   \n[5] J. Romberg, H. Choi, and R. Baraniuk. Bayesian tree-structured image modeling using waveletdomain hidden Markov models. IEEE Trans Image Proc, 10(7), July 2001.   \n[6] L ¸Sendur and I W Selesnick. Bivariate shrinkage functions for wavelet-based denoising exploiting interscale dependency. 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