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+# SNIP: SINGLE-SHOT NETWORK PRUNING BASED ONCONNECTION SENSITIVITY
+
+Namhoon Lee, Thalaiyasingam Ajanthan & Philip H. S. Torr University of Oxford {namhoon,ajanthan,phst}@robots.ox.ac.uk
+
+# ABSTRACT
+
+Pruning large neural networks while maintaining their performance is often desirable due to the reduced space and time complexity. In existing methods, pruning is done within an iterative optimization procedure with either heuristically designed pruning schedules or additional hyperparameters, undermining their utility. In this work, we present a new approach that prunes a given network once at initialization prior to training. To achieve this, we introduce a saliency criterion based on connection sensitivity that identifies structurally important connections in the network for the given task. This eliminates the need for both pretraining and the complex pruning schedule while making it robust to architecture variations. After pruning, the sparse network is trained in the standard way. Our method obtains extremely sparse networks with virtually the same accuracy as the reference network on the MNIST, CIFAR-10, and Tiny-ImageNet classification tasks and is broadly applicable to various architectures including convolutional, residual and recurrent networks. Unlike existing methods, our approach enables us to demonstrate that the retained connections are indeed relevant to the given task.
+
+# 1 INTRODUCTION
+
+Despite the success of deep neural networks in machine learning, they are often found to be highly overparametrized making them computationally expensive with excessive memory requirements. Pruning such large networks with minimal loss in performance is appealing for real-time applications, especially on resource-limited devices. In addition, compressed neural networks utilize the model capacity efficiently, and this interpretation can be used to derive better generalization bounds for neural networks (Arora et al. (2018)).
+
+In network pruning, given a large reference neural network, the goal is to learn a much smaller subnetwork that mimics the performance of the reference network. The majority of existing methods in the literature attempt to find a subset of weights from the pretrained reference network either based on a saliency criterion (Mozer & Smolensky (1989); LeCun et al. (1990); Han et al. (2015)) or utilizing sparsity enforcing penalties (Chauvin (1989); Carreira-Perpin˜an & Idelbayev (2018)). ´ Unfortunately, since pruning is included as a part of an iterative optimization procedure, all these methods require many expensive prune – retrain cycles and heuristic design choices with additional hyperparameters, making them non-trivial to extend to new architectures and tasks.
+
+In this work, we introduce a saliency criterion that identifies connections in the network that are important to the given task in a data-dependent way before training. Specifically, we discover important connections based on their influence on the loss function at a variance scaling initialization, which we call connection sensitivity. Given the desired sparsity level, redundant connections are pruned once prior to training (i.e., single-shot), and then the sparse pruned network is trained in the standard way. Our approach has several attractive properties:
+
+• Simplicity. Since the network is pruned once prior to training, there is no need for pretraining and complex pruning schedules. Our method has no additional hyperparameters and once pruned, training of the sparse network is performed in the standard way.   
+• Versatility. Since our saliency criterion chooses structurally important connections, it is robust to architecture variations. Therefore our method can be applied to various architectures including convolutional, residual and recurrent networks with no modifications.
+
+• Interpretability. Our method determines important connections with a mini-batch of data at single-shot. By varying this mini-batch used for pruning, our method enables us to verify that the retained connections are indeed essential for the given task.
+
+We evaluate our method on MNIST, CIFAR-10, and Tiny-ImageNet classification datasets with widely varying architectures. Despite being the simplest, our method obtains extremely sparse networks with virtually the same accuracy as the existing baselines across all tested architectures. Furthermore, we investigate the relevance of the retained connections as well as the effect of the network initialization and the dataset on the saliency score.
+
+# 2 RELATED WORK
+
+Classical methods. Essentially, early works in network pruning can be categorized into two groups (Reed (1993)): 1) those that utilize sparsity enforcing penalties; and 2) methods that prune the network based on some saliency criterion. The methods from the former category (Chauvin (1989); Weigend et al. (1991); Ishikawa (1996)) augment the loss function with some sparsity enforcing penalty terms (e.g., $L _ { 0 }$ or $L _ { 1 }$ norm), so that back-propagation effectively penalizes the magnitude of the weights during training. Then weights below a certain threshold may be removed. On the other hand, classical saliency criteria include the sensitivity of the loss with respect to the neurons (Mozer & Smolensky (1989)) or the weights (Karnin (1990)) and Hessian of the loss with respect to the weights (LeCun et al. (1990); Hassibi et al. (1993)). Since these criteria are heavily dependent on the scale of the weights and are designed to be incorporated within the learning process, these methods are prohibitively slow requiring many iterations of pruning and learning steps. Our approach identifies redundant weights from an architectural point of view and prunes them once at the beginning before training.
+
+Modern advances. In recent years, the increased space and time complexities as well as the risk of overfitting in deep neural networks prompted a surge of further investigation in network pruning. While Hessian based approaches employ the diagonal approximation due to its computational simplicity, impressive results (i.e., extreme sparsity without loss in accuracy) are achieved using magnitude of the weights as the criterion (Han et al. (2015)). This made them the de facto standard method for network pruning and led to various implementations (Guo et al. (2016); Carreira-Perpin˜an & ´ Idelbayev (2018)). The magnitude criterion is also extended to recurrent neural networks (Narang et al. (2017)), yet with heavily tuned hyperparameter setting. Unlike our approach, the main drawbacks of magnitude based approaches are the reliance on pretraining and the expensive prune – retrain cycles. Furthermore, since pruning and learning steps are intertwined, they often require highly heuristic design choices which make them non-trivial to be extended to new architectures and different tasks. Meanwhile, Bayesian methods are also applied to network pruning (Ullrich et al. (2017); Molchanov et al. (2017a)) where the former extends the soft weight sharing in Nowlan & Hinton (1992) to obtain a sparse and compressed network, and the latter uses variational inference to learn the dropout rate which can then be used to prune the network. Unlike the above methods, our approach is simple and easily adaptable to any given architecture or task without modifying the pruning procedure.
+
+Network compression in general. Apart from weight pruning, there are approaches focused on structured simplification such as pruning filters (Li et al. (2017); Molchanov et al. (2017b)), structured sparsity with regularizers (Wen et al. (2016)), low-rank approximation (Jaderberg et al. (2014)), matrix and tensor factorization (Novikov et al. (2015)), and sparsification using expander graphs (Prabhu et al. (2018)) or Erdos-R ˝ enyi random graph (Mocanu et al. (2018)). In addition, ´ there is a large body of work on compressing the representation of weights. A non-exhaustive list includes quantization (Gong et al. (2014)), reduced precision (Gupta et al. (2015)) and binary weights (Hubara et al. (2016)). In this work, we focus on weight pruning that is free from structural constraints and amenable to further compression schemes.
+
+# 3 NEURAL NETWORK PRUNING
+
+The main hypothesis behind the neural network pruning literature is that neural networks are usually overparametrized, and comparable performance can be obtained by a much smaller network (Reed (1993)) while improving generalization (Arora et al. (2018)). To this end, the objective is to learn
+
+a sparse network while maintaining the accuracy of the standard reference network. Let us first formulate neural network pruning as an optimization problem.
+
+Given a dataset $\mathbfcal { D } = \{ ( \mathbf { x } _ { i } , \mathbf { y } _ { i } ) \} _ { i = 1 } ^ { n }$ , and a desired sparsity level $\kappa$ (i.e., the number of non-zero weights) neural network pruning can be written as the following constrained optimization problem:
+
+$$
+\begin{array} { l } { \displaystyle \operatorname* { m i n } _ { \mathbf { w } } L ( \mathbf { w } ; \mathcal { D } ) = \displaystyle \operatorname* { m i n } _ { \mathbf { w } } \frac { 1 } { n } \sum _ { i = 1 } ^ { n } \ell ( \mathbf { w } ; ( \mathbf { x } _ { i } , \mathbf { y } _ { i } ) ) ~ , } \\ { \mathrm { s . t . } \quad \mathbf { w } \in \mathbb { R } ^ { m } , \quad \| \mathbf { w } \| _ { 0 } \leq \kappa ~ . } \end{array}
+$$
+
+Here, $\ell ( \cdot )$ is the standard loss function (e.g., cross-entropy loss), w is the set of parameters of the neural network, $m$ is the total number of parameters and $\| \cdot \| _ { 0 }$ is the standard $L _ { 0 }$ norm.
+
+The conventional approach to optimize the above problem is by adding sparsity enforcing penalty terms (Chauvin (1989); Weigend et al. (1991); Ishikawa (1996)). Recently, Carreira-Perpin˜an´ $\&$ Idelbayev (2018) attempts to minimize the above constrained optimization problem using the stochastic version of projected gradient descent (where the projection is accomplished by pruning). However, these methods often turn out to be inferior to saliency based methods in terms of resulting sparsity and require heavily tuned hyperparameter settings to obtain comparable results.
+
+On the other hand, saliency based methods treat the above problem as selectively removing redundant parameters (or connections) in the neural network. In order to do so, one has to come up with a good criterion to identify such redundant connections. Popular criteria include magnitude of the weights, i.e., weights below a certain threshold are redundant (Han et al. (2015); Guo et al. (2016)) and Hessian of the loss with respect to the weights, i.e., the higher the value of Hessian, the higher the importance of the parameters (LeCun et al. (1990); Hassibi et al. (1993)), defined as follows:
+
+$$
+s _ { j } = \left\{ \begin{array} { l l } { \left| w _ { j } \right| , } & { \mathrm { f o r m a g n i t u d e ~ b a s e d } } \\ { \frac { w _ { j } ^ { 2 } H _ { j j } } { 2 } } & { \mathrm { o r } \frac { w _ { j } ^ { 2 } } { 2 H _ { j j } ^ { - 1 } } } & { \mathrm { f o r } \mathrm { H e s s i a n ~ b a s e d } . } \end{array} \right.
+$$
+
+Here, for connection $j , s _ { j }$ is the saliency score, $w _ { j }$ is the weight, and $H _ { j j }$ is the value of the Hessian matrix, where the Hessian $\mathbf { H } = \partial ^ { 2 } L / \partial \mathbf { w } ^ { 2 } \in \mathbb { R } ^ { m \times m }$ . Considering Hessian based methods, the Hessian matrix is neither diagonal nor positive definite in general, approximate at best, and intractable to compute for large networks.
+
+Despite being popular, both of these criteria depend on the scale of the weights and in turn require pretraining and are very sensitive to the architectural choices. For instance, different normalization layers affect the scale of the weights in a different way, and this would non-trivially affect the saliency score. Furthermore, pruning and the optimization steps are alternated many times throughout training, resulting in highly expensive prune – retrain cycles. Such an exorbitant requirement hinders the use of pruning methods in large-scale applications and raises questions about the credibility of the existing pruning criteria.
+
+In this work, we design a criterion which directly measures the connection importance in a datadependent manner. This alleviates the dependency on the weights and enables us to prune the network once at the beginning, and then the training can be performed on the sparse pruned network. Therefore, our method eliminates the need for the expensive prune – retrain cycles, and in theory, it can be an order of magnitude faster than the standard neural network training as it can be implemented using software libraries that support sparse matrix computations.
+
+# 4 SINGLE-SHOT NETWORK PRUNING BASED ON CONNECTION SENSITIVITY
+
+Given a neural network and a dataset, our goal is to design a method that can selectively prune redundant connections for the given task in a data-dependent way even before training. To this end, we first introduce a criterion to identify important connections and then discuss its benefits.
+
+# 4.1 CONNECTION SENSITIVITY: ARCHITECTURAL PERSPECTIVE
+
+Since we intend to measure the importance (or sensitivity) of each connection independently of its weight, we introduce auxiliary indicator variables $\mathbf { c } \in \{ 0 , 1 \} ^ { m }$ representing the connectivity of
+
+parameters w.1 Now, given the sparsity level $\kappa$ , Equation 1 can be correspondingly modified as:
+
+$$
+\begin{array} { r l } { \displaystyle \operatorname* { m i n } _ { \mathbf { c } , \mathbf { w } } L ( \mathbf { c } \odot \mathbf { w } ; \mathcal { D } ) = \displaystyle \operatorname* { m i n } _ { \mathbf { c } , \mathbf { w } } \frac { 1 } { n } \sum _ { i = 1 } ^ { n } \ell ( \mathbf { c } \odot \mathbf { w } ; ( \mathbf { x } _ { i } , \mathbf { y } _ { i } ) ) ~ , } & { } \\ { \mathrm { s . t . } \quad \mathbf { w } \in \mathbb { R } ^ { m } ~ , } & { } \\ { \displaystyle \quad \mathbf { c } \in \{ 0 , 1 \} ^ { m } , \quad \| \mathbf { c } \| _ { 0 } \leq \kappa ~ , } \end{array}
+$$
+
+where $\odot$ denotes the Hadamard product. Compared to Equation 1, we have doubled the number of learnable parameters in the network and directly optimizing the above problem is even more difficult. However, the idea here is that since we have separated the weight of the connection (w) from whether the connection is present or not (c), we may be able to determine the importance of each connection by measuring its effect on the loss function.
+
+For instance, the value of $c _ { j }$ indicates whether the connection $j$ is active $( c _ { j } = 1 )$ ) in the network or pruned $( c _ { j } = 0 )$ . Therefore, to measure the effect of connection $j$ on the loss, one can try to measure the difference in loss when $c _ { j } = 1$ and $c _ { j } = 0$ , keeping everything else constant. Precisely, the effect of removing connection $j$ can be measured by,
+
+$$
+\begin{array} { r } { \Delta L _ { j } ( \mathbf { w } ; \mathcal { D } ) = L \big ( \mathbf { 1 } \odot \mathbf { w } ; \mathcal { D } \big ) - L \big ( \big ( \mathbf { 1 } - \mathbf { e } _ { j } \big ) \odot \mathbf { w } ; \mathcal { D } \big ) , } \end{array}
+$$
+
+where $\mathbf { e } _ { j }$ is the indicator vector of element $j$ (i.e., zeros everywhere except at the index $j$ where it is one) and 1 is the vector of dimension $m$ .
+
+Note that computing $\Delta L _ { j }$ for each $j \in \{ 1 \ldots m \}$ is prohibitively expensive as it requires $m + 1$ (usually in the order of millions) forward passes over the dataset. In fact, since $\mathbf { c }$ is binary, $L$ is not differentiable with respect to $\mathbf { c }$ , and it is easy to see that $\Delta L _ { j }$ attempts to measure the influence of connection $j$ on the loss function in this discrete setting. Therefore, by relaxing the binary constraint on the indicator variables c, $\Delta L _ { j }$ can be approximated by the derivative of $L$ with respect to $c _ { j }$ , which we denote $g _ { j } ( \mathbf { w } ; \mathcal { D } )$ . Hence, the effect of connection $j$ on the loss can be written as:
+
+$$
+\Delta L _ { j } ( \mathbf { w } ; \mathcal { D } ) \approx g _ { j } ( \mathbf { w } ; \mathcal { D } ) = \left. \frac { \partial L ( \mathbf { c } \odot \mathbf { w } ; \mathcal { D } ) } { \partial c _ { j } } \right| _ { \mathbf { c } = \mathbf { 1 } } = \operatorname* { l i m } _ { \delta \to 0 } \left. \frac { L ( \mathbf { c } \odot \mathbf { w } ; \mathcal { D } ) - L ( ( \mathbf { c } - \delta \mathbf { e } _ { j } ) \odot \mathbf { w } ; \mathcal { D } ) } { \delta } \right| _ { \mathbf { c } = \mathbf { 1 } } .
+$$
+
+In fact, $\partial L / \partial c _ { j }$ is an infinitesimal version of $\Delta L _ { j }$ , that measures the rate of change of $L$ with respect to an infinitesimal change in $c _ { j }$ from $1  1 - \delta$ . This can be computed efficiently in one forward-backward pass using automatic differentiation, for all $j$ at once. Notice, this formulation can be viewed as perturbing the weight $w _ { j }$ by a multiplicative factor $\delta$ and measuring the change in loss. This approximation is similar in spirit to Koh & Liang (2017) where they try to measure the influence of a datapoint to the loss function. Here we measure the influence of connections. Furthermore, $\partial L / \partial c _ { j }$ is not to be confused with the gradient with respect to the weights $( \partial L / \partial w _ { j } )$ , where the change in loss is measured with respect to an additive change in weight $w _ { j }$ .
+
+Notably, our interest is to discover important (or sensitive) connections in the architecture, so that we can prune unimportant ones in single-shot, disentangling the pruning process from the iterative optimization cycles. To this end, we take the magnitude of the derivatives $g _ { j }$ as the saliency criterion. Note that if the magnitude of the derivative is high (regardless of the sign), it essentially means that the connection $c _ { j }$ has a considerable effect on the loss (either positive or negative), and it has to be preserved to allow learning on $w _ { j }$ . Based on this hypothesis, we define connection sensitivity as the normalized magnitude of the derivatives:
+
+$$
+s _ { j } = \frac { | g _ { j } ( \mathbf { w } ; \mathcal { D } ) | } { \sum _ { k = 1 } ^ { m } | g _ { k } ( \mathbf { w } ; \mathcal { D } ) | } .
+$$
+
+Once the sensitivity is computed, only the top- $\kappa$ connections are retained, where $\kappa$ denotes the desired number of non-zero weights. Precisely, the indicator variables $\mathbf { c }$ are set as follows:
+
+$$
+c _ { j } = \mathbb { 1 } [ s _ { j } - \tilde { s } _ { \kappa } \geq 0 ] , \quad \forall j \in \{ 1 \ldots m \} ,
+$$
+
+where $\tilde { s } _ { \kappa }$ is the $\kappa$ -th largest element in the vector s and $\mathbb { 1 } [ \cdot ]$ is the indicator function. Here, for exactly $\kappa$ connections to be retained, ties can be broken arbitrarily.
+
+We would like to clarify that the above criterion (Equation 6) is different from the criteria used in early works by Mozer & Smolensky (1989) or Karnin (1990) which do not entirely capture the connection sensitivity. The fundamental idea behind them is to identify elements (e.g. weights or neurons) that least degrade the performance when removed. This means that their saliency criteria (i.e. $- \partial L / \partial \mathbf { w }$ or $- \partial L / \partial \pmb { \alpha }$ ; $_ { \pmb { \alpha } }$ refers to the connectivity of neurons), in fact, depend on the loss value before pruning, which in turn, require the network to be pre-trained and iterative optimization cycles to ensure minimal loss in performance. They also suffer from the same drawbacks as the magnitude and Hessian based methods as discussed in Section 3. In contrast, our saliency criterion (Equation 6) is designed to measure the sensitivity as to how much influence elements have on the loss function regardless of whether it is positive or negative. This criterion alleviates the dependency on the value of the loss, eliminating the need for pre-training. These fundamental differences enable the network to be pruned at single-shot prior to training, which we discuss further in the next section.
+
+<table><tr><td colspan="3">Algorithm1 SNIP: Single-shot Network Pruning based on Connection Sensitivity</td></tr><tr><td>Ensure: | w*|lo ≤ κ</td><td>Require: Loss function L, training dataset D, sparsity level K</td><td>Refer Equation 3</td></tr><tr><td></td><td>1:w_← VarianceScalingInitialization</td><td>Refer Section 4.2</td></tr><tr><td></td><td>2:Db={（xi,yi）}=1 ~D</td><td>&gt; Sample a mini-batch of training data</td></tr><tr><td>3:Sj←</td><td>l9j(w;Db) ∑=1l9k(（w;Db)l ， ∀j∈{1...m}</td><td>Connection sensitivity</td></tr><tr><td></td><td>4:s ← SortDescending(s)</td><td></td></tr><tr><td></td><td>5:cj←1[sj-$κ≥0]，∀j∈{1...m}</td><td>&gt;Pruning: choose top-k connections</td></tr><tr><td>7: w* ← c⊙w*</td><td>6: W* ← arg minw∈Rm L(c ③ w;D)</td><td>Regular training</td></tr></table>
+
+# 4.2 SINGLE-SHOT PRUNING AT INITIALIZATION
+
+Note that the saliency measure defined in Equation 6 depends on the value of weights w used to evaluate the derivative as well as the dataset $\mathcal { D }$ and the loss function $L$ . In this section, we discuss the effect of each of them and show that it can be used to prune the network in single-shot with initial weights w.
+
+Firstly, in order to minimize the impact of weights on the derivatives $\partial L / \partial c _ { j }$ , we need to choose these weights carefully. For instance, if the weights are too large, the activations after the non-linear function (e.g., sigmoid) will be saturated, which would result in uninformative gradients. Therefore, the weights should be within a sensible range. In particular, there is a body of work on neural network initialization (Goodfellow et al. (2016)) that ensures the gradients to be in a reasonable range, and our saliency measure can be used to prune neural networks at any such initialization.
+
+Furthermore, we are interested in making our saliency measure robust to architecture variations. Note that initializing neural networks is a random process, typically done using normal distribution. However, if the initial weights have a fixed variance, the signal passing through each layer no longer guarantees to have the same variance, as noted by LeCun et al. (1998). This would make the gradient and in turn our saliency measure, to be dependent on the architectural characteristics. Thus, we advocate the use of variance scaling methods (e.g., Glorot & Bengio (2010)) to initialize the weights, such that the variance remains the same throughout the network. By ensuring this, we empirically show that our saliency measure computed at initialization is robust to variations in the architecture.
+
+Next, since the dataset and the loss function defines the task at hand, by relying on both of them, our saliency criterion in fact discovers the connections in the network that are important to the given task. However, the practitioner needs to make a choice on whether to use the whole training set, or a mini-batch or the validation set to compute the connection saliency. Moreover, in case there are memory limitations (e.g., large model or dataset), one can accumulate the saliency measure over multiple batches or take an exponential moving average. In our experiments, we show that using only one mini-batch of a reasonable number of training examples can lead to effective pruning.
+
+Finally, in contrast to the previous approaches, our criterion for finding redundant connections is simple and directly based on the sensitivity of the connections. This allows us to effectively identify and prune redundant connections in a single step even before training. Then, training can be performed on the resulting pruned (sparse) network. We name our method SNIP for Single-shot Network Pruning, and the complete algorithm is given in Algorithm 1.
+
+![](images/3926bf85ac622a47d0b4130ae5dbb2c6cc89a43e80cedae36061229911cdf321.jpg)  
+Figure 1: Test errors of LeNets pruned at varying sparsity levels $\bar { \kappa }$ , where $\bar { \kappa } = 0$ refers to the reference network trained without pruning. Our approach performs as good as the reference network across varying sparsity levels on both the models.
+
+# 5 EXPERIMENTS
+
+We evaluate our method, SNIP, on MNIST, CIFAR-10 and Tiny-ImageNet classification tasks with a variety of network architectures. Our results show that SNIP yields extremely sparse models with minimal or no loss in accuracy across all tested architectures, while being much simpler than other state-of-the-art alternatives. We also provide clear evidence that our method prunes genuinely explainable connections rather than performing blind pruning.
+
+Experiment setup For brevity, we define the sparsity level to be $\bar { \kappa } = ( m - \kappa ) / m \cdot 1 0 0 ( \% )$ , where $m$ is the total number of parameters and $\kappa$ is the desired number of non-zero weights. For a given sparsity level $\bar { \kappa }$ , the sensitivity scores are computed using a batch of 100 and 128 examples for MNIST and CIFAR experiments, respectively. After pruning, the pruned network is trained in the standard way. Specifically, we train the models using SGD with momentum of 0.9, batch size of 100 for MNIST and 128 for CIFAR experiments and the weight decay rate of 0.0005, unless stated otherwise. The initial learning rate is set to 0.1 and decayed by 0.1 at every 25k or $3 0 \mathrm { k }$ iterations for MNIST and CIFAR, respectively. Our algorithm requires no other hyperparameters or complex learning/pruning schedules as in most pruning algorithms. We spare $10 \%$ of the training data as a validation set and used only $90 \%$ for training. For CIFAR experiments, we use the standard data augmentation (i.e., random horizontal flip and translation up to 4 pixels) for both the reference and sparse models. The code can be found here: https://github.com/namhoonlee/snip-public.
+
+# 5.1 PRUNING LENETS WITH VARYING LEVELS OF SPARSITY
+
+We first test our approach on two standard networks for pruning, LeNet-300-100 and LeNet-5-Caffe. LeNet-300-100 consists of three fully-connected (fc) layers with $2 6 7 \mathrm { k }$ parameters and LeNet-5-Caffe consists of two convolutional (conv) layers and two fc layers with 431k parameters. We prune the LeNets for different sparsity levels $\bar { \kappa }$ and report the performance in error on the MNIST image classification task. We run the experiment 20 times for each $\bar { \kappa }$ by changing random seeds for dataset and network initialization. The results are reported in Figure 1.
+
+The pruned sparse LeNet-300-100 achieves performances similar to the reference $( \bar { \kappa } = 0$ ), only with negligible loss at $\bar { \kappa } = 9 0$ . For LeNet-5-Caffe, the performance degradation is nearly invisible. Note that our saliency measure does not require the network to be pre-trained and is computed at random initialization. Despite such simplicity, our approach prunes LeNets quickly (single-shot) and effectively (minimal accuracy loss) at varying sparsity levels.
+
+# 5.2 COMPARISONS TO EXISTING APPROACHES
+
+What happens if we increase the target sparsity to an extreme level? For example, would a model with only $1 \%$ of the total parameters still be trainable and perform well? We test our approach for extreme sparsity levels (e.g., up to $9 9 \%$ sparsity on LeNet-5-Caffe) and compare with various pruning algorithms as follows: LWC (Han et al. (2015)), DNS (Guo et al. (2016)), LC (Carreira-Perpin˜ an & ´
+
+Table 1: Pruning results on LeNets and comparisons to other approaches. Here, “many” refers to an arbitrary number often in the order of total learning steps, and “soft” refers to soft pruning in Bayesian based methods. Our approach is capable of pruning up to $98 \%$ for LeNet-300-100 and $9 9 \%$ for LeNet-5-Caffe with marginal increases in error from the reference network. Notably, our approach is considerably simpler than other approaches, with no requirements such as pretraining, additional hyperparameters, augmented training objective or architecture dependent constraints.   
+
+<table><tr><td rowspan="2">Method</td><td rowspan="2">Criterion</td><td colspan="2">LeNet-300-100</td><td colspan="2">LeNet-5-Caffe</td><td rowspan="2">Pretrain</td><td rowspan="2">#Prune</td><td rowspan="2">Additional hyperparam.</td><td rowspan="2">Augment objective</td><td rowspan="2">Arch. constraints</td></tr><tr><td>K(%)</td><td>err. (%)</td><td>K(%)</td><td>err. (%)</td></tr><tr><td>Ref.</td><td></td><td></td><td>1.7</td><td>一</td><td>0.9</td><td></td><td>1</td><td>-&gt;</td><td>-xx&gt;</td><td>√</td></tr><tr><td>LWC</td><td>Magnitude</td><td>91.7</td><td>1.6</td><td>91.7</td><td>0.8</td><td></td><td>many</td><td></td><td></td><td></td></tr><tr><td>DNS</td><td>Magnitude</td><td>98.2</td><td>2.0</td><td>99.1</td><td>0.9</td><td></td><td>many</td><td></td><td></td><td>√</td></tr><tr><td>LC</td><td>Magnitude</td><td>99.0</td><td>3.2</td><td>99.0</td><td>1.1</td><td></td><td>many</td><td>√</td><td></td><td>X</td></tr><tr><td>SWS</td><td>Bayesian</td><td>95.6</td><td>1.9</td><td>99.5</td><td>1.0</td><td></td><td>soft</td><td>√</td><td>√</td><td>X</td></tr><tr><td>SVD</td><td>Bayesian</td><td>98.5</td><td>1.9</td><td>99.6</td><td>0.8</td><td>-&gt;&gt;&gt;&gt;&gt;</td><td>soft</td><td>√</td><td>√</td><td>X</td></tr><tr><td>OBD</td><td>Hessian</td><td>92.0</td><td>2.0</td><td>92.0</td><td>2.7</td><td>√</td><td>many</td><td>√</td><td>X</td><td>X</td></tr><tr><td>L-OBS</td><td>Hessian</td><td>98.5</td><td>2.0</td><td>99.0</td><td>2.1</td><td>√</td><td>many</td><td>√</td><td>X</td><td>√</td></tr><tr><td rowspan="2">SNIP (ours)</td><td>Connection</td><td>95.0</td><td>1.6</td><td>98.0</td><td>0.8</td><td>×</td><td></td><td>×</td><td>×</td><td>×</td></tr><tr><td>sensitivity</td><td>98.0</td><td>2.4</td><td>99.0</td><td>1.1</td><td></td><td>1</td><td></td><td></td><td></td></tr></table>
+
+Idelbayev (2018)), SWS (Ullrich et al. (2017)), SVD (Molchanov et al. (2017a)), OBD (LeCun et al.   
+(1990)), L-OBS (Dong et al. (2017)). The results are summarized in Table 1.
+
+We achieve errors that are comparable to the reference model, degrading approximately $0 . 7 \%$ and $0 . 3 \%$ while pruning $98 \%$ and $9 9 \%$ of the parameters in LeNet-300-100 and LeNet-5-Caffe respectively. For slightly relaxed sparsities (i.e., $9 5 \%$ for LeNet-300-100 and $98 \%$ for LeNet-5-Caffe), the sparse models pruned by SNIP record better performances than the dense reference network. Considering $9 9 \%$ sparsity, our method efficiently finds $1 \%$ of the connections even before training, that are sufficient to learn as good as the reference network. Moreover, SNIP is competitive to other methods, yet it is unparalleled in terms of algorithm simplicity.
+
+To be more specific, we enumerate some key points and non-trivial aspects of other algorithms and highlight the benefit of our approach. First of all, the aforementioned methods require networks to be fully trained (if not partly) before pruning. These approaches typically perform many pruning operations even if the network is well pretrained, and require additional hyperparameters (e.g., pruning frequency in Guo et al. (2016), annealing schedule in Carreira-Perpin˜an & Idelbayev (2018)). Some ´ methods augment the training objective to handle pruning together with training, increasing the complexity of the algorithm (e.g., augmented Lagrangian in Carreira-Perpin˜an & Idelbayev (2018), ´ variational inference in Molchanov et al. (2017a)). Furthermore, there are approaches designed to include architecture dependent constraints (e.g., layer-wise pruning schemes in Dong et al. (2017)).
+
+Compared to the above approaches, ours seems to cost almost nothing; it requires no pretraining or additional hyperparameters, and is applied only once at initialization. This means that one can easily plug-in SNIP as a preprocessor before training neural networks. Since SNIP prunes the network at the beginning, we could potentially expedite the training phase by training only the survived parameters (e.g., reduced expected FLOPs in Louizos et al. (2018)). Notice that this is not possible for the aforementioned approaches as they obtain the maximum sparsity at the end of the process.
+
+# 5.3 VARIOUS MODERN ARCHITECTURES
+
+In this section we show that our approach is generally applicable to more complex modern network architectures including deep convolutional, residual and recurrent ones. Specifically, our method is applied to the following models:
+
+• AlexNet-s and AlexNet-b: Models similar to Krizhevsky et al. (2012) in terms of the number of layers and size of kernels. We set the size of fc layers to 512 (AlexNet-s) and to 1024 (AlexNet-b) to adapt for CIFAR-10 and use strides of 2 for all conv layers instead of using pooling layers. • VGG-C, VGG-D and VGG-like: Models similar to the original VGG models described in Simonyan & Zisserman (2015). VGG-like (Zagoruyko (2015)) is a popular variant adapted for CIFAR-10 which has one less fc layers. For all VGG models, we set the size of fc layers to 512, remove dropout layers to avoid any effect on sparsification and use batch normalization instead. • WRN-16-8, WRN-16-10 and WRN-22-8: Same models as in Zagoruyko & Komodakis (2016).
+
+<table><tr><td>Architecture</td><td>Model</td><td>Sparsity (%)</td><td># Parameters</td><td>Error (%)</td><td></td><td>△</td></tr><tr><td rowspan="5">Convolutional</td><td>AlexNet-s</td><td>90.0</td><td>5.1m → 507k</td><td>14.12 →</td><td>14.99</td><td>+0.87</td></tr><tr><td>AlexNet-b</td><td>90.0</td><td>8.5m → 849k</td><td>13.92 →</td><td>14.50</td><td>+0.58</td></tr><tr><td>VGG-C</td><td>95.0</td><td>10.5m → 526k</td><td>6.82 →</td><td>7.27</td><td>+0.45</td></tr><tr><td>VGG-D</td><td>95.0</td><td>15.2m → 762k</td><td>6.76 →</td><td>7.09</td><td>+0.33</td></tr><tr><td>VGG-like</td><td>97.0</td><td>15.0m → 449k</td><td>8.26 →</td><td>8.00</td><td>-0.26</td></tr><tr><td rowspan="3">Residual</td><td>WRN-16-8</td><td>95.0</td><td>10.0m → 548k</td><td>6.21 →</td><td>6.63</td><td>+0.42</td></tr><tr><td>WRN-16-10</td><td>95.0</td><td>17.1m → 856k</td><td>5.91 →</td><td>6.43</td><td>+0.52</td></tr><tr><td>WRN-22-8</td><td>95.0</td><td>17.2m → 858k</td><td>6.14 →</td><td>5.85</td><td>-0.29</td></tr><tr><td rowspan="4">Recurrent</td><td>LSTM-s</td><td>95.0</td><td>137k → 6.8k</td><td>1.88 →</td><td>1.57</td><td>-0.31</td></tr><tr><td>LSTM-b</td><td>95.0</td><td>535k → 26.8k</td><td>1.15 →</td><td>1.35</td><td>+0.20</td></tr><tr><td>GRU-s</td><td>95.0</td><td>104k → 5.2k</td><td>1.87 →</td><td>2.41</td><td>+0.54</td></tr><tr><td>GRU-b</td><td>95.0</td><td>404k→ 20.2k</td><td>1.71 →</td><td>1.52</td><td>-0.19</td></tr></table>
+
+Table 2: Pruning results of the proposed approach on various modern architectures (before after). AlexNets, VGGs and WRNs are evaluated on CIFAR-10, and LSTMs and GRUs are evaluated on the sequential MNIST classification task. The approach is generally applicable regardless of architecture types and models and results in a significant amount of reduction in the number of parameters with minimal or no loss in performance.
+
+• LSTM-s, LSTM-b, GRU-s, GRU-b: One layer RNN networks with either LSTM (Zaremba et al. (2014)) or GRU (Cho et al. (2014)) cells. We develop two unit sizes for each cell type, 128 and 256 for $\{ \cdot \}$ -s and $\{ \cdot \}$ -b, respectively. The model is adapted for the sequential MNIST classification task, similar to Le et al. (2015). Instead of processing pixel-by-pixel, however, we perform rowby-row processing (i.e., the RNN cell receives each row at a time).
+
+The results are summarized in Table 2. Overall, our approach prunes a substantial amount of parameters in a variety of network models with minimal or no loss in accuracy $( < 1 \% )$ . Our pruning procedure does not need to be modified for specific architectural variations (e.g., recurrent connections), indicating that it is indeed versatile and scalable. Note that prior art that use a saliency criterion based on the weights (i.e., magnitude or Hessian based) would require considerable adjustments in their pruning schedules as per changes in the model.
+
+We note of a few challenges in directly comparing against others: different network specifications, learning policies, datasets and tasks. Nonetheless, we provide a few comparison points that we found in the literature. On CIFAR-10, SVD prunes $9 7 . 9 \%$ of the connections in VGG-like with no loss in accuracy (ours: $9 7 \%$ sparsity) while SWS obtained $9 3 . 4 \%$ sparsity on WRN-16-4 but with a non-negligible loss in accuracy of $2 \%$ . There are a couple of works attempting to prune RNNs (e.g., GRU in Narang et al. (2017) and LSTM in See et al. (2016)). Even though these methods are specifically designed for RNNs, none of them are able to obtain extreme sparsity without substantial loss in accuracy reflecting the challenges of pruning RNNs. To the best of our knowledge, we are the first to demonstrate on convolutional, residual and recurrent networks for extreme sparsities without requiring additional hyperparameters or modifying the pruning procedure.
+
+# 5.4 UNDERSTANDING WHICH CONNECTIONS ARE BEING PRUNED
+
+So far we have shown that our approach can prune a variety of deep neural network architectures for extreme sparsities without losing much on accuracy. However, it is not clear yet which connections are actually being pruned away or whether we are pruning the right (i.e., unimportant) ones. What if we could actually peep through our approach into this inspection?
+
+Consider the first layer in LeNet-300-100 parameterized by $\mathbf { w } _ { l = 1 } ~ \in ~ \mathbb { R } ^ { 7 8 4 \times 3 0 0 }$ . This is a layer fully connected to the input where input images are of size $2 8 \times 2 8 \ : = \ : 7 8 4$ . In order to understand which connections are retained, we can visualize the binary connectivity mask for this layer $\mathbf { c } _ { l = 1 }$ , by averaging across columns and then reshaping the vector into 2D matrix (i.e., $\begin{array} { r } { \mathbf { c } _ { l = 1 } ^ { \check { } } \in \{ \bar { 0 } , 1 \} ^ { \check { } 8 4 \times 3 0 \widetilde { 0 } }  \mathbb { R } ^ { 7 8 4 }  \mathbb { R } ^ { 2 8 \times 2 8 } } \end{array}$ ). Recall that our method computes c using a minibatch of examples. In this experiment, we curate the mini-batch of examples of the same class and see which weights are retained for that mini-batch of data. We repeat this experiment for all classes (i.e., digits for MNIST and fashion items for Fashion-MNIST) with varying sparsity levels $\bar { \kappa }$ . The results are displayed in Figure 2 (see Appendix A for more results).
+
+![](images/0f4107c55d7dc6d96c089d84572497bc1ec5a1fdb8c53251ac813dd698b02584.jpg)  
+Figure 2: Visualizations of pruned parameters of the first layer in LeNet-300-100; the parameters are reshaped to be visualized as an image. Each column represents the visualizations for a particular class obtained using a batch of 100 examples with varying levels of sparsity $\bar { \kappa }$ , from 10 (top) to 90 (bottom). Bright pixels indicate that the parameters connected to these region had high importance scores (s) and survived from pruning. As the sparsity increases, the parameters connected to the discriminative part of the image for classification survive and the irrelevant parts get pruned.
+
+The results are significant; important connections seem to reconstruct either the complete image (MNIST) or silhouettes (Fashion-MNIST) of input class. When we use a batch of examples of the digit 0 (i.e., the first column of MNIST results), for example, the parameters connected to the foreground of the digit 0 survive from pruning while the majority of background is removed. Also, one can easily determine the identity of items from Fashion-MNIST results. This clearly indicates that our method indeed prunes the unimportant connections in performing the classification task, receiving signals only from the most discriminative part of the input. This stands in stark contrast to other pruning methods from which carrying out such inspection is not straightforward.
+
+# 5.5 EFFECTS OF DATA AND WEIGHT INITIALIZATION
+
+Recall that our connection saliency measure depends on the network weights w as well as the given data $\mathcal { D }$ (Section 4.2). We study the effect of each of these in this section.
+
+Effect of data. Our connection saliency measure depends on a mini-batch of train examples $\mathcal { D } ^ { b }$ (see Algorithm 1). To study the effect of data, we vary the batch size used to compute the saliency $( | \mathcal { D } ^ { b } | )$ and check which connections are being pruned as well as how much performance change this results in on the corresponding sparse network. We test with LeNet-300-100 to visualize the remaining parameters, and set the sparsity level $\bar { \kappa } = 9 0$ . Note that the batch size used for training remains the same as 100 for all cases. The results are displayed in Figure 3.
+
+Effect of initialization. Our approach prunes a network at a stochastic initialization as discussed. We study the effect of the following initialization methods: 1) RN (random normal), 2) TN (truncated random normal), 3) VS-X (a variance scaling method using Glorot & Bengio (2010)), and 4) VS-H (a variance scaling method He et al. (2015)). We test on LeNets and RNNs on MNIST and run 20 sets of experiments by varying the seed for initialization. We set the sparsity level $\bar { \kappa } = 9 0$ , and train with Adam optimizer (Kingma & Ba (2015)) with learning rate of 0.001 without weight decay. Note that for training VS-X initialization is used in all the cases. The results are reported in Figure 3.
+
+For all models, VS-H achieves the best performance. The differences between initializers are marginal on LeNets, however, variance scaling methods indeed turns out to be essential for complex RNN models. This effect is significant especially for GRU where without variance scaling initialization, the pruned networks are unable to achieve good accuracies, even with different optimizers. Overall, initializing with a variance scaling method seems crucial to making our saliency measure reliable and model-agnostic.
+
+![](images/0571d02738677c85bfcc4968a17cec170d1e05716329724896a5e65b46ef5437.jpg)
+
+Figure 3: The effect of different batch sizes: (top-row) survived parameters in the first layer of LeNet-300-100 from pruning visualized as images; (bottom-row) the performance in errors of the pruned networks. For $| \mathcal { D } ^ { b } | \overset { - } { = } 1$ , the sampled example was 8; our pruning precisely retains the valid connections. As $| \mathcal { D } ^ { b } |$ increases, survived parameters get close to the average of all examples in the train set (last column), and the error decreases.   
+
+<table><tr><td>Init.</td><td>LeNet-300-100</td><td>LeNet-5-Caffe</td><td>LSTM-s</td><td>GRU-s</td></tr><tr><td>RN</td><td>1.90 ± (0.09)</td><td>0.89 ± (0.04)</td><td>2.93 ± (0.20)</td><td>47.61 ± (20.49)</td></tr><tr><td>TN</td><td>1.96 ± (0.11)</td><td>0.87 ± (0.05)</td><td>3.03 ± (0.17)</td><td>46.48± (22.25)</td></tr><tr><td>VS-X</td><td>1.91 ± (0.10)</td><td>0.88 ± (0.07)</td><td>1.48 ± (0.09)</td><td>1.80 ± (0.10)</td></tr><tr><td>VS-H</td><td>1.88 ± (0.10)</td><td>0.85 ± (0.05)</td><td>1.47 ± (0.08)</td><td>1.80 ± (0.14)</td></tr></table>
+
+Table 3: The effect of initialization on our saliency score. We report the classification errors ( $\pm$ std).   
+Variance scaling initialization (VS-X, VS-H) improves the performance, especially for RNNs.
+
+# 5.6 FITTING RANDOM LABELS
+
+To further explore the use cases of SNIP, we run the experiment introduced in Zhang et al. (2017) and check whether the sparse network obtained by SNIP memorizes the dataset. Specifically, we train LeNet-5-Caffe for both the reference model and pruned model (with $\bar { \kappa } = 9 9 $ ) on MNIST with either true or randomly shuffled labels. To compute the connection sensitivity, always true labels are used. The results are plotted in Figure 4.
+
+Given true labels, both the reference (red) and pruned (blue) models quickly reach to almost zero training loss. However, the reference model provided with random labels (green) also reaches to very low training loss, even with an explicit L2 regularizer (purple), indicating that neural networks have enough capacity to memorize completely random data. In contrast, the model pruned by SNIP (orange) fails to fit the random labels (high training error). The potential explanation is that the pruned network does not have sufficient capacity to fit the random labels, but it is able to classify MNIST with true labels, reinforcing the significance of our saliency criterion. It is possible that a similar experiment can be done with other pruning methods (Molchanov et al. (2017a)), however, being simple, SNIP enables such exploration much easier. We provide a further analysis on the effect of varying $\bar { \kappa }$ in Appendix B.
+
+![](images/9a651ab94be553eb9324682211e6a7c4d4dcea5b1a266aa2431d015c01647a2d.jpg)  
+Figure 4: The sparse model pruned by SNIP does not fit the random labels.
+
+# 6 DISCUSSION AND FUTURE WORK
+
+In this work, we have presented a new approach, SNIP, that is simple, versatile and interpretable; it prunes irrelevant connections for a given task at single-shot prior to training and is applicable to a variety of neural network models without modifications. While SNIP results in extremely sparse models, we find that our connection sensitivity measure itself is noteworthy in that it diagnoses important connections in the network from a purely untrained network. We believe that this opens up new possibilities beyond pruning in the topics of understanding of neural network architectures, multi-task transfer learning and structural regularization, to name a few. In addition to these potential directions, we intend to explore the generalization capabilities of sparse networks.
+
+# ACKNOWLEDGEMENTS
+
+This work was supported by the Korean Government Graduate Scholarship, the ERC grant ERC2012-AdG 321162-HELIOS, EPSRC grant Seebibyte EP/M013774/1 and EPSRC/MURI grant EP/N019474/1. We would also like to acknowledge the Royal Academy of Engineering and FiveAI.
+
+# REFERENCES
+
+Sanjeev Arora, Rong Ge, Behnam Neyshabur, and Yi Zhang. Stronger generalization bounds for deep nets via a compression approach. ICML, 2018.
+
+Leo Breiman. Better subset regression using the nonnegative garrote. Technometrics, 1995.
+
+Miguel A. Carreira-Perpi ´ n˜an and Yerlan Idelbayev. “Learning-compression” algorithms for neural ´ net pruning. CVPR, 2018.
+
+Yves Chauvin. A back-propagation algorithm with optimal use of hidden units. NIPS, 1989.
+
+Kyunghyun Cho, Bart Van Merrienboer, Caglar Gulcehre, Dzmitry Bahdanau, Fethi Bougares, Hol- ¨ ger Schwenk, and Yoshua Bengio. Learning phrase representations using rnn encoder-decoder for statistical machine translation. EMNLP, 2014.
+
+Xin Dong, Shangyu Chen, and Sinno Pan. Learning to prune deep neural networks via layer-wise optimal brain surgeon. NIPS, 2017.
+
+Xavier Glorot and Yoshua Bengio. Understanding the difficulty of training deep feedforward neural networks. AISTATS, 2010.
+
+Yunchao Gong, Liu Liu, Ming Yang, and Lubomir Bourdev. Compressing deep convolutional networks using vector quantization. arXiv preprint arXiv:1412.6115, 2014.
+
+Ian Goodfellow, Yoshua Bengio, Aaron Courville, and Yoshua Bengio. Deep learning. MIT press Cambridge, 2016.
+
+Yiwen Guo, Anbang Yao, and Yurong Chen. Dynamic network surgery for efficient dnns. NIPS, 2016.
+
+Suyog Gupta, Ankur Agrawal, Kailash Gopalakrishnan, and Pritish Narayanan. Deep learning with limited numerical precision. ICML, 2015.
+
+Song Han, Jeff Pool, John Tran, and William Dally. Learning both weights and connections for efficient neural network. NIPS, 2015.
+
+Babak Hassibi, David G Stork, and Gregory J Wolff. Optimal brain surgeon and general network pruning. Neural Networks, 1993.
+
+Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Delving deep into rectifiers: Surpassing human-level performance on imagenet classification. ICCV, 2015.
+
+Itay Hubara, Matthieu Courbariaux, Daniel Soudry, Ran El-Yaniv, and Yoshua Bengio. Binarized neural networks. NIPS, 2016.
+
+Masumi Ishikawa. Structural learning with forgetting. Neural Networks, 1996.
+
+Max Jaderberg, Andrea Vedaldi, and Andrew Zisserman. Speeding up convolutional neural networks with low rank expansions. BMVC, 2014.
+
+Ehud D Karnin. A simple procedure for pruning back-propagation trained neural networks. Neural Networks, 1990.
+
+Diederik P Kingma and Jimmy Ba. Adam: A method for stochastic optimization. ICLR, 2015.
+
+Pang Wei Koh and Percy Liang. Understanding black-box predictions via influence functions. ICML, 2017.
+
+Alex Krizhevsky, Ilya Sutskever, and Geoffrey E Hinton. Imagenet classification with deep convolutional neural networks. 2012.
+
+Quoc V Le, Navdeep Jaitly, and Geoffrey E Hinton. A simple way to initialize recurrent networks of rectified linear units. CoRR, 2015.
+
+Yann LeCun, John S Denker, and Sara A Solla. Optimal brain damage. NIPS, 1990.
+
+Yann LeCun, Leon Bottou, Genevieve B. Orr, and Klaus-Robert M ´ uller. Efficient backprop. ¨ Neural Networks: Tricks of the Trade, 1998.
+
+Hao Li, Asim Kadav, Igor Durdanovic, Hanan Samet, and Hans Peter Graf. Pruning filters for efficient convnets. ICLR, 2017.
+
+Christos Louizos, Max Welling, and Diederik P Kingma. Learning sparse neural networks through $l _ { 0 }$ regularization. ICLR, 2018.
+
+Decebal Constantin Mocanu, Elena Mocanu, Peter Stone, Phuong H Nguyen, Madeleine Gibescu, and Antonio Liotta. Scalable training of artificial neural networks with adaptive sparse connectivity inspired by network science. Nature Communications, 2018.
+
+Dmitry Molchanov, Arsenii Ashukha, and Dmitry Vetrov. Variational dropout sparsifies deep neural networks. ICML, 2017a.
+
+Pavlo Molchanov, Stephen Tyree, Tero Karras, Timo Aila, and Jan Kautz. Pruning convolutional neural networks for resource efficient inference. ICLR, 2017b.
+
+Michael C Mozer and Paul Smolensky. Skeletonization: A technique for trimming the fat from a network via relevance assessment. NIPS, 1989.
+
+Sharan Narang, Erich Elsen, Gregory Diamos, and Shubho Sengupta. Exploring sparsity in recurrent neural networks. ICLR, 2017.
+
+Alexander Novikov, Dmitrii Podoprikhin, Anton Osokin, and Dmitry P Vetrov. Tensorizing neural networks. NIPS, 2015.
+
+Steven J Nowlan and Geoffrey E Hinton. Simplifying neural networks by soft weight-sharing. Neural Computation, 1992.
+
+Ameya Prabhu, Girish Varma, and Anoop Namboodiri. Deep expander networks: Efficient deep networks from graph theory. ECCV, 2018.
+
+Russell Reed. Pruning algorithms-a survey. Neural Networks, 1993.
+
+Abigail See, Minh-Thang Luong, and Christopher D Manning. Compression of neural machine translation models via pruning. CoNLL, 2016.
+
+Karen Simonyan and Andrew Zisserman. Very deep convolutional networks for large-scale image recognition. ICLR, 2015.
+
+Karen Ullrich, Edward Meeds, and Max Welling. Soft weight-sharing for neural network compression. ICLR, 2017.
+
+Andreas S Weigend, David E Rumelhart, and Bernardo A Huberman. Generalization by weightelimination with application to forecasting. NIPS, 1991.
+
+Wei Wen, Chunpeng Wu, Yandan Wang, Yiran Chen, and Hai Li. Learning structured sparsity in deep neural networks. NIPS, 2016.
+
+Sergey Zagoruyko. $9 2 . 4 5 \%$ on cifar-10 in torch. Torch Blog, 2015.
+
+Sergey Zagoruyko and Nikos Komodakis. Wide residual networks. BMVC, 2016.
+
+Wojciech Zaremba, Ilya Sutskever, and Oriol Vinyals. Recurrent neural network regularization. arXiv preprint arXiv:1409.2329, 2014.
+
+Chiyuan Zhang, Samy Bengio, Moritz Hardt, Benjamin Recht, and Oriol Vinyals. Understanding deep learning requires rethinking generalization. ICLR, 2017.
+
+![](images/cc69ae2f5789c064a9d7ec25c2cae8be85125a7807f27c075058ab31684ccd3c.jpg)  
+Figure 5: Results of pruning with SNIP on inverted (Fashion-)MNIST (i.e., dark and bright regions are swapped). Notably, even if the data is inverted, the results are the same as the ones on the original (Fashion-)MNIST in Figure 2.
+
+![](images/7e10adb4cd3b78aa3523f4d7e8ead3c6621045e90fb560498f3758f598063b9e.jpg)  
+Figure 6: Results of pruning with $\partial L / \partial$ w on the original and inverted (Fashion-)MNIST. Notably, compared to the case of using SNIP (Figures 2 and 5), the results are different: Firstly, the results on the original (Fashion-)MNIST (i.e., (a) and (c) above) are not the same as the ones using SNIP (i.e., (a) and (b) in Figure 2). Moreover, the pruning patterns are inconsistent with different sparsity levels, either intra-class or inter-class. Furthermore, using ${ \partial L } / { \partial \mathbf { w } }$ results in different pruning patterns between the original and inverted data in some cases (e.g., the $2 ^ { \mathrm { n d } }$ columns between (c) and (d)).
+
+![](images/2c60ed92201d216f7acfecb7839cd7dcf12f0266b4e0e0b0daf88b490479c204.jpg)  
+Figure 7: The effect of varying sparsity levels $\left( \hat { \kappa } \right)$ . The lower $\bar { \kappa }$ becomes, the lower training loss is recorded, meaning that a network with more parameters is more vulnerable to fitting random labels. Recall, however, that all pruned models are able to learn to perform the classification task without losing much accuracy (see Figure 1). This potentially indicates that the pruned network does not have sufficient capacity to fit the random labels, but it is capable of performing the classification.
+
+# C TINY-IMAGENET
+
+<table><tr><td>Architecture</td><td>Model</td><td>Sparsity (%)</td><td># Parameters</td><td>Error (%)</td><td>△</td></tr><tr><td rowspan="5">Convolutional</td><td>AlexNet-s</td><td>90.0</td><td>5.1m → 507k</td><td>62.52 → 65.27</td><td>+2.75</td></tr><tr><td>AlexNet-b</td><td>90.0</td><td>8.5m → 849k</td><td>62.76 → 65.54</td><td>+2.78</td></tr><tr><td>VGG-C</td><td>95.0</td><td>10.5m → 526k</td><td>56.49 → 57.48</td><td>+0.99</td></tr><tr><td>VGG-D</td><td>95.0</td><td>15.2m → 762k</td><td>56.85 → 57.00</td><td>+0.15</td></tr><tr><td>VGG-like</td><td>95.0</td><td>15.0m → 749k</td><td>54.86 → 55.73</td><td>+0.87</td></tr></table>
+
+Table 4: Pruning results of SNIP on Tiny-ImageNet (before after). Tiny-ImageNet2 is a subset of the full ImageNet: there are 200 classes in total, each class has 500 and 50 images for training and validation respectively, and each image has the spatial resolution of $6 4 \times 6 4$ . Compared to CIFAR-10, the resolution is doubled, and to deal with this, the stride of the first convolution in all architectures is doubled, following the standard practice for this dataset. In general, the Tiny-ImageNet classification task is considered much more complex than MNIST or CIFAR-10. Even on Tiny-ImageNet, however, SNIP is still able to prune a large amount of parameters with minimal loss in performance. AlexNet models lose more accuracies than VGGs, which may be attributed to the fact that the first convolution stride for AlexNet is set to be 4 (by its design of no pooling) which is too large and could lead to high loss of information when pruned.
+
+D ARCHITECTURE DETAILS   
+
+<table><tr><td rowspan=1 colspan=8>Module         Weight         Stride     Bias      BatchNorm  ReLU</td></tr><tr><td rowspan=1 colspan=1>Conv</td><td rowspan=1 colspan=1>[11,11, 3,96]</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>[2,2]</td><td rowspan=1 colspan=3>[96]          √</td><td rowspan=1 colspan=1>√</td></tr><tr><td rowspan=1 colspan=1>Conv</td><td rowspan=1 colspan=1>[5,5,96,256]</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>2j</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>[256]</td><td rowspan=1 colspan=1>√</td><td rowspan=1 colspan=1></td></tr><tr><td rowspan=1 colspan=1>Conv</td><td rowspan=1 colspan=1>[3,3,256,384]</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>2.2</td><td rowspan=1 colspan=2>[384]</td><td rowspan=1 colspan=2>√</td></tr><tr><td rowspan=1 colspan=1>Conv</td><td rowspan=1 colspan=1>[3,3,384,384]</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=5>[384]</td></tr><tr><td rowspan=1 colspan=1>Conv</td><td rowspan=1 colspan=1>[3,3,384,256]</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>2,2</td><td rowspan=1 colspan=2>[256]</td><td rowspan=1 colspan=2>（</td></tr><tr><td rowspan=1 colspan=1>Linear</td><td rowspan=1 colspan=1>[256,1024 ×k]</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=3>[1024×k]       √</td><td rowspan=1 colspan=1>√</td></tr><tr><td rowspan=1 colspan=3>Linear  [1024 × k,1024 ×k]</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=3>[1024 × k]       √</td><td rowspan=1 colspan=1>√</td></tr><tr><td rowspan=1 colspan=8>Linear       [1024 × k,c]                    [c]           X         X</td></tr></table>
+
+Table 5: AlexNet-s $k = 1 ,$ ) and AlexNet-b $( k = 2 )$ ). In the last layer, $c$ denotes the number of possible classes: $c = 1 0$ for CIFAR-10 and $c = 2 0 0$ for Tiny-ImageNet. The strides in the first convolution layer for Tiny-ImageNet are set [4, 4] instead of [2, 2] to deal with the increase in the image resolution.   
+
+<table><tr><td>Module</td><td>Weight</td><td>Stride</td><td>Bias</td><td>BatchNorm</td><td>ReLU</td></tr><tr><td>Conv</td><td>[3,3,3,64]</td><td>[1,1]</td><td>[64]</td><td></td><td></td></tr><tr><td>Conv</td><td>[3,3, 64, 64]</td><td></td><td>[64]</td><td>广</td><td></td></tr><tr><td>Pool</td><td></td><td></td><td></td><td>×</td><td>&lt;&gt;x&gt;</td></tr><tr><td>Conv</td><td>[3,3,64,128]</td><td>1j</td><td>[128]</td><td>√</td><td></td></tr><tr><td>Conv</td><td>[3,3,128,128]</td><td>1j</td><td>[128]</td><td>√</td><td>√</td></tr><tr><td>Pool</td><td></td><td>18E.83. 2</td><td></td><td>X</td><td>X</td></tr><tr><td>Conv</td><td>[3,3,128,256]</td><td></td><td>[256]</td><td>√</td><td></td></tr><tr><td>Conv</td><td>[3,3,256,256]</td><td>1</td><td>[256]</td><td></td><td></td></tr><tr><td>Conv</td><td>[1/3/3,1/3/3,256,256]</td><td>1j</td><td>[256]</td><td>√</td><td></td></tr><tr><td>Pool</td><td></td><td>2j</td><td></td><td>X</td><td>X</td></tr><tr><td>Conv</td><td>[3,3,256,512]</td><td>1</td><td>[512]</td><td></td><td></td></tr><tr><td>Conv</td><td>[3,3,512, 512]</td><td>1j</td><td>[512]</td><td></td><td></td></tr><tr><td>Conv</td><td>[1/3/3,1/3/3,512,512]</td><td>1j</td><td>[512]</td><td></td><td></td></tr><tr><td>Pool</td><td></td><td>2</td><td></td><td></td><td></td></tr><tr><td>Conv</td><td>[3,3,512, 512]</td><td>1j</td><td>[512]</td><td></td><td></td></tr><tr><td>Conv</td><td>[3,3, 512,512]</td><td>1]</td><td>[512]</td><td></td><td></td></tr><tr><td>Conv</td><td>[1/3/3,1/3/3,512,512]</td><td>1]</td><td>[512]</td><td></td><td></td></tr><tr><td>Pool</td><td></td><td></td><td></td><td>X</td><td></td></tr><tr><td>Linear</td><td>[512, 512]</td><td></td><td>[512]</td><td>√</td><td>√</td></tr><tr><td>Linear</td><td>[512, 512]</td><td></td><td>[512]</td><td>√</td><td>√</td></tr><tr><td>Linear</td><td>[512,c]</td><td></td><td>[c]</td><td>X</td><td>X</td></tr></table>
+
+Table 6: VGG-C/D/like. In the last layer, $c$ denotes the number of possible classes: $c = 1 0$ for CIFAR10 and $c = 2 0 0$ for Tiny-ImageNet. The strides in the first convolution layer for Tiny-ImageNet are set [2, 2] instead of [1, 1] to deal with the increase in the image resolution. The second Linear layer is only used in VGG-C/D.
\ No newline at end of file
diff --git a/parse/train/B1VZqjAcYX/B1VZqjAcYX_content_list.json b/parse/train/B1VZqjAcYX/B1VZqjAcYX_content_list.json
new file mode 100644
index 0000000000000000000000000000000000000000..3e5a3b173450f63624a3b2ecf3f74debc510628b
--- /dev/null
+++ b/parse/train/B1VZqjAcYX/B1VZqjAcYX_content_list.json
@@ -0,0 +1,1773 @@
+[
+    {
+        "type": "text",
+        "text": "SNIP: SINGLE-SHOT NETWORK PRUNING BASED ONCONNECTION SENSITIVITY",
+        "text_level": 1,
+        "bbox": [
+            176,
+            98,
+            805,
+            146
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Namhoon Lee, Thalaiyasingam Ajanthan & Philip H. S. Torr University of Oxford {namhoon,ajanthan,phst}@robots.ox.ac.uk ",
+        "bbox": [
+            183,
+            170,
+            607,
+            212
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "ABSTRACT ",
+        "text_level": 1,
+        "bbox": [
+            454,
+            250,
+            544,
+            263
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Pruning large neural networks while maintaining their performance is often desirable due to the reduced space and time complexity. In existing methods, pruning is done within an iterative optimization procedure with either heuristically designed pruning schedules or additional hyperparameters, undermining their utility. In this work, we present a new approach that prunes a given network once at initialization prior to training. To achieve this, we introduce a saliency criterion based on connection sensitivity that identifies structurally important connections in the network for the given task. This eliminates the need for both pretraining and the complex pruning schedule while making it robust to architecture variations. After pruning, the sparse network is trained in the standard way. Our method obtains extremely sparse networks with virtually the same accuracy as the reference network on the MNIST, CIFAR-10, and Tiny-ImageNet classification tasks and is broadly applicable to various architectures including convolutional, residual and recurrent networks. Unlike existing methods, our approach enables us to demonstrate that the retained connections are indeed relevant to the given task. ",
+        "bbox": [
+            233,
+            280,
+            764,
+            487
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            512,
+            336,
+            529
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Despite the success of deep neural networks in machine learning, they are often found to be highly overparametrized making them computationally expensive with excessive memory requirements. Pruning such large networks with minimal loss in performance is appealing for real-time applications, especially on resource-limited devices. In addition, compressed neural networks utilize the model capacity efficiently, and this interpretation can be used to derive better generalization bounds for neural networks (Arora et al. (2018)). ",
+        "bbox": [
+            174,
+            544,
+            825,
+            627
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "In network pruning, given a large reference neural network, the goal is to learn a much smaller subnetwork that mimics the performance of the reference network. The majority of existing methods in the literature attempt to find a subset of weights from the pretrained reference network either based on a saliency criterion (Mozer & Smolensky (1989); LeCun et al. (1990); Han et al. (2015)) or utilizing sparsity enforcing penalties (Chauvin (1989); Carreira-Perpin˜an & Idelbayev (2018)). ´ Unfortunately, since pruning is included as a part of an iterative optimization procedure, all these methods require many expensive prune – retrain cycles and heuristic design choices with additional hyperparameters, making them non-trivial to extend to new architectures and tasks. ",
+        "bbox": [
+            174,
+            635,
+            825,
+            746
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "In this work, we introduce a saliency criterion that identifies connections in the network that are important to the given task in a data-dependent way before training. Specifically, we discover important connections based on their influence on the loss function at a variance scaling initialization, which we call connection sensitivity. Given the desired sparsity level, redundant connections are pruned once prior to training (i.e., single-shot), and then the sparse pruned network is trained in the standard way. Our approach has several attractive properties: ",
+        "bbox": [
+            174,
+            752,
+            825,
+            837
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "• Simplicity. Since the network is pruned once prior to training, there is no need for pretraining and complex pruning schedules. Our method has no additional hyperparameters and once pruned, training of the sparse network is performed in the standard way.   \n• Versatility. Since our saliency criterion chooses structurally important connections, it is robust to architecture variations. Therefore our method can be applied to various architectures including convolutional, residual and recurrent networks with no modifications. ",
+        "bbox": [
+            174,
+            840,
+            825,
+            924
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "• Interpretability. Our method determines important connections with a mini-batch of data at single-shot. By varying this mini-batch used for pruning, our method enables us to verify that the retained connections are indeed essential for the given task. ",
+        "bbox": [
+            178,
+            103,
+            823,
+            145
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "We evaluate our method on MNIST, CIFAR-10, and Tiny-ImageNet classification datasets with widely varying architectures. Despite being the simplest, our method obtains extremely sparse networks with virtually the same accuracy as the existing baselines across all tested architectures. Furthermore, we investigate the relevance of the retained connections as well as the effect of the network initialization and the dataset on the saliency score. ",
+        "bbox": [
+            174,
+            156,
+            823,
+            226
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2 RELATED WORK ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            244,
+            341,
+            261
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Classical methods. Essentially, early works in network pruning can be categorized into two groups (Reed (1993)): 1) those that utilize sparsity enforcing penalties; and 2) methods that prune the network based on some saliency criterion. The methods from the former category (Chauvin (1989); Weigend et al. (1991); Ishikawa (1996)) augment the loss function with some sparsity enforcing penalty terms (e.g., $L _ { 0 }$ or $L _ { 1 }$ norm), so that back-propagation effectively penalizes the magnitude of the weights during training. Then weights below a certain threshold may be removed. On the other hand, classical saliency criteria include the sensitivity of the loss with respect to the neurons (Mozer & Smolensky (1989)) or the weights (Karnin (1990)) and Hessian of the loss with respect to the weights (LeCun et al. (1990); Hassibi et al. (1993)). Since these criteria are heavily dependent on the scale of the weights and are designed to be incorporated within the learning process, these methods are prohibitively slow requiring many iterations of pruning and learning steps. Our approach identifies redundant weights from an architectural point of view and prunes them once at the beginning before training. ",
+        "bbox": [
+            174,
+            276,
+            825,
+            455
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Modern advances. In recent years, the increased space and time complexities as well as the risk of overfitting in deep neural networks prompted a surge of further investigation in network pruning. While Hessian based approaches employ the diagonal approximation due to its computational simplicity, impressive results (i.e., extreme sparsity without loss in accuracy) are achieved using magnitude of the weights as the criterion (Han et al. (2015)). This made them the de facto standard method for network pruning and led to various implementations (Guo et al. (2016); Carreira-Perpin˜an & ´ Idelbayev (2018)). The magnitude criterion is also extended to recurrent neural networks (Narang et al. (2017)), yet with heavily tuned hyperparameter setting. Unlike our approach, the main drawbacks of magnitude based approaches are the reliance on pretraining and the expensive prune – retrain cycles. Furthermore, since pruning and learning steps are intertwined, they often require highly heuristic design choices which make them non-trivial to be extended to new architectures and different tasks. Meanwhile, Bayesian methods are also applied to network pruning (Ullrich et al. (2017); Molchanov et al. (2017a)) where the former extends the soft weight sharing in Nowlan & Hinton (1992) to obtain a sparse and compressed network, and the latter uses variational inference to learn the dropout rate which can then be used to prune the network. Unlike the above methods, our approach is simple and easily adaptable to any given architecture or task without modifying the pruning procedure. ",
+        "bbox": [
+            174,
+            463,
+            825,
+            699
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Network compression in general. Apart from weight pruning, there are approaches focused on structured simplification such as pruning filters (Li et al. (2017); Molchanov et al. (2017b)), structured sparsity with regularizers (Wen et al. (2016)), low-rank approximation (Jaderberg et al. (2014)), matrix and tensor factorization (Novikov et al. (2015)), and sparsification using expander graphs (Prabhu et al. (2018)) or Erdos-R ˝ enyi random graph (Mocanu et al. (2018)). In addition, ´ there is a large body of work on compressing the representation of weights. A non-exhaustive list includes quantization (Gong et al. (2014)), reduced precision (Gupta et al. (2015)) and binary weights (Hubara et al. (2016)). In this work, we focus on weight pruning that is free from structural constraints and amenable to further compression schemes. ",
+        "bbox": [
+            174,
+            707,
+            825,
+            832
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "3 NEURAL NETWORK PRUNING ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            852,
+            446,
+            867
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "The main hypothesis behind the neural network pruning literature is that neural networks are usually overparametrized, and comparable performance can be obtained by a much smaller network (Reed (1993)) while improving generalization (Arora et al. (2018)). To this end, the objective is to learn ",
+        "bbox": [
+            176,
+            882,
+            823,
+            924
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "a sparse network while maintaining the accuracy of the standard reference network. Let us first formulate neural network pruning as an optimization problem. ",
+        "bbox": [
+            171,
+            103,
+            823,
+            132
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Given a dataset $\\mathbfcal { D } = \\{ ( \\mathbf { x } _ { i } , \\mathbf { y } _ { i } ) \\} _ { i = 1 } ^ { n }$ , and a desired sparsity level $\\kappa$ (i.e., the number of non-zero weights) neural network pruning can be written as the following constrained optimization problem: ",
+        "bbox": [
+            173,
+            138,
+            821,
+            167
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/ebd04375ac44347d780918c47861ac8c8cb91d7f6944a11ee1010af8262106cf.jpg",
+        "text": "$$\n\\begin{array} { l } { \\displaystyle \\operatorname* { m i n } _ { \\mathbf { w } } L ( \\mathbf { w } ; \\mathcal { D } ) = \\displaystyle \\operatorname* { m i n } _ { \\mathbf { w } } \\frac { 1 } { n } \\sum _ { i = 1 } ^ { n } \\ell ( \\mathbf { w } ; ( \\mathbf { x } _ { i } , \\mathbf { y } _ { i } ) ) ~ , } \\\\ { \\mathrm { s . t . } \\quad \\mathbf { w } \\in \\mathbb { R } ^ { m } , \\quad \\| \\mathbf { w } \\| _ { 0 } \\leq \\kappa ~ . } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            354,
+            171,
+            640,
+            232
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Here, $\\ell ( \\cdot )$ is the standard loss function (e.g., cross-entropy loss), w is the set of parameters of the neural network, $m$ is the total number of parameters and $\\| \\cdot \\| _ { 0 }$ is the standard $L _ { 0 }$ norm. ",
+        "bbox": [
+            173,
+            236,
+            826,
+            265
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The conventional approach to optimize the above problem is by adding sparsity enforcing penalty terms (Chauvin (1989); Weigend et al. (1991); Ishikawa (1996)). Recently, Carreira-Perpin˜an´ $\\&$ Idelbayev (2018) attempts to minimize the above constrained optimization problem using the stochastic version of projected gradient descent (where the projection is accomplished by pruning). However, these methods often turn out to be inferior to saliency based methods in terms of resulting sparsity and require heavily tuned hyperparameter settings to obtain comparable results. ",
+        "bbox": [
+            174,
+            271,
+            825,
+            356
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "On the other hand, saliency based methods treat the above problem as selectively removing redundant parameters (or connections) in the neural network. In order to do so, one has to come up with a good criterion to identify such redundant connections. Popular criteria include magnitude of the weights, i.e., weights below a certain threshold are redundant (Han et al. (2015); Guo et al. (2016)) and Hessian of the loss with respect to the weights, i.e., the higher the value of Hessian, the higher the importance of the parameters (LeCun et al. (1990); Hassibi et al. (1993)), defined as follows: ",
+        "bbox": [
+            173,
+            362,
+            825,
+            446
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/c088681f4071600c4852356681f774de0be83b26f0fa5008c7ee00bef5d07c4c.jpg",
+        "text": "$$\ns _ { j } = \\left\\{ \\begin{array} { l l } { \\left| w _ { j } \\right| , } & { \\mathrm { f o r m a g n i t u d e ~ b a s e d } } \\\\ { \\frac { w _ { j } ^ { 2 } H _ { j j } } { 2 } } & { \\mathrm { o r } \\frac { w _ { j } ^ { 2 } } { 2 H _ { j j } ^ { - 1 } } } & { \\mathrm { f o r } \\mathrm { H e s s i a n ~ b a s e d } . } \\end{array} \\right.\n$$",
+        "text_format": "latex",
+        "bbox": [
+            338,
+            452,
+            655,
+            503
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Here, for connection $j , s _ { j }$ is the saliency score, $w _ { j }$ is the weight, and $H _ { j j }$ is the value of the Hessian matrix, where the Hessian $\\mathbf { H } = \\partial ^ { 2 } L / \\partial \\mathbf { w } ^ { 2 } \\in \\mathbb { R } ^ { m \\times m }$ . Considering Hessian based methods, the Hessian matrix is neither diagonal nor positive definite in general, approximate at best, and intractable to compute for large networks. ",
+        "bbox": [
+            174,
+            507,
+            825,
+            564
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Despite being popular, both of these criteria depend on the scale of the weights and in turn require pretraining and are very sensitive to the architectural choices. For instance, different normalization layers affect the scale of the weights in a different way, and this would non-trivially affect the saliency score. Furthermore, pruning and the optimization steps are alternated many times throughout training, resulting in highly expensive prune – retrain cycles. Such an exorbitant requirement hinders the use of pruning methods in large-scale applications and raises questions about the credibility of the existing pruning criteria. ",
+        "bbox": [
+            173,
+            570,
+            825,
+            669
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In this work, we design a criterion which directly measures the connection importance in a datadependent manner. This alleviates the dependency on the weights and enables us to prune the network once at the beginning, and then the training can be performed on the sparse pruned network. Therefore, our method eliminates the need for the expensive prune – retrain cycles, and in theory, it can be an order of magnitude faster than the standard neural network training as it can be implemented using software libraries that support sparse matrix computations. ",
+        "bbox": [
+            174,
+            675,
+            825,
+            760
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "4 SINGLE-SHOT NETWORK PRUNING BASED ON CONNECTION SENSITIVITY",
+        "text_level": 1,
+        "bbox": [
+            173,
+            780,
+            805,
+            795
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Given a neural network and a dataset, our goal is to design a method that can selectively prune redundant connections for the given task in a data-dependent way even before training. To this end, we first introduce a criterion to identify important connections and then discuss its benefits. ",
+        "bbox": [
+            174,
+            810,
+            825,
+            853
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "4.1 CONNECTION SENSITIVITY: ARCHITECTURAL PERSPECTIVE ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            871,
+            629,
+            883
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Since we intend to measure the importance (or sensitivity) of each connection independently of its weight, we introduce auxiliary indicator variables $\\mathbf { c } \\in \\{ 0 , 1 \\} ^ { m }$ representing the connectivity of ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "parameters w.1 Now, given the sparsity level $\\kappa$ , Equation 1 can be correspondingly modified as: ",
+        "bbox": [
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+            102,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/ad23c70798958ceacba7cc412e5f4821e5a573dd20685c7c524d2a4992c31a21.jpg",
+        "text": "$$\n\\begin{array} { r l } { \\displaystyle \\operatorname* { m i n } _ { \\mathbf { c } , \\mathbf { w } } L ( \\mathbf { c } \\odot \\mathbf { w } ; \\mathcal { D } ) = \\displaystyle \\operatorname* { m i n } _ { \\mathbf { c } , \\mathbf { w } } \\frac { 1 } { n } \\sum _ { i = 1 } ^ { n } \\ell ( \\mathbf { c } \\odot \\mathbf { w } ; ( \\mathbf { x } _ { i } , \\mathbf { y } _ { i } ) ) ~ , } & { } \\\\ { \\mathrm { s . t . } \\quad \\mathbf { w } \\in \\mathbb { R } ^ { m } ~ , } & { } \\\\ { \\displaystyle \\quad \\mathbf { c } \\in \\{ 0 , 1 \\} ^ { m } , \\quad \\| \\mathbf { c } \\| _ { 0 } \\leq \\kappa ~ , } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
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+            119,
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+            194
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where $\\odot$ denotes the Hadamard product. Compared to Equation 1, we have doubled the number of learnable parameters in the network and directly optimizing the above problem is even more difficult. However, the idea here is that since we have separated the weight of the connection (w) from whether the connection is present or not (c), we may be able to determine the importance of each connection by measuring its effect on the loss function. ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "For instance, the value of $c _ { j }$ indicates whether the connection $j$ is active $( c _ { j } = 1 )$ ) in the network or pruned $( c _ { j } = 0 )$ . Therefore, to measure the effect of connection $j$ on the loss, one can try to measure the difference in loss when $c _ { j } = 1$ and $c _ { j } = 0$ , keeping everything else constant. Precisely, the effect of removing connection $j$ can be measured by, ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/e6365ca8d23c010ba62a5254564ce85692ebeab191c5a566631d07f8358e87d8.jpg",
+        "text": "$$\n\\begin{array} { r } { \\Delta L _ { j } ( \\mathbf { w } ; \\mathcal { D } ) = L \\big ( \\mathbf { 1 } \\odot \\mathbf { w } ; \\mathcal { D } \\big ) - L \\big ( \\big ( \\mathbf { 1 } - \\mathbf { e } _ { j } \\big ) \\odot \\mathbf { w } ; \\mathcal { D } \\big ) , } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            321,
+            335,
+            674,
+            353
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where $\\mathbf { e } _ { j }$ is the indicator vector of element $j$ (i.e., zeros everywhere except at the index $j$ where it is one) and 1 is the vector of dimension $m$ . ",
+        "bbox": [
+            174,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Note that computing $\\Delta L _ { j }$ for each $j \\in \\{ 1 \\ldots m \\}$ is prohibitively expensive as it requires $m + 1$ (usually in the order of millions) forward passes over the dataset. In fact, since $\\mathbf { c }$ is binary, $L$ is not differentiable with respect to $\\mathbf { c }$ , and it is easy to see that $\\Delta L _ { j }$ attempts to measure the influence of connection $j$ on the loss function in this discrete setting. Therefore, by relaxing the binary constraint on the indicator variables c, $\\Delta L _ { j }$ can be approximated by the derivative of $L$ with respect to $c _ { j }$ , which we denote $g _ { j } ( \\mathbf { w } ; \\mathcal { D } )$ . Hence, the effect of connection $j$ on the loss can be written as: ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/42176d39e7cf3667a3a141ea6f0addeb9f8d4f8297d5e9bce08d1f31245171b5.jpg",
+        "text": "$$\n\\Delta L _ { j } ( \\mathbf { w } ; \\mathcal { D } ) \\approx g _ { j } ( \\mathbf { w } ; \\mathcal { D } ) = \\left. \\frac { \\partial L ( \\mathbf { c } \\odot \\mathbf { w } ; \\mathcal { D } ) } { \\partial c _ { j } } \\right| _ { \\mathbf { c } = \\mathbf { 1 } } = \\operatorname* { l i m } _ { \\delta \\to 0 } \\left. \\frac { L ( \\mathbf { c } \\odot \\mathbf { w } ; \\mathcal { D } ) - L ( ( \\mathbf { c } - \\delta \\mathbf { e } _ { j } ) \\odot \\mathbf { w } ; \\mathcal { D } ) } { \\delta } \\right| _ { \\mathbf { c } = \\mathbf { 1 } } .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            181,
+            481,
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+            517
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In fact, $\\partial L / \\partial c _ { j }$ is an infinitesimal version of $\\Delta L _ { j }$ , that measures the rate of change of $L$ with respect to an infinitesimal change in $c _ { j }$ from $1  1 - \\delta$ . This can be computed efficiently in one forward-backward pass using automatic differentiation, for all $j$ at once. Notice, this formulation can be viewed as perturbing the weight $w _ { j }$ by a multiplicative factor $\\delta$ and measuring the change in loss. This approximation is similar in spirit to Koh & Liang (2017) where they try to measure the influence of a datapoint to the loss function. Here we measure the influence of connections. Furthermore, $\\partial L / \\partial c _ { j }$ is not to be confused with the gradient with respect to the weights $( \\partial L / \\partial w _ { j } )$ , where the change in loss is measured with respect to an additive change in weight $w _ { j }$ . ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Notably, our interest is to discover important (or sensitive) connections in the architecture, so that we can prune unimportant ones in single-shot, disentangling the pruning process from the iterative optimization cycles. To this end, we take the magnitude of the derivatives $g _ { j }$ as the saliency criterion. Note that if the magnitude of the derivative is high (regardless of the sign), it essentially means that the connection $c _ { j }$ has a considerable effect on the loss (either positive or negative), and it has to be preserved to allow learning on $w _ { j }$ . Based on this hypothesis, we define connection sensitivity as the normalized magnitude of the derivatives: ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/a8bb08f585f88b41a5785256eb41527e77555af8cf3e2c39ba70d686ef13e47a.jpg",
+        "text": "$$\ns _ { j } = \\frac { | g _ { j } ( \\mathbf { w } ; \\mathcal { D } ) | } { \\sum _ { k = 1 } ^ { m } | g _ { k } ( \\mathbf { w } ; \\mathcal { D } ) | } .\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Once the sensitivity is computed, only the top- $\\kappa$ connections are retained, where $\\kappa$ denotes the desired number of non-zero weights. Precisely, the indicator variables $\\mathbf { c }$ are set as follows: ",
+        "bbox": [
+            171,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/3bb568d384e6a4f34d439518abd1c66f802cd3f1ae4c509d77bbe48a995b13fe.jpg",
+        "text": "$$\nc _ { j } = \\mathbb { 1 } [ s _ { j } - \\tilde { s } _ { \\kappa } \\geq 0 ] , \\quad \\forall j \\in \\{ 1 \\ldots m \\} ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            359,
+            815,
+            635,
+            833
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where $\\tilde { s } _ { \\kappa }$ is the $\\kappa$ -th largest element in the vector s and $\\mathbb { 1 } [ \\cdot ]$ is the indicator function. Here, for exactly $\\kappa$ connections to be retained, ties can be broken arbitrarily. ",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We would like to clarify that the above criterion (Equation 6) is different from the criteria used in early works by Mozer & Smolensky (1989) or Karnin (1990) which do not entirely capture the connection sensitivity. The fundamental idea behind them is to identify elements (e.g. weights or neurons) that least degrade the performance when removed. This means that their saliency criteria (i.e. $- \\partial L / \\partial \\mathbf { w }$ or $- \\partial L / \\partial \\pmb { \\alpha }$ ; $_ { \\pmb { \\alpha } }$ refers to the connectivity of neurons), in fact, depend on the loss value before pruning, which in turn, require the network to be pre-trained and iterative optimization cycles to ensure minimal loss in performance. They also suffer from the same drawbacks as the magnitude and Hessian based methods as discussed in Section 3. In contrast, our saliency criterion (Equation 6) is designed to measure the sensitivity as to how much influence elements have on the loss function regardless of whether it is positive or negative. This criterion alleviates the dependency on the value of the loss, eliminating the need for pre-training. These fundamental differences enable the network to be pruned at single-shot prior to training, which we discuss further in the next section. ",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "table",
+        "img_path": "images/ba832c82fdeca45ec305823a28416cffe95432383608d5e24276e28ddf126a8e.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td colspan=\"3\">Algorithm1 SNIP: Single-shot Network Pruning based on Connection Sensitivity</td></tr><tr><td>Ensure: | w*|lo ≤ κ</td><td>Require: Loss function L, training dataset D, sparsity level K</td><td>Refer Equation 3</td></tr><tr><td></td><td>1:w_← VarianceScalingInitialization</td><td>Refer Section 4.2</td></tr><tr><td></td><td>2:Db={（xi,yi）}=1 ~D</td><td>&gt; Sample a mini-batch of training data</td></tr><tr><td>3:Sj←</td><td>l9j(w;Db) ∑=1l9k(（w;Db)l ， ∀j∈{1...m}</td><td>Connection sensitivity</td></tr><tr><td></td><td>4:s ← SortDescending(s)</td><td></td></tr><tr><td></td><td>5:cj←1[sj-$κ≥0]，∀j∈{1...m}</td><td>&gt;Pruning: choose top-k connections</td></tr><tr><td>7: w* ← c⊙w*</td><td>6: W* ← arg minw∈Rm L(c ③ w;D)</td><td>Regular training</td></tr></table>",
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+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.2 SINGLE-SHOT PRUNING AT INITIALIZATION",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Note that the saliency measure defined in Equation 6 depends on the value of weights w used to evaluate the derivative as well as the dataset $\\mathcal { D }$ and the loss function $L$ . In this section, we discuss the effect of each of them and show that it can be used to prune the network in single-shot with initial weights w. ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Firstly, in order to minimize the impact of weights on the derivatives $\\partial L / \\partial c _ { j }$ , we need to choose these weights carefully. For instance, if the weights are too large, the activations after the non-linear function (e.g., sigmoid) will be saturated, which would result in uninformative gradients. Therefore, the weights should be within a sensible range. In particular, there is a body of work on neural network initialization (Goodfellow et al. (2016)) that ensures the gradients to be in a reasonable range, and our saliency measure can be used to prune neural networks at any such initialization. ",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Furthermore, we are interested in making our saliency measure robust to architecture variations. Note that initializing neural networks is a random process, typically done using normal distribution. However, if the initial weights have a fixed variance, the signal passing through each layer no longer guarantees to have the same variance, as noted by LeCun et al. (1998). This would make the gradient and in turn our saliency measure, to be dependent on the architectural characteristics. Thus, we advocate the use of variance scaling methods (e.g., Glorot & Bengio (2010)) to initialize the weights, such that the variance remains the same throughout the network. By ensuring this, we empirically show that our saliency measure computed at initialization is robust to variations in the architecture. ",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Next, since the dataset and the loss function defines the task at hand, by relying on both of them, our saliency criterion in fact discovers the connections in the network that are important to the given task. However, the practitioner needs to make a choice on whether to use the whole training set, or a mini-batch or the validation set to compute the connection saliency. Moreover, in case there are memory limitations (e.g., large model or dataset), one can accumulate the saliency measure over multiple batches or take an exponential moving average. In our experiments, we show that using only one mini-batch of a reasonable number of training examples can lead to effective pruning. ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Finally, in contrast to the previous approaches, our criterion for finding redundant connections is simple and directly based on the sensitivity of the connections. This allows us to effectively identify and prune redundant connections in a single step even before training. Then, training can be performed on the resulting pruned (sparse) network. We name our method SNIP for Single-shot Network Pruning, and the complete algorithm is given in Algorithm 1. ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/3926bf85ac622a47d0b4130ae5dbb2c6cc89a43e80cedae36061229911cdf321.jpg",
+        "image_caption": [
+            "Figure 1: Test errors of LeNets pruned at varying sparsity levels $\\bar { \\kappa }$ , where $\\bar { \\kappa } = 0$ refers to the reference network trained without pruning. Our approach performs as good as the reference network across varying sparsity levels on both the models. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5 EXPERIMENTS ",
+        "text_level": 1,
+        "bbox": [
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+            330,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We evaluate our method, SNIP, on MNIST, CIFAR-10 and Tiny-ImageNet classification tasks with a variety of network architectures. Our results show that SNIP yields extremely sparse models with minimal or no loss in accuracy across all tested architectures, while being much simpler than other state-of-the-art alternatives. We also provide clear evidence that our method prunes genuinely explainable connections rather than performing blind pruning. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Experiment setup For brevity, we define the sparsity level to be $\\bar { \\kappa } = ( m - \\kappa ) / m \\cdot 1 0 0 ( \\% )$ , where $m$ is the total number of parameters and $\\kappa$ is the desired number of non-zero weights. For a given sparsity level $\\bar { \\kappa }$ , the sensitivity scores are computed using a batch of 100 and 128 examples for MNIST and CIFAR experiments, respectively. After pruning, the pruned network is trained in the standard way. Specifically, we train the models using SGD with momentum of 0.9, batch size of 100 for MNIST and 128 for CIFAR experiments and the weight decay rate of 0.0005, unless stated otherwise. The initial learning rate is set to 0.1 and decayed by 0.1 at every 25k or $3 0 \\mathrm { k }$ iterations for MNIST and CIFAR, respectively. Our algorithm requires no other hyperparameters or complex learning/pruning schedules as in most pruning algorithms. We spare $10 \\%$ of the training data as a validation set and used only $90 \\%$ for training. For CIFAR experiments, we use the standard data augmentation (i.e., random horizontal flip and translation up to 4 pixels) for both the reference and sparse models. The code can be found here: https://github.com/namhoonlee/snip-public. ",
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5.1 PRUNING LENETS WITH VARYING LEVELS OF SPARSITY ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We first test our approach on two standard networks for pruning, LeNet-300-100 and LeNet-5-Caffe. LeNet-300-100 consists of three fully-connected (fc) layers with $2 6 7 \\mathrm { k }$ parameters and LeNet-5-Caffe consists of two convolutional (conv) layers and two fc layers with 431k parameters. We prune the LeNets for different sparsity levels $\\bar { \\kappa }$ and report the performance in error on the MNIST image classification task. We run the experiment 20 times for each $\\bar { \\kappa }$ by changing random seeds for dataset and network initialization. The results are reported in Figure 1. ",
+        "bbox": [
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+        "page_idx": 5
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+    {
+        "type": "text",
+        "text": "The pruned sparse LeNet-300-100 achieves performances similar to the reference $( \\bar { \\kappa } = 0$ ), only with negligible loss at $\\bar { \\kappa } = 9 0$ . For LeNet-5-Caffe, the performance degradation is nearly invisible. Note that our saliency measure does not require the network to be pre-trained and is computed at random initialization. Despite such simplicity, our approach prunes LeNets quickly (single-shot) and effectively (minimal accuracy loss) at varying sparsity levels. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5.2 COMPARISONS TO EXISTING APPROACHES",
+        "text_level": 1,
+        "bbox": [
+            178,
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "What happens if we increase the target sparsity to an extreme level? For example, would a model with only $1 \\%$ of the total parameters still be trainable and perform well? We test our approach for extreme sparsity levels (e.g., up to $9 9 \\%$ sparsity on LeNet-5-Caffe) and compare with various pruning algorithms as follows: LWC (Han et al. (2015)), DNS (Guo et al. (2016)), LC (Carreira-Perpin˜ an & ´ ",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/c5c09ddcf38a7e654111aab6f939c07bb19eb493c1e1176b36e965541c1d4383.jpg",
+        "table_caption": [
+            "Table 1: Pruning results on LeNets and comparisons to other approaches. Here, “many” refers to an arbitrary number often in the order of total learning steps, and “soft” refers to soft pruning in Bayesian based methods. Our approach is capable of pruning up to $98 \\%$ for LeNet-300-100 and $9 9 \\%$ for LeNet-5-Caffe with marginal increases in error from the reference network. Notably, our approach is considerably simpler than other approaches, with no requirements such as pretraining, additional hyperparameters, augmented training objective or architecture dependent constraints. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td rowspan=\"2\">Criterion</td><td colspan=\"2\">LeNet-300-100</td><td colspan=\"2\">LeNet-5-Caffe</td><td rowspan=\"2\">Pretrain</td><td rowspan=\"2\">#Prune</td><td rowspan=\"2\">Additional hyperparam.</td><td rowspan=\"2\">Augment objective</td><td rowspan=\"2\">Arch. constraints</td></tr><tr><td>K(%)</td><td>err. (%)</td><td>K(%)</td><td>err. (%)</td></tr><tr><td>Ref.</td><td></td><td></td><td>1.7</td><td>一</td><td>0.9</td><td></td><td>1</td><td>-&gt;</td><td>-xx&gt;</td><td>√</td></tr><tr><td>LWC</td><td>Magnitude</td><td>91.7</td><td>1.6</td><td>91.7</td><td>0.8</td><td></td><td>many</td><td></td><td></td><td></td></tr><tr><td>DNS</td><td>Magnitude</td><td>98.2</td><td>2.0</td><td>99.1</td><td>0.9</td><td></td><td>many</td><td></td><td></td><td>√</td></tr><tr><td>LC</td><td>Magnitude</td><td>99.0</td><td>3.2</td><td>99.0</td><td>1.1</td><td></td><td>many</td><td>√</td><td></td><td>X</td></tr><tr><td>SWS</td><td>Bayesian</td><td>95.6</td><td>1.9</td><td>99.5</td><td>1.0</td><td></td><td>soft</td><td>√</td><td>√</td><td>X</td></tr><tr><td>SVD</td><td>Bayesian</td><td>98.5</td><td>1.9</td><td>99.6</td><td>0.8</td><td>-&gt;&gt;&gt;&gt;&gt;</td><td>soft</td><td>√</td><td>√</td><td>X</td></tr><tr><td>OBD</td><td>Hessian</td><td>92.0</td><td>2.0</td><td>92.0</td><td>2.7</td><td>√</td><td>many</td><td>√</td><td>X</td><td>X</td></tr><tr><td>L-OBS</td><td>Hessian</td><td>98.5</td><td>2.0</td><td>99.0</td><td>2.1</td><td>√</td><td>many</td><td>√</td><td>X</td><td>√</td></tr><tr><td rowspan=\"2\">SNIP (ours)</td><td>Connection</td><td>95.0</td><td>1.6</td><td>98.0</td><td>0.8</td><td>×</td><td></td><td>×</td><td>×</td><td>×</td></tr><tr><td>sensitivity</td><td>98.0</td><td>2.4</td><td>99.0</td><td>1.1</td><td></td><td>1</td><td></td><td></td><td></td></tr></table>",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Idelbayev (2018)), SWS (Ullrich et al. (2017)), SVD (Molchanov et al. (2017a)), OBD (LeCun et al.   \n(1990)), L-OBS (Dong et al. (2017)). The results are summarized in Table 1. ",
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+    {
+        "type": "text",
+        "text": "We achieve errors that are comparable to the reference model, degrading approximately $0 . 7 \\%$ and $0 . 3 \\%$ while pruning $98 \\%$ and $9 9 \\%$ of the parameters in LeNet-300-100 and LeNet-5-Caffe respectively. For slightly relaxed sparsities (i.e., $9 5 \\%$ for LeNet-300-100 and $98 \\%$ for LeNet-5-Caffe), the sparse models pruned by SNIP record better performances than the dense reference network. Considering $9 9 \\%$ sparsity, our method efficiently finds $1 \\%$ of the connections even before training, that are sufficient to learn as good as the reference network. Moreover, SNIP is competitive to other methods, yet it is unparalleled in terms of algorithm simplicity. ",
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+        "type": "text",
+        "text": "To be more specific, we enumerate some key points and non-trivial aspects of other algorithms and highlight the benefit of our approach. First of all, the aforementioned methods require networks to be fully trained (if not partly) before pruning. These approaches typically perform many pruning operations even if the network is well pretrained, and require additional hyperparameters (e.g., pruning frequency in Guo et al. (2016), annealing schedule in Carreira-Perpin˜an & Idelbayev (2018)). Some ´ methods augment the training objective to handle pruning together with training, increasing the complexity of the algorithm (e.g., augmented Lagrangian in Carreira-Perpin˜an & Idelbayev (2018), ´ variational inference in Molchanov et al. (2017a)). Furthermore, there are approaches designed to include architecture dependent constraints (e.g., layer-wise pruning schemes in Dong et al. (2017)). ",
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+        "type": "text",
+        "text": "Compared to the above approaches, ours seems to cost almost nothing; it requires no pretraining or additional hyperparameters, and is applied only once at initialization. This means that one can easily plug-in SNIP as a preprocessor before training neural networks. Since SNIP prunes the network at the beginning, we could potentially expedite the training phase by training only the survived parameters (e.g., reduced expected FLOPs in Louizos et al. (2018)). Notice that this is not possible for the aforementioned approaches as they obtain the maximum sparsity at the end of the process. ",
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+    {
+        "type": "text",
+        "text": "5.3 VARIOUS MODERN ARCHITECTURES ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "In this section we show that our approach is generally applicable to more complex modern network architectures including deep convolutional, residual and recurrent ones. Specifically, our method is applied to the following models: ",
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+        "type": "text",
+        "text": "• AlexNet-s and AlexNet-b: Models similar to Krizhevsky et al. (2012) in terms of the number of layers and size of kernels. We set the size of fc layers to 512 (AlexNet-s) and to 1024 (AlexNet-b) to adapt for CIFAR-10 and use strides of 2 for all conv layers instead of using pooling layers. • VGG-C, VGG-D and VGG-like: Models similar to the original VGG models described in Simonyan & Zisserman (2015). VGG-like (Zagoruyko (2015)) is a popular variant adapted for CIFAR-10 which has one less fc layers. For all VGG models, we set the size of fc layers to 512, remove dropout layers to avoid any effect on sparsification and use batch normalization instead. • WRN-16-8, WRN-16-10 and WRN-22-8: Same models as in Zagoruyko & Komodakis (2016). ",
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+        "table_caption": [],
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+        "table_body": "<table><tr><td>Architecture</td><td>Model</td><td>Sparsity (%)</td><td># Parameters</td><td>Error (%)</td><td></td><td>△</td></tr><tr><td rowspan=\"5\">Convolutional</td><td>AlexNet-s</td><td>90.0</td><td>5.1m → 507k</td><td>14.12 →</td><td>14.99</td><td>+0.87</td></tr><tr><td>AlexNet-b</td><td>90.0</td><td>8.5m → 849k</td><td>13.92 →</td><td>14.50</td><td>+0.58</td></tr><tr><td>VGG-C</td><td>95.0</td><td>10.5m → 526k</td><td>6.82 →</td><td>7.27</td><td>+0.45</td></tr><tr><td>VGG-D</td><td>95.0</td><td>15.2m → 762k</td><td>6.76 →</td><td>7.09</td><td>+0.33</td></tr><tr><td>VGG-like</td><td>97.0</td><td>15.0m → 449k</td><td>8.26 →</td><td>8.00</td><td>-0.26</td></tr><tr><td rowspan=\"3\">Residual</td><td>WRN-16-8</td><td>95.0</td><td>10.0m → 548k</td><td>6.21 →</td><td>6.63</td><td>+0.42</td></tr><tr><td>WRN-16-10</td><td>95.0</td><td>17.1m → 856k</td><td>5.91 →</td><td>6.43</td><td>+0.52</td></tr><tr><td>WRN-22-8</td><td>95.0</td><td>17.2m → 858k</td><td>6.14 →</td><td>5.85</td><td>-0.29</td></tr><tr><td rowspan=\"4\">Recurrent</td><td>LSTM-s</td><td>95.0</td><td>137k → 6.8k</td><td>1.88 →</td><td>1.57</td><td>-0.31</td></tr><tr><td>LSTM-b</td><td>95.0</td><td>535k → 26.8k</td><td>1.15 →</td><td>1.35</td><td>+0.20</td></tr><tr><td>GRU-s</td><td>95.0</td><td>104k → 5.2k</td><td>1.87 →</td><td>2.41</td><td>+0.54</td></tr><tr><td>GRU-b</td><td>95.0</td><td>404k→ 20.2k</td><td>1.71 →</td><td>1.52</td><td>-0.19</td></tr></table>",
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+        "type": "text",
+        "text": "Table 2: Pruning results of the proposed approach on various modern architectures (before after). AlexNets, VGGs and WRNs are evaluated on CIFAR-10, and LSTMs and GRUs are evaluated on the sequential MNIST classification task. The approach is generally applicable regardless of architecture types and models and results in a significant amount of reduction in the number of parameters with minimal or no loss in performance. ",
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+        "text": "• LSTM-s, LSTM-b, GRU-s, GRU-b: One layer RNN networks with either LSTM (Zaremba et al. (2014)) or GRU (Cho et al. (2014)) cells. We develop two unit sizes for each cell type, 128 and 256 for $\\{ \\cdot \\}$ -s and $\\{ \\cdot \\}$ -b, respectively. The model is adapted for the sequential MNIST classification task, similar to Le et al. (2015). Instead of processing pixel-by-pixel, however, we perform rowby-row processing (i.e., the RNN cell receives each row at a time). ",
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+        "type": "text",
+        "text": "The results are summarized in Table 2. Overall, our approach prunes a substantial amount of parameters in a variety of network models with minimal or no loss in accuracy $( < 1 \\% )$ . Our pruning procedure does not need to be modified for specific architectural variations (e.g., recurrent connections), indicating that it is indeed versatile and scalable. Note that prior art that use a saliency criterion based on the weights (i.e., magnitude or Hessian based) would require considerable adjustments in their pruning schedules as per changes in the model. ",
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+    {
+        "type": "text",
+        "text": "We note of a few challenges in directly comparing against others: different network specifications, learning policies, datasets and tasks. Nonetheless, we provide a few comparison points that we found in the literature. On CIFAR-10, SVD prunes $9 7 . 9 \\%$ of the connections in VGG-like with no loss in accuracy (ours: $9 7 \\%$ sparsity) while SWS obtained $9 3 . 4 \\%$ sparsity on WRN-16-4 but with a non-negligible loss in accuracy of $2 \\%$ . There are a couple of works attempting to prune RNNs (e.g., GRU in Narang et al. (2017) and LSTM in See et al. (2016)). Even though these methods are specifically designed for RNNs, none of them are able to obtain extreme sparsity without substantial loss in accuracy reflecting the challenges of pruning RNNs. To the best of our knowledge, we are the first to demonstrate on convolutional, residual and recurrent networks for extreme sparsities without requiring additional hyperparameters or modifying the pruning procedure. ",
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+    {
+        "type": "text",
+        "text": "5.4 UNDERSTANDING WHICH CONNECTIONS ARE BEING PRUNED ",
+        "text_level": 1,
+        "bbox": [
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+        "type": "text",
+        "text": "So far we have shown that our approach can prune a variety of deep neural network architectures for extreme sparsities without losing much on accuracy. However, it is not clear yet which connections are actually being pruned away or whether we are pruning the right (i.e., unimportant) ones. What if we could actually peep through our approach into this inspection? ",
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+        "type": "text",
+        "text": "Consider the first layer in LeNet-300-100 parameterized by $\\mathbf { w } _ { l = 1 } ~ \\in ~ \\mathbb { R } ^ { 7 8 4 \\times 3 0 0 }$ . This is a layer fully connected to the input where input images are of size $2 8 \\times 2 8 \\ : = \\ : 7 8 4$ . In order to understand which connections are retained, we can visualize the binary connectivity mask for this layer $\\mathbf { c } _ { l = 1 }$ , by averaging across columns and then reshaping the vector into 2D matrix (i.e., $\\begin{array} { r } { \\mathbf { c } _ { l = 1 } ^ { \\check { } } \\in \\{ \\bar { 0 } , 1 \\} ^ { \\check { } 8 4 \\times 3 0 \\widetilde { 0 } }  \\mathbb { R } ^ { 7 8 4 }  \\mathbb { R } ^ { 2 8 \\times 2 8 } } \\end{array}$ ). Recall that our method computes c using a minibatch of examples. In this experiment, we curate the mini-batch of examples of the same class and see which weights are retained for that mini-batch of data. We repeat this experiment for all classes (i.e., digits for MNIST and fashion items for Fashion-MNIST) with varying sparsity levels $\\bar { \\kappa }$ . The results are displayed in Figure 2 (see Appendix A for more results). ",
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+    {
+        "type": "image",
+        "img_path": "images/0f4107c55d7dc6d96c089d84572497bc1ec5a1fdb8c53251ac813dd698b02584.jpg",
+        "image_caption": [
+            "Figure 2: Visualizations of pruned parameters of the first layer in LeNet-300-100; the parameters are reshaped to be visualized as an image. Each column represents the visualizations for a particular class obtained using a batch of 100 examples with varying levels of sparsity $\\bar { \\kappa }$ , from 10 (top) to 90 (bottom). Bright pixels indicate that the parameters connected to these region had high importance scores (s) and survived from pruning. As the sparsity increases, the parameters connected to the discriminative part of the image for classification survive and the irrelevant parts get pruned. "
+        ],
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+        "type": "text",
+        "text": "",
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+        "type": "text",
+        "text": "The results are significant; important connections seem to reconstruct either the complete image (MNIST) or silhouettes (Fashion-MNIST) of input class. When we use a batch of examples of the digit 0 (i.e., the first column of MNIST results), for example, the parameters connected to the foreground of the digit 0 survive from pruning while the majority of background is removed. Also, one can easily determine the identity of items from Fashion-MNIST results. This clearly indicates that our method indeed prunes the unimportant connections in performing the classification task, receiving signals only from the most discriminative part of the input. This stands in stark contrast to other pruning methods from which carrying out such inspection is not straightforward. ",
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+    {
+        "type": "text",
+        "text": "5.5 EFFECTS OF DATA AND WEIGHT INITIALIZATION",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Recall that our connection saliency measure depends on the network weights w as well as the given data $\\mathcal { D }$ (Section 4.2). We study the effect of each of these in this section. ",
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+    {
+        "type": "text",
+        "text": "Effect of data. Our connection saliency measure depends on a mini-batch of train examples $\\mathcal { D } ^ { b }$ (see Algorithm 1). To study the effect of data, we vary the batch size used to compute the saliency $( | \\mathcal { D } ^ { b } | )$ and check which connections are being pruned as well as how much performance change this results in on the corresponding sparse network. We test with LeNet-300-100 to visualize the remaining parameters, and set the sparsity level $\\bar { \\kappa } = 9 0$ . Note that the batch size used for training remains the same as 100 for all cases. The results are displayed in Figure 3. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Effect of initialization. Our approach prunes a network at a stochastic initialization as discussed. We study the effect of the following initialization methods: 1) RN (random normal), 2) TN (truncated random normal), 3) VS-X (a variance scaling method using Glorot & Bengio (2010)), and 4) VS-H (a variance scaling method He et al. (2015)). We test on LeNets and RNNs on MNIST and run 20 sets of experiments by varying the seed for initialization. We set the sparsity level $\\bar { \\kappa } = 9 0$ , and train with Adam optimizer (Kingma & Ba (2015)) with learning rate of 0.001 without weight decay. Note that for training VS-X initialization is used in all the cases. The results are reported in Figure 3. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "For all models, VS-H achieves the best performance. The differences between initializers are marginal on LeNets, however, variance scaling methods indeed turns out to be essential for complex RNN models. This effect is significant especially for GRU where without variance scaling initialization, the pruned networks are unable to achieve good accuracies, even with different optimizers. Overall, initializing with a variance scaling method seems crucial to making our saliency measure reliable and model-agnostic. ",
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+        "img_path": "images/0571d02738677c85bfcc4968a17cec170d1e05716329724896a5e65b46ef5437.jpg",
+        "image_caption": [],
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+    },
+    {
+        "type": "table",
+        "img_path": "images/a505a44a37956c2130096a5ae7d1716db983bfb2c703887f7d1cd3760d02587e.jpg",
+        "table_caption": [
+            "Figure 3: The effect of different batch sizes: (top-row) survived parameters in the first layer of LeNet-300-100 from pruning visualized as images; (bottom-row) the performance in errors of the pruned networks. For $| \\mathcal { D } ^ { b } | \\overset { - } { = } 1$ , the sampled example was 8; our pruning precisely retains the valid connections. As $| \\mathcal { D } ^ { b } |$ increases, survived parameters get close to the average of all examples in the train set (last column), and the error decreases. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Init.</td><td>LeNet-300-100</td><td>LeNet-5-Caffe</td><td>LSTM-s</td><td>GRU-s</td></tr><tr><td>RN</td><td>1.90 ± (0.09)</td><td>0.89 ± (0.04)</td><td>2.93 ± (0.20)</td><td>47.61 ± (20.49)</td></tr><tr><td>TN</td><td>1.96 ± (0.11)</td><td>0.87 ± (0.05)</td><td>3.03 ± (0.17)</td><td>46.48± (22.25)</td></tr><tr><td>VS-X</td><td>1.91 ± (0.10)</td><td>0.88 ± (0.07)</td><td>1.48 ± (0.09)</td><td>1.80 ± (0.10)</td></tr><tr><td>VS-H</td><td>1.88 ± (0.10)</td><td>0.85 ± (0.05)</td><td>1.47 ± (0.08)</td><td>1.80 ± (0.14)</td></tr></table>",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Table 3: The effect of initialization on our saliency score. We report the classification errors ( $\\pm$ std).   \nVariance scaling initialization (VS-X, VS-H) improves the performance, especially for RNNs. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "5.6 FITTING RANDOM LABELS ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "To further explore the use cases of SNIP, we run the experiment introduced in Zhang et al. (2017) and check whether the sparse network obtained by SNIP memorizes the dataset. Specifically, we train LeNet-5-Caffe for both the reference model and pruned model (with $\\bar { \\kappa } = 9 9 $ ) on MNIST with either true or randomly shuffled labels. To compute the connection sensitivity, always true labels are used. The results are plotted in Figure 4. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Given true labels, both the reference (red) and pruned (blue) models quickly reach to almost zero training loss. However, the reference model provided with random labels (green) also reaches to very low training loss, even with an explicit L2 regularizer (purple), indicating that neural networks have enough capacity to memorize completely random data. In contrast, the model pruned by SNIP (orange) fails to fit the random labels (high training error). The potential explanation is that the pruned network does not have sufficient capacity to fit the random labels, but it is able to classify MNIST with true labels, reinforcing the significance of our saliency criterion. It is possible that a similar experiment can be done with other pruning methods (Molchanov et al. (2017a)), however, being simple, SNIP enables such exploration much easier. We provide a further analysis on the effect of varying $\\bar { \\kappa }$ in Appendix B. ",
+        "bbox": [
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+    },
+    {
+        "type": "image",
+        "img_path": "images/9a651ab94be553eb9324682211e6a7c4d4dcea5b1a266aa2431d015c01647a2d.jpg",
+        "image_caption": [
+            "Figure 4: The sparse model pruned by SNIP does not fit the random labels. "
+        ],
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+        "text": "",
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+    {
+        "type": "text",
+        "text": "6 DISCUSSION AND FUTURE WORK ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "In this work, we have presented a new approach, SNIP, that is simple, versatile and interpretable; it prunes irrelevant connections for a given task at single-shot prior to training and is applicable to a variety of neural network models without modifications. While SNIP results in extremely sparse models, we find that our connection sensitivity measure itself is noteworthy in that it diagnoses important connections in the network from a purely untrained network. We believe that this opens up new possibilities beyond pruning in the topics of understanding of neural network architectures, multi-task transfer learning and structural regularization, to name a few. In addition to these potential directions, we intend to explore the generalization capabilities of sparse networks. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "ACKNOWLEDGEMENTS ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "This work was supported by the Korean Government Graduate Scholarship, the ERC grant ERC2012-AdG 321162-HELIOS, EPSRC grant Seebibyte EP/M013774/1 and EPSRC/MURI grant EP/N019474/1. We would also like to acknowledge the Royal Academy of Engineering and FiveAI. ",
+        "bbox": [
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+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "REFERENCES ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            190,
+            287,
+            207
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Sanjeev Arora, Rong Ge, Behnam Neyshabur, and Yi Zhang. Stronger generalization bounds for deep nets via a compression approach. ICML, 2018. ",
+        "bbox": [
+            174,
+            214,
+            823,
+            243
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Leo Breiman. Better subset regression using the nonnegative garrote. Technometrics, 1995. ",
+        "bbox": [
+            169,
+            252,
+            772,
+            267
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Miguel A. Carreira-Perpi ´ n˜an and Yerlan Idelbayev. “Learning-compression” algorithms for neural ´ net pruning. CVPR, 2018. ",
+        "bbox": [
+            173,
+            277,
+            823,
+            306
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Yves Chauvin. A back-propagation algorithm with optimal use of hidden units. NIPS, 1989. ",
+        "bbox": [
+            178,
+            315,
+            781,
+            332
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Kyunghyun Cho, Bart Van Merrienboer, Caglar Gulcehre, Dzmitry Bahdanau, Fethi Bougares, Hol- ¨ ger Schwenk, and Yoshua Bengio. Learning phrase representations using rnn encoder-decoder for statistical machine translation. EMNLP, 2014. ",
+        "bbox": [
+            176,
+            339,
+            825,
+            382
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Xin Dong, Shangyu Chen, and Sinno Pan. Learning to prune deep neural networks via layer-wise optimal brain surgeon. NIPS, 2017. ",
+        "bbox": [
+            171,
+            391,
+            823,
+            421
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Xavier Glorot and Yoshua Bengio. Understanding the difficulty of training deep feedforward neural networks. AISTATS, 2010. ",
+        "bbox": [
+            171,
+            429,
+            823,
+            458
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Yunchao Gong, Liu Liu, Ming Yang, and Lubomir Bourdev. Compressing deep convolutional networks using vector quantization. arXiv preprint arXiv:1412.6115, 2014. ",
+        "bbox": [
+            171,
+            467,
+            823,
+            497
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Ian Goodfellow, Yoshua Bengio, Aaron Courville, and Yoshua Bengio. Deep learning. MIT press Cambridge, 2016. ",
+        "bbox": [
+            173,
+            505,
+            823,
+            535
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Yiwen Guo, Anbang Yao, and Yurong Chen. Dynamic network surgery for efficient dnns. NIPS, 2016. ",
+        "bbox": [
+            176,
+            542,
+            823,
+            573
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Suyog Gupta, Ankur Agrawal, Kailash Gopalakrishnan, and Pritish Narayanan. Deep learning with limited numerical precision. ICML, 2015. ",
+        "bbox": [
+            174,
+            580,
+            823,
+            611
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Song Han, Jeff Pool, John Tran, and William Dally. Learning both weights and connections for efficient neural network. NIPS, 2015. ",
+        "bbox": [
+            174,
+            618,
+            823,
+            648
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Babak Hassibi, David G Stork, and Gregory J Wolff. Optimal brain surgeon and general network pruning. Neural Networks, 1993. ",
+        "bbox": [
+            176,
+            656,
+            823,
+            686
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Delving deep into rectifiers: Surpassing human-level performance on imagenet classification. ICCV, 2015. ",
+        "bbox": [
+            174,
+            694,
+            823,
+            724
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Itay Hubara, Matthieu Courbariaux, Daniel Soudry, Ran El-Yaniv, and Yoshua Bengio. Binarized neural networks. NIPS, 2016. ",
+        "bbox": [
+            174,
+            732,
+            823,
+            762
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Masumi Ishikawa. Structural learning with forgetting. Neural Networks, 1996. ",
+        "bbox": [
+            173,
+            771,
+            694,
+            786
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Max Jaderberg, Andrea Vedaldi, and Andrew Zisserman. Speeding up convolutional neural networks with low rank expansions. BMVC, 2014. ",
+        "bbox": [
+            173,
+            795,
+            820,
+            824
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Ehud D Karnin. A simple procedure for pruning back-propagation trained neural networks. Neural Networks, 1990. ",
+        "bbox": [
+            174,
+            833,
+            823,
+            862
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Diederik P Kingma and Jimmy Ba. Adam: A method for stochastic optimization. ICLR, 2015. ",
+        "bbox": [
+            173,
+            871,
+            792,
+            887
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Pang Wei Koh and Percy Liang. Understanding black-box predictions via influence functions. ICML, 2017. ",
+        "bbox": [
+            173,
+            895,
+            821,
+            922
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Alex Krizhevsky, Ilya Sutskever, and Geoffrey E Hinton. Imagenet classification with deep convolutional neural networks. 2012. ",
+        "bbox": [
+            171,
+            103,
+            823,
+            132
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Quoc V Le, Navdeep Jaitly, and Geoffrey E Hinton. A simple way to initialize recurrent networks of rectified linear units. CoRR, 2015. ",
+        "bbox": [
+            174,
+            138,
+            823,
+            169
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Yann LeCun, John S Denker, and Sara A Solla. Optimal brain damage. NIPS, 1990. ",
+        "bbox": [
+            174,
+            175,
+            727,
+            190
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Yann LeCun, Leon Bottou, Genevieve B. Orr, and Klaus-Robert M ´ uller. Efficient backprop. ¨ Neural Networks: Tricks of the Trade, 1998. ",
+        "bbox": [
+            176,
+            198,
+            823,
+            227
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Hao Li, Asim Kadav, Igor Durdanovic, Hanan Samet, and Hans Peter Graf. Pruning filters for efficient convnets. ICLR, 2017. ",
+        "bbox": [
+            173,
+            233,
+            823,
+            263
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Christos Louizos, Max Welling, and Diederik P Kingma. Learning sparse neural networks through $l _ { 0 }$ regularization. ICLR, 2018. ",
+        "bbox": [
+            173,
+            270,
+            821,
+            299
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Decebal Constantin Mocanu, Elena Mocanu, Peter Stone, Phuong H Nguyen, Madeleine Gibescu, and Antonio Liotta. Scalable training of artificial neural networks with adaptive sparse connectivity inspired by network science. Nature Communications, 2018. ",
+        "bbox": [
+            174,
+            305,
+            820,
+            349
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Dmitry Molchanov, Arsenii Ashukha, and Dmitry Vetrov. Variational dropout sparsifies deep neural networks. ICML, 2017a. ",
+        "bbox": [
+            173,
+            356,
+            823,
+            386
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Pavlo Molchanov, Stephen Tyree, Tero Karras, Timo Aila, and Jan Kautz. Pruning convolutional neural networks for resource efficient inference. ICLR, 2017b. ",
+        "bbox": [
+            173,
+            392,
+            823,
+            421
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Michael C Mozer and Paul Smolensky. Skeletonization: A technique for trimming the fat from a network via relevance assessment. NIPS, 1989. ",
+        "bbox": [
+            173,
+            428,
+            823,
+            458
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Sharan Narang, Erich Elsen, Gregory Diamos, and Shubho Sengupta. Exploring sparsity in recurrent neural networks. ICLR, 2017. ",
+        "bbox": [
+            176,
+            464,
+            823,
+            493
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Alexander Novikov, Dmitrii Podoprikhin, Anton Osokin, and Dmitry P Vetrov. Tensorizing neural networks. NIPS, 2015. ",
+        "bbox": [
+            174,
+            500,
+            823,
+            530
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Steven J Nowlan and Geoffrey E Hinton. Simplifying neural networks by soft weight-sharing. Neural Computation, 1992. ",
+        "bbox": [
+            173,
+            536,
+            823,
+            565
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Ameya Prabhu, Girish Varma, and Anoop Namboodiri. Deep expander networks: Efficient deep networks from graph theory. ECCV, 2018. ",
+        "bbox": [
+            171,
+            571,
+            823,
+            602
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Russell Reed. Pruning algorithms-a survey. Neural Networks, 1993. ",
+        "bbox": [
+            173,
+            608,
+            622,
+            625
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Abigail See, Minh-Thang Luong, and Christopher D Manning. Compression of neural machine translation models via pruning. CoNLL, 2016. ",
+        "bbox": [
+            173,
+            631,
+            818,
+            661
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Karen Simonyan and Andrew Zisserman. Very deep convolutional networks for large-scale image recognition. ICLR, 2015. ",
+        "bbox": [
+            173,
+            666,
+            823,
+            696
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Karen Ullrich, Edward Meeds, and Max Welling. Soft weight-sharing for neural network compression. ICLR, 2017. ",
+        "bbox": [
+            173,
+            703,
+            823,
+            733
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Andreas S Weigend, David E Rumelhart, and Bernardo A Huberman. Generalization by weightelimination with application to forecasting. NIPS, 1991. ",
+        "bbox": [
+            171,
+            739,
+            823,
+            768
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Wei Wen, Chunpeng Wu, Yandan Wang, Yiran Chen, and Hai Li. Learning structured sparsity in deep neural networks. NIPS, 2016. ",
+        "bbox": [
+            174,
+            775,
+            823,
+            805
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Sergey Zagoruyko. $9 2 . 4 5 \\%$ on cifar-10 in torch. Torch Blog, 2015. ",
+        "bbox": [
+            174,
+            811,
+            614,
+            827
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Sergey Zagoruyko and Nikos Komodakis. Wide residual networks. BMVC, 2016. ",
+        "bbox": [
+            174,
+            834,
+            707,
+            849
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Wojciech Zaremba, Ilya Sutskever, and Oriol Vinyals. Recurrent neural network regularization. arXiv preprint arXiv:1409.2329, 2014. ",
+        "bbox": [
+            173,
+            856,
+            821,
+            886
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Chiyuan Zhang, Samy Bengio, Moritz Hardt, Benjamin Recht, and Oriol Vinyals. Understanding deep learning requires rethinking generalization. ICLR, 2017. ",
+        "bbox": [
+            173,
+            892,
+            823,
+            921
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "image",
+        "img_path": "images/cc69ae2f5789c064a9d7ec25c2cae8be85125a7807f27c075058ab31684ccd3c.jpg",
+        "image_caption": [
+            "Figure 5: Results of pruning with SNIP on inverted (Fashion-)MNIST (i.e., dark and bright regions are swapped). Notably, even if the data is inverted, the results are the same as the ones on the original (Fashion-)MNIST in Figure 2. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            200,
+            138,
+            797,
+            330
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "image",
+        "img_path": "images/7e10adb4cd3b78aa3523f4d7e8ead3c6621045e90fb560498f3758f598063b9e.jpg",
+        "image_caption": [
+            "Figure 6: Results of pruning with $\\partial L / \\partial$ w on the original and inverted (Fashion-)MNIST. Notably, compared to the case of using SNIP (Figures 2 and 5), the results are different: Firstly, the results on the original (Fashion-)MNIST (i.e., (a) and (c) above) are not the same as the ones using SNIP (i.e., (a) and (b) in Figure 2). Moreover, the pruning patterns are inconsistent with different sparsity levels, either intra-class or inter-class. Furthermore, using ${ \\partial L } / { \\partial \\mathbf { w } }$ results in different pruning patterns between the original and inverted data in some cases (e.g., the $2 ^ { \\mathrm { n d } }$ columns between (c) and (d)). "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            200,
+            407,
+            797,
+            791
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "image",
+        "img_path": "images/2c60ed92201d216f7acfecb7839cd7dcf12f0266b4e0e0b0daf88b490479c204.jpg",
+        "image_caption": [
+            "Figure 7: The effect of varying sparsity levels $\\left( \\hat { \\kappa } \\right)$ . The lower $\\bar { \\kappa }$ becomes, the lower training loss is recorded, meaning that a network with more parameters is more vulnerable to fitting random labels. Recall, however, that all pruned models are able to learn to perform the classification task without losing much accuracy (see Figure 1). This potentially indicates that the pruned network does not have sufficient capacity to fit the random labels, but it is capable of performing the classification. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            315,
+            146,
+            676,
+            364
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "C TINY-IMAGENET ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            491,
+            346,
+            507
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "table",
+        "img_path": "images/a890875fcc5d4f00a5d82860fb17b436412cb4053d5263657ca571f91ea9cdab.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Architecture</td><td>Model</td><td>Sparsity (%)</td><td># Parameters</td><td>Error (%)</td><td>△</td></tr><tr><td rowspan=\"5\">Convolutional</td><td>AlexNet-s</td><td>90.0</td><td>5.1m → 507k</td><td>62.52 → 65.27</td><td>+2.75</td></tr><tr><td>AlexNet-b</td><td>90.0</td><td>8.5m → 849k</td><td>62.76 → 65.54</td><td>+2.78</td></tr><tr><td>VGG-C</td><td>95.0</td><td>10.5m → 526k</td><td>56.49 → 57.48</td><td>+0.99</td></tr><tr><td>VGG-D</td><td>95.0</td><td>15.2m → 762k</td><td>56.85 → 57.00</td><td>+0.15</td></tr><tr><td>VGG-like</td><td>95.0</td><td>15.0m → 749k</td><td>54.86 → 55.73</td><td>+0.87</td></tr></table>",
+        "bbox": [
+            209,
+            526,
+            789,
+            618
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "Table 4: Pruning results of SNIP on Tiny-ImageNet (before after). Tiny-ImageNet2 is a subset of the full ImageNet: there are 200 classes in total, each class has 500 and 50 images for training and validation respectively, and each image has the spatial resolution of $6 4 \\times 6 4$ . Compared to CIFAR-10, the resolution is doubled, and to deal with this, the stride of the first convolution in all architectures is doubled, following the standard practice for this dataset. In general, the Tiny-ImageNet classification task is considered much more complex than MNIST or CIFAR-10. Even on Tiny-ImageNet, however, SNIP is still able to prune a large amount of parameters with minimal loss in performance. AlexNet models lose more accuracies than VGGs, which may be attributed to the fact that the first convolution stride for AlexNet is set to be 4 (by its design of no pooling) which is too large and could lead to high loss of information when pruned. ",
+        "bbox": [
+            173,
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+            768
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "table",
+        "img_path": "images/c5b1c3e32d6a5912780b2b0fa9d9c37ee7cb52c76c52ffcb318e5b2010d8f23e.jpg",
+        "table_caption": [
+            "D ARCHITECTURE DETAILS "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=1 colspan=8>Module         Weight         Stride     Bias      BatchNorm  ReLU</td></tr><tr><td rowspan=1 colspan=1>Conv</td><td rowspan=1 colspan=1>[11,11, 3,96]</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>[2,2]</td><td rowspan=1 colspan=3>[96]          √</td><td rowspan=1 colspan=1>√</td></tr><tr><td rowspan=1 colspan=1>Conv</td><td rowspan=1 colspan=1>[5,5,96,256]</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>2j</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>[256]</td><td rowspan=1 colspan=1>√</td><td rowspan=1 colspan=1></td></tr><tr><td rowspan=1 colspan=1>Conv</td><td rowspan=1 colspan=1>[3,3,256,384]</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>2.2</td><td rowspan=1 colspan=2>[384]</td><td rowspan=1 colspan=2>√</td></tr><tr><td rowspan=1 colspan=1>Conv</td><td rowspan=1 colspan=1>[3,3,384,384]</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=5>[384]</td></tr><tr><td rowspan=1 colspan=1>Conv</td><td rowspan=1 colspan=1>[3,3,384,256]</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>2,2</td><td rowspan=1 colspan=2>[256]</td><td rowspan=1 colspan=2>（</td></tr><tr><td rowspan=1 colspan=1>Linear</td><td rowspan=1 colspan=1>[256,1024 ×k]</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=3>[1024×k]       √</td><td rowspan=1 colspan=1>√</td></tr><tr><td rowspan=1 colspan=3>Linear  [1024 × k,1024 ×k]</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=3>[1024 × k]       √</td><td rowspan=1 colspan=1>√</td></tr><tr><td rowspan=1 colspan=8>Linear       [1024 × k,c]                    [c]           X         X</td></tr></table>",
+        "bbox": [
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+        "page_idx": 14
+    },
+    {
+        "type": "table",
+        "img_path": "images/68cf239c14c0b9bfb6938d081227ddbd93998f5c59b4860fc3ea76177decd0e5.jpg",
+        "table_caption": [
+            "Table 5: AlexNet-s $k = 1 ,$ ) and AlexNet-b $( k = 2 )$ ). In the last layer, $c$ denotes the number of possible classes: $c = 1 0$ for CIFAR-10 and $c = 2 0 0$ for Tiny-ImageNet. The strides in the first convolution layer for Tiny-ImageNet are set [4, 4] instead of [2, 2] to deal with the increase in the image resolution. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Module</td><td>Weight</td><td>Stride</td><td>Bias</td><td>BatchNorm</td><td>ReLU</td></tr><tr><td>Conv</td><td>[3,3,3,64]</td><td>[1,1]</td><td>[64]</td><td></td><td></td></tr><tr><td>Conv</td><td>[3,3, 64, 64]</td><td></td><td>[64]</td><td>广</td><td></td></tr><tr><td>Pool</td><td></td><td></td><td></td><td>×</td><td>&lt;&gt;x&gt;</td></tr><tr><td>Conv</td><td>[3,3,64,128]</td><td>1j</td><td>[128]</td><td>√</td><td></td></tr><tr><td>Conv</td><td>[3,3,128,128]</td><td>1j</td><td>[128]</td><td>√</td><td>√</td></tr><tr><td>Pool</td><td></td><td>18E.83. 2</td><td></td><td>X</td><td>X</td></tr><tr><td>Conv</td><td>[3,3,128,256]</td><td></td><td>[256]</td><td>√</td><td></td></tr><tr><td>Conv</td><td>[3,3,256,256]</td><td>1</td><td>[256]</td><td></td><td></td></tr><tr><td>Conv</td><td>[1/3/3,1/3/3,256,256]</td><td>1j</td><td>[256]</td><td>√</td><td></td></tr><tr><td>Pool</td><td></td><td>2j</td><td></td><td>X</td><td>X</td></tr><tr><td>Conv</td><td>[3,3,256,512]</td><td>1</td><td>[512]</td><td></td><td></td></tr><tr><td>Conv</td><td>[3,3,512, 512]</td><td>1j</td><td>[512]</td><td></td><td></td></tr><tr><td>Conv</td><td>[1/3/3,1/3/3,512,512]</td><td>1j</td><td>[512]</td><td></td><td></td></tr><tr><td>Pool</td><td></td><td>2</td><td></td><td></td><td></td></tr><tr><td>Conv</td><td>[3,3,512, 512]</td><td>1j</td><td>[512]</td><td></td><td></td></tr><tr><td>Conv</td><td>[3,3, 512,512]</td><td>1]</td><td>[512]</td><td></td><td></td></tr><tr><td>Conv</td><td>[1/3/3,1/3/3,512,512]</td><td>1]</td><td>[512]</td><td></td><td></td></tr><tr><td>Pool</td><td></td><td></td><td></td><td>X</td><td></td></tr><tr><td>Linear</td><td>[512, 512]</td><td></td><td>[512]</td><td>√</td><td>√</td></tr><tr><td>Linear</td><td>[512, 512]</td><td></td><td>[512]</td><td>√</td><td>√</td></tr><tr><td>Linear</td><td>[512,c]</td><td></td><td>[c]</td><td>X</td><td>X</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "Table 6: VGG-C/D/like. In the last layer, $c$ denotes the number of possible classes: $c = 1 0$ for CIFAR10 and $c = 2 0 0$ for Tiny-ImageNet. The strides in the first convolution layer for Tiny-ImageNet are set [2, 2] instead of [1, 1] to deal with the increase in the image resolution. The second Linear layer is only used in VGG-C/D. ",
+        "bbox": [
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+        "page_idx": 14
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+]
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diff --git a/parse/train/B1VZqjAcYX/B1VZqjAcYX_middle.json b/parse/train/B1VZqjAcYX/B1VZqjAcYX_middle.json
new file mode 100644
index 0000000000000000000000000000000000000000..41c6942e63aedd92c3c90c126d7846a1a6bfa132
--- /dev/null
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+                                    "content": "(1989); Weigend et al. (1991); Ishikawa (1996)) augment the loss function with some sparsity en-",
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+                                    "content": "the network to be pruned at single-shot prior to training, which we discuss further in the next section.",
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+                                    "score": 1.0,
+                                    "content": ". In this section, we discuss",
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+                                    "score": 1.0,
+                                    "content": "the effect of each of them and show that it can be used to prune the network in single-shot with",
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+                                    "content": "function (e.g., sigmoid) will be saturated, which would result in uninformative gradients. Therefore,",
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+                                    "content": "the weights should be within a sensible range. In particular, there is a body of work on neural",
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+                                    "score": 1.0,
+                                    "content": "network initialization (Goodfellow et al. (2016)) that ensures the gradients to be in a reasonable",
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+                        {
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+                                    "score": 1.0,
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+                                    "type": "text"
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+                    ],
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+                                    "content": "guarantees to have the same variance, as noted by LeCun et al. (1998). This would make the gradient",
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+                                    "content": "and in turn our saliency measure, to be dependent on the architectural characteristics. Thus, we",
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+                        {
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+                                    "score": 1.0,
+                                    "content": "advocate the use of variance scaling methods (e.g., Glorot & Bengio (2010)) to initialize the weights,",
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+                                    "score": 1.0,
+                                    "content": "such that the variance remains the same throughout the network. By ensuring this, we empirically",
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+                        },
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+                    ],
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+                                    "content": "Next, since the dataset and the loss function defines the task at hand, by relying on both of them,",
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+                                    "score": 1.0,
+                                    "content": "task. However, the practitioner needs to make a choice on whether to use the whole training set,",
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+                                    "score": 1.0,
+                                    "content": "or a mini-batch or the validation set to compute the connection saliency. Moreover, in case there",
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+                        {
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+                                    "content": "are memory limitations (e.g., large model or dataset), one can accumulate the saliency measure over",
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+                                    "score": 1.0,
+                                    "content": "multiple batches or take an exponential moving average. In our experiments, we show that using",
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+                        },
+                        {
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+                                    "content": "only one mini-batch of a reasonable number of training examples can lead to effective pruning.",
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+                                    "content": "Finally, in contrast to the previous approaches, our criterion for finding redundant connections is",
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+                                    "content": "simple and directly based on the sensitivity of the connections. This allows us to effectively iden-",
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+                                    "score": 1.0,
+                                    "content": "tify and prune redundant connections in a single step even before training. Then, training can be",
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+                                    "score": 1.0,
+                                    "content": "performed on the resulting pruned (sparse) network. We name our method SNIP for Single-shot",
+                                    "type": "text"
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+                                    "score": 1.0,
+                                    "content": "Network Pruning, and the complete algorithm is given in Algorithm 1.",
+                                    "type": "text"
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+                            "index": 43
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+                                            "html": "<table><tr><td colspan=\"3\">Algorithm1 SNIP: Single-shot Network Pruning based on Connection Sensitivity</td></tr><tr><td>Ensure: | w*|lo ≤ κ</td><td>Require: Loss function L, training dataset D, sparsity level K</td><td>Refer Equation 3</td></tr><tr><td></td><td>1:w_← VarianceScalingInitialization</td><td>Refer Section 4.2</td></tr><tr><td></td><td>2:Db={（xi,yi）}=1 ~D</td><td>&gt; Sample a mini-batch of training data</td></tr><tr><td>3:Sj←</td><td>l9j(w;Db) ∑=1l9k(（w;Db)l ， ∀j∈{1...m}</td><td>Connection sensitivity</td></tr><tr><td></td><td>4:s ← SortDescending(s)</td><td></td></tr><tr><td></td><td>5:cj←1[sj-$κ≥0]，∀j∈{1...m}</td><td>&gt;Pruning: choose top-k connections</td></tr><tr><td>7: w* ← c⊙w*</td><td>6: W* ← arg minw∈Rm L(c ③ w;D)</td><td>Regular training</td></tr></table>",
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+                                    "content": ". In this section, we discuss",
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+                                    "score": 1.0,
+                                    "content": "or a mini-batch or the validation set to compute the connection saliency. Moreover, in case there",
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+                                    "content": "multiple batches or take an exponential moving average. In our experiments, we show that using",
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+                                    "score": 1.0,
+                                    "content": "tify and prune redundant connections in a single step even before training. Then, training can be",
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+                                    "score": 1.0,
+                                    "content": "performed on the resulting pruned (sparse) network. We name our method SNIP for Single-shot",
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+                                            "content": "Figure 1: Test errors of LeNets pruned at varying sparsity levels",
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+                                            "score": 1.0,
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+                                            "score": 1.0,
+                                            "content": "refers to the reference",
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+                                            "score": 1.0,
+                                            "content": "network trained without pruning. Our approach performs as good as the reference network across",
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+                                    "score": 1.0,
+                                    "content": "5 EXPERIMENTS",
+                                    "type": "text"
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+                        }
+                    ],
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+                                    "score": 1.0,
+                                    "content": "We evaluate our method, SNIP, on MNIST, CIFAR-10 and Tiny-ImageNet classification tasks with a",
+                                    "type": "text"
+                                }
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+                        },
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+                                    "content": "variety of network architectures. Our results show that SNIP yields extremely sparse models with",
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+                                    "score": 1.0,
+                                    "content": "minimal or no loss in accuracy across all tested architectures, while being much simpler than other",
+                                    "type": "text"
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+                        },
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+                                    "score": 1.0,
+                                    "content": "state-of-the-art alternatives. We also provide clear evidence that our method prunes genuinely ex-",
+                                    "type": "text"
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+                            ],
+                            "index": 10
+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "plainable connections rather than performing blind pruning.",
+                                    "type": "text"
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+                            ],
+                            "index": 11
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+                    ],
+                    "index": 9
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+                                    "score": 1.0,
+                                    "content": "Experiment setup For brevity, we define the sparsity level to be",
+                                    "type": "text"
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+                                    "content": "\\bar { \\kappa } = ( m - \\kappa ) / m \\cdot 1 0 0 ( \\% )",
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+                                    "score": 1.0,
+                                    "content": "is the total number of parameters and",
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+                                    "score": 0.73,
+                                    "content": "\\kappa",
+                                    "type": "inline_equation"
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+                                {
+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "is the desired number of non-zero weights. For a",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
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+                                    "score": 1.0,
+                                    "content": "given sparsity level",
+                                    "type": "text"
+                                },
+                                {
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+                                        383
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+                                    "score": 0.61,
+                                    "content": "\\bar { \\kappa }",
+                                    "type": "inline_equation"
+                                },
+                                {
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+                                    "score": 1.0,
+                                    "content": ", the sensitivity scores are computed using a batch of 100 and 128 examples",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "for MNIST and CIFAR experiments, respectively. After pruning, the pruned network is trained in the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "standard way. Specifically, we train the models using SGD with momentum of 0.9, batch size of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "100 for MNIST and 128 for CIFAR experiments and the weight decay rate of 0.0005, unless stated",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "otherwise. The initial learning rate is set to 0.1 and decayed by 0.1 at every 25k or",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
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+                                    "score": 0.43,
+                                    "content": "3 0 \\mathrm { k }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "iterations",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
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+                                    "bbox": [
+                                        105,
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+                                        439
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+                                    "score": 1.0,
+                                    "content": "for MNIST and CIFAR, respectively. Our algorithm requires no other hyperparameters or complex",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
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+                                    "bbox": [
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+                                    ],
+                                    "score": 1.0,
+                                    "content": "learning/pruning schedules as in most pruning algorithms. We spare",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
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+                                    "score": 0.87,
+                                    "content": "10 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "of the training data as a",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
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+                                    "bbox": [
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+                                        461
+                                    ],
+                                    "score": 1.0,
+                                    "content": "validation set and used only",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
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+                                        460
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+                                    "score": 0.86,
+                                    "content": "90 \\%",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "for training. For CIFAR experiments, we use the standard data",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "augmentation (i.e., random horizontal flip and translation up to 4 pixels) for both the reference and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
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+                                        105,
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+                                        483
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+                                    "score": 1.0,
+                                    "content": "sparse models. The code can be found here: https://github.com/namhoonlee/snip-public.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        }
+                    ],
+                    "index": 17.5
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+                {
+                    "type": "title",
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+                                    "score": 1.0,
+                                    "content": "5.1 PRUNING LENETS WITH VARYING LEVELS OF SPARSITY",
+                                    "type": "text"
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+                            ],
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+                    ],
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+                                    "score": 1.0,
+                                    "content": "We first test our approach on two standard networks for pruning, LeNet-300-100 and LeNet-5-Caffe.",
+                                    "type": "text"
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+                                    "content": "LeNet-300-100 consists of three fully-connected (fc) layers with",
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+                                    "score": 0.59,
+                                    "content": "2 6 7 \\mathrm { k }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "parameters and LeNet-5-Caffe",
+                                    "type": "text"
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+                            "index": 26
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+                        {
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+                                    "score": 1.0,
+                                    "content": "consists of two convolutional (conv) layers and two fc layers with 431k parameters. We prune",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
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+                                    "bbox": [
+                                        105,
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+                                        568
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the LeNets for different sparsity levels",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
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+                                    "score": 0.73,
+                                    "content": "\\bar { \\kappa }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        271,
+                                        553,
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+                                    ],
+                                    "score": 1.0,
+                                    "content": "and report the performance in error on the MNIST image",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "classification task. We run the experiment 20 times for each",
+                                    "type": "text"
+                                },
+                                {
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+                                    "score": 0.69,
+                                    "content": "\\bar { \\kappa }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "by changing random seeds for dataset",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
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+                            "spans": [
+                                {
+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "and network initialization. The results are reported in Figure 1.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        }
+                    ],
+                    "index": 27.5
+                },
+                {
+                    "type": "text",
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+                                    "score": 1.0,
+                                    "content": "The pruned sparse LeNet-300-100 achieves performances similar to the reference",
+                                    "type": "text"
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+                                    "score": 0.86,
+                                    "content": "( \\bar { \\kappa } = 0",
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+                                    "score": 1.0,
+                                    "content": "), only",
+                                    "type": "text"
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+                                    "score": 1.0,
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+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
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+                                    "score": 1.0,
+                                    "content": "for MNIST and CIFAR, respectively. Our algorithm requires no other hyperparameters or complex",
+                                    "type": "text"
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+                            ],
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+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "learning/pruning schedules as in most pruning algorithms. We spare",
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+                                    "score": 0.87,
+                                    "content": "10 \\%",
+                                    "type": "inline_equation"
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+                                {
+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "of the training data as a",
+                                    "type": "text"
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+                            ],
+                            "index": 20
+                        },
+                        {
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+                            "spans": [
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+                                    "score": 1.0,
+                                    "content": "validation set and used only",
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+                                    "score": 0.86,
+                                    "content": "90 \\%",
+                                    "type": "inline_equation"
+                                },
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "for training. For CIFAR experiments, we use the standard data",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
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+                            "spans": [
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "augmentation (i.e., random horizontal flip and translation up to 4 pixels) for both the reference and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
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+                            "spans": [
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "sparse models. The code can be found here: https://github.com/namhoonlee/snip-public.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        }
+                    ],
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+                                    "content": "5.1 PRUNING LENETS WITH VARYING LEVELS OF SPARSITY",
+                                    "type": "text"
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+                            ],
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+                    ],
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+                                    "score": 0.59,
+                                    "content": "2 6 7 \\mathrm { k }",
+                                    "type": "inline_equation"
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+                                {
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+                                    "score": 1.0,
+                                    "content": "consists of two convolutional (conv) layers and two fc layers with 431k parameters. We prune",
+                                    "type": "text"
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+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "the LeNets for different sparsity levels",
+                                    "type": "text"
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+                                {
+                                    "bbox": [
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+                                    "score": 0.73,
+                                    "content": "\\bar { \\kappa }",
+                                    "type": "inline_equation"
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+                                {
+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "and report the performance in error on the MNIST image",
+                                    "type": "text"
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+                            "index": 28
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+                                    "score": 1.0,
+                                    "content": "classification task. We run the experiment 20 times for each",
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+                                    "score": 1.0,
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+                            "index": 29
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+                        {
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+                                    "score": 1.0,
+                                    "content": "and network initialization. The results are reported in Figure 1.",
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+                            "index": 30
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+                    ],
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+                                    "score": 0.86,
+                                    "content": "( \\bar { \\kappa } = 0",
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+                                    "score": 1.0,
+                                    "content": "with negligible loss at",
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+                                    "score": 0.89,
+                                    "content": "\\bar { \\kappa } = 9 0",
+                                    "type": "inline_equation"
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+                                    "score": 1.0,
+                                    "content": ". For LeNet-5-Caffe, the performance degradation is nearly invisible.",
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+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
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+                                    "content": "Note that our saliency measure does not require the network to be pre-trained and is computed at",
+                                    "type": "text"
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+                            ],
+                            "index": 33
+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "random initialization. Despite such simplicity, our approach prunes LeNets quickly (single-shot) and",
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+                                    "content": "effectively (minimal accuracy loss) at varying sparsity levels.",
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+                                    "content": "5.2 COMPARISONS TO EXISTING APPROACHES",
+                                    "type": "text"
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+                                    "score": 1.0,
+                                    "content": "of the total parameters still be trainable and perform well? We test our approach for",
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+                                    "score": 0.87,
+                                    "content": "9 9 \\%",
+                                    "type": "inline_equation"
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+                                    "score": 1.0,
+                                    "content": "sparsity on LeNet-5-Caffe) and compare with various pruning",
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+                                    "score": 1.0,
+                                    "content": "algorithms as follows: LWC (Han et al. (2015)), DNS (Guo et al. (2016)), LC (Carreira-Perpin˜ an & ´",
+                                    "type": "text"
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+                                            "html": "<table><tr><td rowspan=\"2\">Method</td><td rowspan=\"2\">Criterion</td><td colspan=\"2\">LeNet-300-100</td><td colspan=\"2\">LeNet-5-Caffe</td><td rowspan=\"2\">Pretrain</td><td rowspan=\"2\">#Prune</td><td rowspan=\"2\">Additional hyperparam.</td><td rowspan=\"2\">Augment objective</td><td rowspan=\"2\">Arch. constraints</td></tr><tr><td>K(%)</td><td>err. (%)</td><td>K(%)</td><td>err. (%)</td></tr><tr><td>Ref.</td><td></td><td></td><td>1.7</td><td>一</td><td>0.9</td><td></td><td>1</td><td>-&gt;</td><td>-xx&gt;</td><td>√</td></tr><tr><td>LWC</td><td>Magnitude</td><td>91.7</td><td>1.6</td><td>91.7</td><td>0.8</td><td></td><td>many</td><td></td><td></td><td></td></tr><tr><td>DNS</td><td>Magnitude</td><td>98.2</td><td>2.0</td><td>99.1</td><td>0.9</td><td></td><td>many</td><td></td><td></td><td>√</td></tr><tr><td>LC</td><td>Magnitude</td><td>99.0</td><td>3.2</td><td>99.0</td><td>1.1</td><td></td><td>many</td><td>√</td><td></td><td>X</td></tr><tr><td>SWS</td><td>Bayesian</td><td>95.6</td><td>1.9</td><td>99.5</td><td>1.0</td><td></td><td>soft</td><td>√</td><td>√</td><td>X</td></tr><tr><td>SVD</td><td>Bayesian</td><td>98.5</td><td>1.9</td><td>99.6</td><td>0.8</td><td>-&gt;&gt;&gt;&gt;&gt;</td><td>soft</td><td>√</td><td>√</td><td>X</td></tr><tr><td>OBD</td><td>Hessian</td><td>92.0</td><td>2.0</td><td>92.0</td><td>2.7</td><td>√</td><td>many</td><td>√</td><td>X</td><td>X</td></tr><tr><td>L-OBS</td><td>Hessian</td><td>98.5</td><td>2.0</td><td>99.0</td><td>2.1</td><td>√</td><td>many</td><td>√</td><td>X</td><td>√</td></tr><tr><td rowspan=\"2\">SNIP (ours)</td><td>Connection</td><td>95.0</td><td>1.6</td><td>98.0</td><td>0.8</td><td>×</td><td></td><td>×</td><td>×</td><td>×</td></tr><tr><td>sensitivity</td><td>98.0</td><td>2.4</td><td>99.0</td><td>1.1</td><td></td><td>1</td><td></td><td></td><td></td></tr></table>",
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+                                    "content": "highlight the benefit of our approach. First of all, the aforementioned methods require networks to",
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+                                    "content": "frequency in Guo et al. (2016), annealing schedule in Carreira-Perpin˜an & Idelbayev (2018)). Some ´",
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+                                    "content": "methods augment the training objective to handle pruning together with training, increasing the",
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+                                    "score": 1.0,
+                                    "content": "complexity of the algorithm (e.g., augmented Lagrangian in Carreira-Perpin˜an & Idelbayev (2018), ´",
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+                                    "score": 1.0,
+                                    "content": "variational inference in Molchanov et al. (2017a)). Furthermore, there are approaches designed to",
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+                                    "score": 1.0,
+                                    "content": "include architecture dependent constraints (e.g., layer-wise pruning schemes in Dong et al. (2017)).",
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+                                    "content": "additional hyperparameters, and is applied only once at initialization. This means that one can easily",
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+                                    "score": 1.0,
+                                    "content": "beginning, we could potentially expedite the training phase by training only the survived parameters",
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+                                    "score": 1.0,
+                                    "content": "(e.g., reduced expected FLOPs in Louizos et al. (2018)). Notice that this is not possible for the",
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+                                    "score": 1.0,
+                                    "content": "aforementioned approaches as they obtain the maximum sparsity at the end of the process.",
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+                                    "content": "applied to the following models:",
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+                                    "content": "• AlexNet-s and AlexNet-b: Models similar to Krizhevsky et al. (2012) in terms of the number of",
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+                                    "content": "layers and size of kernels. We set the size of fc layers to 512 (AlexNet-s) and to 1024 (AlexNet-b)",
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+                            "index": 38
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+                                    "content": "to adapt for CIFAR-10 and use strides of 2 for all conv layers instead of using pooling layers.",
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+                                    "content": "& Zisserman (2015). VGG-like (Zagoruyko (2015)) is a popular variant adapted for CIFAR-10",
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+                                    "score": 1.0,
+                                    "content": "which has one less fc layers. For all VGG models, we set the size of fc layers to 512, remove",
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+                            "index": 42
+                        },
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+                                    "score": 1.0,
+                                    "content": "dropout layers to avoid any effect on sparsification and use batch normalization instead.",
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+                                    "content": "• WRN-16-8, WRN-16-10 and WRN-22-8: Same models as in Zagoruyko & Komodakis (2016).",
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+                                    "content": "Table 2: Pruning results of the proposed approach on various modern architectures (before",
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+                                    "content": ". There are a couple of works attempting to prune RNNs",
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+                                    "score": 1.0,
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+                                    "score": 1.0,
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+                                    "score": 1.0,
+                                    "content": ". In order to un-",
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+                                    "score": 1.0,
+                                    "content": "derstand which connections are retained, we can visualize the binary connectivity mask for this",
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+                                    "content": ". There are a couple of works attempting to prune RNNs",
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+                                    "score": 1.0,
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+                                    "score": 1.0,
+                                    "content": "). Recall that our method computes c using a mini-",
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+                                    "content": "results are displayed in Figure 2 (see Appendix A for more results).",
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+                                    "score": 1.0,
+                                    "content": "0 (i.e., the first column of MNIST results), for example, the parameters connected to the foreground",
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+                                    "score": 1.0,
+                                    "content": "of the digit 0 survive from pruning while the majority of background is removed. Also, one can",
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+                                    "score": 1.0,
+                                    "content": "easily determine the identity of items from Fashion-MNIST results. This clearly indicates that our",
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+                                    "score": 1.0,
+                                    "content": "method indeed prunes the unimportant connections in performing the classification task, receiving",
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+                            "index": 16
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+                        {
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+                                    "score": 1.0,
+                                    "content": "signals only from the most discriminative part of the input. This stands in stark contrast to other",
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+                        {
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+                                    "score": 1.0,
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+                                    "score": 1.0,
+                                    "content": "(Section 4.2). We study the effect of each of these in this section.",
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+                                    "content": "(see Algorithm 1). To study the effect of data, we vary the batch size used to compute the saliency",
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+                                    "score": 1.0,
+                                    "content": "and check which connections are being pruned as well as how much performance change",
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+                        {
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+                                    "score": 1.0,
+                                    "content": "this results in on the corresponding sparse network. We test with LeNet-300-100 to visualize the",
+                                    "type": "text"
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+                                    "score": 1.0,
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+                                    "type": "text"
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+                                    "score": 0.89,
+                                    "content": "\\bar { \\kappa } = 9 0",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": ". Note that the batch size used for training",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
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+                            "spans": [
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+                                    "score": 1.0,
+                                    "content": "remains the same as 100 for all cases. The results are displayed in Figure 3.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
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+                    ],
+                    "index": 24.5
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+                {
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+                                    "score": 1.0,
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+                        {
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+                                    "type": "text"
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+                                    "score": 1.0,
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+                                            "score": 1.0,
+                                            "content": ", from 10 (top) to 90",
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+                                            "score": 1.0,
+                                            "content": "(bottom). Bright pixels indicate that the parameters connected to these region had high importance",
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+                                            "score": 1.0,
+                                            "content": "scores (s) and survived from pruning. As the sparsity increases, the parameters connected to the",
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+                                            "score": 1.0,
+                                            "content": "discriminative part of the image for classification survive and the irrelevant parts get pruned.",
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+                                    "index": 8
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+                                    "score": 1.0,
+                                    "content": "(MNIST) or silhouettes (Fashion-MNIST) of input class. When we use a batch of examples of the digit",
+                                    "type": "text"
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+                                    "score": 1.0,
+                                    "content": "0 (i.e., the first column of MNIST results), for example, the parameters connected to the foreground",
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+                                    "score": 1.0,
+                                    "content": "of the digit 0 survive from pruning while the majority of background is removed. Also, one can",
+                                    "type": "text"
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+                        {
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+                                    "score": 1.0,
+                                    "content": "easily determine the identity of items from Fashion-MNIST results. This clearly indicates that our",
+                                    "type": "text"
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+                            ],
+                            "index": 15
+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "method indeed prunes the unimportant connections in performing the classification task, receiving",
+                                    "type": "text"
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+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
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+                                    "score": 1.0,
+                                    "content": "signals only from the most discriminative part of the input. This stands in stark contrast to other",
+                                    "type": "text"
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+                            ],
+                            "index": 17
+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "pruning methods from which carrying out such inspection is not straightforward.",
+                                    "type": "text"
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+                    ],
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+                                    "score": 1.0,
+                                    "content": "5.5 EFFECTS OF DATA AND WEIGHT INITIALIZATION",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        }
+                    ],
+                    "index": 19
+                },
+                {
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+                                    "score": 1.0,
+                                    "content": "Recall that our connection saliency measure depends on the network weights w as well as the given",
+                                    "type": "text"
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+                            ],
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+                        },
+                        {
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+                                    "score": 0.78,
+                                    "content": "\\mathcal { D }",
+                                    "type": "inline_equation"
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+                                    "score": 1.0,
+                                    "content": "(Section 4.2). We study the effect of each of these in this section.",
+                                    "type": "text"
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+                    ],
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+                                    "score": 1.0,
+                                    "content": "Effect of data. Our connection saliency measure depends on a mini-batch of train examples",
+                                    "type": "text"
+                                },
+                                {
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+                                    "score": 0.86,
+                                    "content": "\\mathcal { D } ^ { b }",
+                                    "type": "inline_equation"
+                                }
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+                            "index": 22
+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "(see Algorithm 1). To study the effect of data, we vary the batch size used to compute the saliency",
+                                    "type": "text"
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+                            ],
+                            "index": 23
+                        },
+                        {
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+                                    "score": 0.92,
+                                    "content": "( | \\mathcal { D } ^ { b } | )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "and check which connections are being pruned as well as how much performance change",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
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+                            "spans": [
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+                                    "bbox": [
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+                                        557
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+                                    "score": 1.0,
+                                    "content": "this results in on the corresponding sparse network. We test with LeNet-300-100 to visualize the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
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+                            "spans": [
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+                                    "score": 1.0,
+                                    "content": "remaining parameters, and set the sparsity level",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
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+                                    "score": 0.89,
+                                    "content": "\\bar { \\kappa } = 9 0",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": ". Note that the batch size used for training",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
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+                            "spans": [
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+                                    "score": 1.0,
+                                    "content": "remains the same as 100 for all cases. The results are displayed in Figure 3.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        }
+                    ],
+                    "index": 24.5,
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+                {
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+                    "bbox": [
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+                    "lines": [
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+                            "spans": [
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+                                    "score": 1.0,
+                                    "content": "Effect of initialization. Our approach prunes a network at a stochastic initialization as discussed.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
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+                                    "content": "We study the effect of the following initialization methods: 1) RN (random normal), 2) TN (truncated",
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+                                    "content": "random normal), 3) VS-X (a variance scaling method using Glorot & Bengio (2010)), and 4) VS-H",
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+                                    "score": 1.0,
+                                    "content": "(a variance scaling method He et al. (2015)). We test on LeNets and RNNs on MNIST and run 20 sets",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
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+                                    "score": 1.0,
+                                    "content": "of experiments by varying the seed for initialization. We set the sparsity level",
+                                    "type": "text"
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+                                {
+                                    "bbox": [
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+                                    "score": 0.9,
+                                    "content": "\\bar { \\kappa } = 9 0",
+                                    "type": "inline_equation"
+                                },
+                                {
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+                                    "score": 1.0,
+                                    "content": ", and train with",
+                                    "type": "text"
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+                            ],
+                            "index": 32
+                        },
+                        {
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "Adam optimizer (Kingma & Ba (2015)) with learning rate of 0.001 without weight decay. Note that",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
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+                            "spans": [
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+                                    "score": 1.0,
+                                    "content": "for training VS-X initialization is used in all the cases. The results are reported in Figure 3.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        }
+                    ],
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+                                    "score": 1.0,
+                                    "content": "For all models, VS-H achieves the best performance. The differences between initializers are",
+                                    "type": "text"
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+                            ],
+                            "index": 35
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+                                    "content": "marginal on LeNets, however, variance scaling methods indeed turns out to be essential for complex",
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+                            ],
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+                        },
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+                                    "score": 1.0,
+                                    "content": "RNN models. This effect is significant especially for GRU where without variance scaling initial-",
+                                    "type": "text"
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+                            ],
+                            "index": 37
+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "ization, the pruned networks are unable to achieve good accuracies, even with different optimizers.",
+                                    "type": "text"
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+                        },
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+                                    "score": 1.0,
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+                                    "score": 1.0,
+                                    "content": "forcing the significance of our saliency criterion. It is possible that a similar experiment can be done",
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+                                    "score": 1.0,
+                                    "content": "with other pruning methods (Molchanov et al. (2017a)), however, being simple, SNIP enables such",
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+                                    "content": "in Appendix B.",
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+                                    "score": 1.0,
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+                                    "score": 1.0,
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+                                    "score": 1.0,
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+                                    "score": 1.0,
+                                    "content": "with an explicit L2 regularizer (purple), indicating that neural networks have enough capacity to",
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+                            ],
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+                                    "score": 1.0,
+                                    "content": "memorize completely random data. In contrast, the model pruned by SNIP (orange) fails to fit the",
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+                                    "score": 1.0,
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+                                    "score": 1.0,
+                                    "content": "forcing the significance of our saliency criterion. It is possible that a similar experiment can be done",
+                                    "type": "text"
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+                            ],
+                            "index": 34
+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "with other pruning methods (Molchanov et al. (2017a)), however, being simple, SNIP enables such",
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+                                    "score": 1.0,
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+                                    "score": 1.0,
+                                    "content": "in Appendix B.",
+                                    "type": "text"
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+                                    "content": "This work was supported by the Korean Government Graduate Scholarship, the ERC grant ERC-",
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+                                    "content": "EP/N019474/1. We would also like to acknowledge the Royal Academy of Engineering and FiveAI.",
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+                                    "content": "REFERENCES",
+                                    "type": "text"
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+                                    "score": 1.0,
+                                    "content": "Sanjeev Arora, Rong Ge, Behnam Neyshabur, and Yi Zhang. Stronger generalization bounds for",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
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+                                    "content": "deep nets via a compression approach. ICML, 2018.",
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+                        }
+                    ],
+                    "index": 7
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+                            ],
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+                                        115,
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+                                        263
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+                            ],
+                            "index": 10
+                        }
+                    ],
+                    "index": 10
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+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
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+                            ],
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+                        },
+                        {
+                            "bbox": [
+                                116,
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+                                        116,
+                                        292,
+                                        317,
+                                        303
+                                    ],
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+                            "index": 13
+                        }
+                    ],
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+                                    "type": "text"
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+                            ],
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+                        },
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+                            ],
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+                            "bbox": [
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+                                        370,
+                                        505,
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+                        },
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+                                116,
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+                            "index": 21
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+                                        444
+                                    ],
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+                        },
+                        {
+                            "bbox": [
+                                114,
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+                    ],
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+                                    "type": "text"
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+                            ],
+                            "index": 4
+                        }
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+                    "index": 4
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        170,
+                        504,
+                        193
+                    ],
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+                        {
+                            "bbox": [
+                                106,
+                                169,
+                                506,
+                                184
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        169,
+                                        506,
+                                        184
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Sanjeev Arora, Rong Ge, Behnam Neyshabur, and Yi Zhang. Stronger generalization bounds for",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                181,
+                                327,
+                                194
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        181,
+                                        327,
+                                        194
+                                    ],
+                                    "score": 1.0,
+                                    "content": "deep nets via a compression approach. ICML, 2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        }
+                    ],
+                    "index": 5.5,
+                    "bbox_fs": [
+                        106,
+                        169,
+                        506,
+                        194
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        104,
+                        200,
+                        473,
+                        212
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                200,
+                                474,
+                                214
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        200,
+                                        474,
+                                        214
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Leo Breiman. Better subset regression using the nonnegative garrote. Technometrics, 1995.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        }
+                    ],
+                    "index": 7,
+                    "bbox_fs": [
+                        105,
+                        200,
+                        474,
+                        214
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        220,
+                        504,
+                        243
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                219,
+                                505,
+                                234
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        219,
+                                        505,
+                                        234
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Miguel A. Carreira-Perpi ´ n˜an and Yerlan Idelbayev. “Learning-compression” algorithms for neural ´",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                231,
+                                223,
+                                244
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        231,
+                                        223,
+                                        244
+                                    ],
+                                    "score": 1.0,
+                                    "content": "net pruning. CVPR, 2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        }
+                    ],
+                    "index": 8.5,
+                    "bbox_fs": [
+                        105,
+                        219,
+                        505,
+                        244
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        109,
+                        250,
+                        478,
+                        263
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                249,
+                                478,
+                                263
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        249,
+                                        478,
+                                        263
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Yves Chauvin. A back-propagation algorithm with optimal use of hidden units. NIPS, 1989.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        }
+                    ],
+                    "index": 10,
+                    "bbox_fs": [
+                        106,
+                        249,
+                        478,
+                        263
+                    ]
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+                    "type": "text",
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+                        108,
+                        269,
+                        505,
+                        303
+                    ],
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+                        {
+                            "bbox": [
+                                105,
+                                269,
+                                505,
+                                282
+                            ],
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+                                {
+                                    "bbox": [
+                                        105,
+                                        269,
+                                        505,
+                                        282
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Kyunghyun Cho, Bart Van Merrienboer, Caglar Gulcehre, Dzmitry Bahdanau, Fethi Bougares, Hol- ¨",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                280,
+                                505,
+                                293
+                            ],
+                            "spans": [
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+                                    "bbox": [
+                                        115,
+                                        280,
+                                        505,
+                                        293
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ger Schwenk, and Yoshua Bengio. Learning phrase representations using rnn encoder-decoder",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                292,
+                                317,
+                                303
+                            ],
+                            "spans": [
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+                                    "bbox": [
+                                        116,
+                                        292,
+                                        317,
+                                        303
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for statistical machine translation. EMNLP, 2014.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        }
+                    ],
+                    "index": 12,
+                    "bbox_fs": [
+                        105,
+                        269,
+                        505,
+                        303
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+                        105,
+                        310,
+                        504,
+                        334
+                    ],
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+                                105,
+                                309,
+                                505,
+                                324
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+                                    "bbox": [
+                                        105,
+                                        309,
+                                        505,
+                                        324
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Xin Dong, Shangyu Chen, and Sinno Pan. Learning to prune deep neural networks via layer-wise",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
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+                                322,
+                                261,
+                                334
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+                                        116,
+                                        322,
+                                        261,
+                                        334
+                                    ],
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+                                    "type": "text"
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+                            ],
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+                        }
+                    ],
+                    "index": 14.5,
+                    "bbox_fs": [
+                        105,
+                        309,
+                        505,
+                        334
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+                    "type": "text",
+                    "bbox": [
+                        105,
+                        340,
+                        504,
+                        363
+                    ],
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+                        {
+                            "bbox": [
+                                105,
+                                340,
+                                505,
+                                354
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+                                    "bbox": [
+                                        105,
+                                        340,
+                                        505,
+                                        354
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+                                    "type": "text"
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+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                115,
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+                                        115,
+                                        352,
+                                        224,
+                                        363
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+                        105,
+                        370,
+                        504,
+                        394
+                    ],
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+                                370,
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+                                        370,
+                                        505,
+                                        384
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+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                116,
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+                                        116,
+                                        382,
+                                        408,
+                                        394
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+                            ],
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+                        }
+                    ],
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+                                        505,
+                                        415
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+                                    "type": "text"
+                                }
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+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                411,
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+                        504,
+                        454
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+                                429,
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+                                        444
+                                    ],
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+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                441,
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+                        460,
+                        504,
+                        484
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+                                        474
+                                    ],
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+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                471,
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+                                    "bbox": [
+                                        115,
+                                        471,
+                                        286,
+                                        484
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+                                    "type": "text"
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+                            "index": 25
+                        }
+                    ],
+                    "index": 24.5,
+                    "bbox_fs": [
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+                        490,
+                        504,
+                        514
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+                            ],
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+                        },
+                        {
+                            "bbox": [
+                                117,
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+                                        117,
+                                        502,
+                                        268,
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+                        }
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+                        544
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+                                        520,
+                                        505,
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+                                    ],
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+                                    "content": "Babak Hassibi, David G Stork, and Gregory J Wolff. Optimal brain surgeon and general network",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                115,
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+                                        115,
+                                        533,
+                                        251,
+                                        544
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+                                    "type": "text"
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+                            ],
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+                        }
+                    ],
+                    "index": 28.5,
+                    "bbox_fs": [
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+                                    "type": "text"
+                                }
+                            ],
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+                        },
+                        {
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+                            "index": 31
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+                    ],
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+                            ],
+                            "index": 32
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+                                        105,
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+                            "index": 34
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+                    ],
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+                            ],
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+                        },
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+                            ],
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+                        },
+                        {
+                            "bbox": [
+                                116,
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+                                        116,
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+                                        138,
+                                        444,
+                                        153
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+                        }
+                    ],
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+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                168,
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+                                        116,
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+                                        265,
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+                            ],
+                            "index": 6
+                        }
+                    ],
+                    "index": 5.5
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+                {
+                    "type": "text",
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+                        185,
+                        504,
+                        209
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+                            "bbox": [
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+                                185,
+                                505,
+                                198
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+                                    "bbox": [
+                                        106,
+                                        185,
+                                        505,
+                                        198
+                                    ],
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+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                116,
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+                                        116,
+                                        197,
+                                        244,
+                                        208
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+                            "index": 8
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+                                213,
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+                                        213,
+                                        505,
+                                        228
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+                                    "type": "text"
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+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                116,
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+                                239,
+                                237
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+                                        126,
+                                        226,
+                                        239,
+                                        237
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+                                    "type": "text"
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+                            ],
+                            "index": 10
+                        }
+                    ],
+                    "index": 9.5
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+                        242,
+                        502,
+                        277
+                    ],
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+                        },
+                        {
+                            "bbox": [
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+                                253,
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+                                        116,
+                                        253,
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+                                    "type": "text"
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+                            "index": 12
+                        },
+                        {
+                            "bbox": [
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+                                277
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+                                        116,
+                                        265,
+                                        385,
+                                        277
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+                            "index": 13
+                        }
+                    ],
+                    "index": 12
+                },
+                {
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+                        282,
+                        504,
+                        306
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+                                105,
+                                281,
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+                                296
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+                                        296
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+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                115,
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+                                306
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+                                        115,
+                                        293,
+                                        218,
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+                                    "score": 1.0,
+                                    "content": "networks. ICML, 2017a.",
+                                    "type": "text"
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+                            ],
+                            "index": 15
+                        }
+                    ],
+                    "index": 14.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        311,
+                        504,
+                        334
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+                            "bbox": [
+                                106,
+                                312,
+                                505,
+                                323
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+                                    "bbox": [
+                                        106,
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+                                        323
+                                    ],
+                                    "score": 1.0,
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+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                322,
+                                367,
+                                334
+                            ],
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+                                    "bbox": [
+                                        116,
+                                        322,
+                                        367,
+                                        334
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+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        }
+                    ],
+                    "index": 16.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        339,
+                        504,
+                        363
+                    ],
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+                        {
+                            "bbox": [
+                                105,
+                                338,
+                                506,
+                                353
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        338,
+                                        506,
+                                        353
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+                                    "score": 1.0,
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+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
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+                                351,
+                                307,
+                                362
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+                                    "bbox": [
+                                        116,
+                                        351,
+                                        307,
+                                        362
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+                                    "content": "network via relevance assessment. NIPS, 1989.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        }
+                    ],
+                    "index": 18.5
+                },
+                {
+                    "type": "text",
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+                        108,
+                        368,
+                        504,
+                        391
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+                                    "bbox": [
+                                        106,
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+                                        382
+                                    ],
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+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                380,
+                                239,
+                                390
+                            ],
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+                                    "bbox": [
+                                        115,
+                                        380,
+                                        239,
+                                        390
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+                                    "score": 1.0,
+                                    "content": "neural networks. ICLR, 2017.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        }
+                    ],
+                    "index": 20.5
+                },
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+                    "type": "text",
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+                        107,
+                        396,
+                        504,
+                        420
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+                            "bbox": [
+                                105,
+                                395,
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+                                410
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+                                    "bbox": [
+                                        105,
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+                                        505,
+                                        410
+                                    ],
+                                    "score": 1.0,
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+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                115,
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+                                        115,
+                                        408,
+                                        210,
+                                        419
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+                                    "score": 1.0,
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+                            ],
+                            "index": 23
+                        }
+                    ],
+                    "index": 22.5
+                },
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+                        504,
+                        448
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+                                        105,
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+                                    "content": "Steven J Nowlan and Geoffrey E Hinton. Simplifying neural networks by soft weight-sharing.",
+                                    "type": "text"
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+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
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+                        },
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+                            "bbox": [
+                                116,
+                                253,
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+                                267
+                            ],
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+                                {
+                                    "bbox": [
+                                        116,
+                                        253,
+                                        504,
+                                        267
+                                    ],
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+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
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+                                265,
+                                385,
+                                277
+                            ],
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+                                        116,
+                                        265,
+                                        385,
+                                        277
+                                    ],
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+                                    "content": "tivity inspired by network science. Nature Communications, 2018.",
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+                            "index": 13
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+                    ],
+                    "index": 12,
+                    "bbox_fs": [
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+                        505,
+                        277
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+                        504,
+                        306
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+                                281,
+                                505,
+                                296
+                            ],
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+                                    "bbox": [
+                                        105,
+                                        281,
+                                        505,
+                                        296
+                                    ],
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+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                293,
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+                                306
+                            ],
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+                                    "bbox": [
+                                        115,
+                                        293,
+                                        218,
+                                        306
+                                    ],
+                                    "score": 1.0,
+                                    "content": "networks. ICML, 2017a.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        }
+                    ],
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+                    "bbox_fs": [
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+                        281,
+                        505,
+                        306
+                    ]
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+                        106,
+                        311,
+                        504,
+                        334
+                    ],
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+                            "bbox": [
+                                106,
+                                312,
+                                505,
+                                323
+                            ],
+                            "spans": [
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+                                    "bbox": [
+                                        106,
+                                        312,
+                                        505,
+                                        323
+                                    ],
+                                    "score": 1.0,
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+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                322,
+                                367,
+                                334
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        322,
+                                        367,
+                                        334
+                                    ],
+                                    "score": 1.0,
+                                    "content": "neural networks for resource efficient inference. ICLR, 2017b.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        }
+                    ],
+                    "index": 16.5,
+                    "bbox_fs": [
+                        106,
+                        312,
+                        505,
+                        334
+                    ]
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+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        339,
+                        504,
+                        363
+                    ],
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+                        {
+                            "bbox": [
+                                105,
+                                338,
+                                506,
+                                353
+                            ],
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+                                {
+                                    "bbox": [
+                                        105,
+                                        338,
+                                        506,
+                                        353
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Michael C Mozer and Paul Smolensky. Skeletonization: A technique for trimming the fat from a",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                351,
+                                307,
+                                362
+                            ],
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+                                    "bbox": [
+                                        116,
+                                        351,
+                                        307,
+                                        362
+                                    ],
+                                    "score": 1.0,
+                                    "content": "network via relevance assessment. NIPS, 1989.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        }
+                    ],
+                    "index": 18.5,
+                    "bbox_fs": [
+                        105,
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+                        362
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+                        108,
+                        368,
+                        504,
+                        391
+                    ],
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+                                367,
+                                505,
+                                382
+                            ],
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+                                {
+                                    "bbox": [
+                                        106,
+                                        367,
+                                        505,
+                                        382
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Sharan Narang, Erich Elsen, Gregory Diamos, and Shubho Sengupta. Exploring sparsity in recurrent",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                380,
+                                239,
+                                390
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        380,
+                                        239,
+                                        390
+                                    ],
+                                    "score": 1.0,
+                                    "content": "neural networks. ICLR, 2017.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        }
+                    ],
+                    "index": 20.5,
+                    "bbox_fs": [
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+                        367,
+                        505,
+                        390
+                    ]
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+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        396,
+                        504,
+                        420
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                395,
+                                505,
+                                410
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        395,
+                                        505,
+                                        410
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Alexander Novikov, Dmitrii Podoprikhin, Anton Osokin, and Dmitry P Vetrov. Tensorizing neural",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                408,
+                                210,
+                                419
+                            ],
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+                                    "bbox": [
+                                        115,
+                                        408,
+                                        210,
+                                        419
+                                    ],
+                                    "score": 1.0,
+                                    "content": "networks. NIPS, 2015.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        }
+                    ],
+                    "index": 22.5,
+                    "bbox_fs": [
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+                        106,
+                        425,
+                        504,
+                        448
+                    ],
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+                                105,
+                                423,
+                                505,
+                                439
+                            ],
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+                                    "bbox": [
+                                        105,
+                                        423,
+                                        505,
+                                        439
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Steven J Nowlan and Geoffrey E Hinton. Simplifying neural networks by soft weight-sharing.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                436,
+                                229,
+                                449
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        436,
+                                        229,
+                                        449
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Neural Computation, 1992.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        }
+                    ],
+                    "index": 24.5,
+                    "bbox_fs": [
+                        105,
+                        423,
+                        505,
+                        449
+                    ]
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+                    "type": "text",
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+                        105,
+                        453,
+                        504,
+                        477
+                    ],
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+                        {
+                            "bbox": [
+                                105,
+                                452,
+                                506,
+                                468
+                            ],
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+                                    "bbox": [
+                                        105,
+                                        452,
+                                        506,
+                                        468
+                                    ],
+                                    "score": 1.0,
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+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                465,
+                                289,
+                                477
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        465,
+                                        289,
+                                        477
+                                    ],
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+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        }
+                    ],
+                    "index": 26.5,
+                    "bbox_fs": [
+                        105,
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+                        506,
+                        477
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+                    "type": "text",
+                    "bbox": [
+                        106,
+                        482,
+                        381,
+                        495
+                    ],
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+                        {
+                            "bbox": [
+                                105,
+                                482,
+                                381,
+                                496
+                            ],
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+                                    "bbox": [
+                                        105,
+                                        482,
+                                        381,
+                                        496
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Russell Reed. Pruning algorithms-a survey. Neural Networks, 1993.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        }
+                    ],
+                    "index": 28,
+                    "bbox_fs": [
+                        105,
+                        482,
+                        381,
+                        496
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+                    "type": "text",
+                    "bbox": [
+                        106,
+                        500,
+                        501,
+                        524
+                    ],
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+                            "bbox": [
+                                106,
+                                499,
+                                504,
+                                513
+                            ],
+                            "spans": [
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+                                    "bbox": [
+                                        106,
+                                        499,
+                                        504,
+                                        513
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Abigail See, Minh-Thang Luong, and Christopher D Manning. Compression of neural machine",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                512,
+                                303,
+                                523
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        512,
+                                        303,
+                                        523
+                                    ],
+                                    "score": 1.0,
+                                    "content": "translation models via pruning. CoNLL, 2016.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        }
+                    ],
+                    "index": 29.5,
+                    "bbox_fs": [
+                        106,
+                        499,
+                        504,
+                        523
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        528,
+                        504,
+                        552
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                527,
+                                505,
+                                543
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        527,
+                                        505,
+                                        543
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Karen Simonyan and Andrew Zisserman. Very deep convolutional networks for large-scale image",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                540,
+                                220,
+                                552
+                            ],
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+                                    "bbox": [
+                                        115,
+                                        540,
+                                        220,
+                                        552
+                                    ],
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+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        }
+                    ],
+                    "index": 31.5,
+                    "bbox_fs": [
+                        105,
+                        527,
+                        505,
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+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        557,
+                        504,
+                        581
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+                        {
+                            "bbox": [
+                                105,
+                                556,
+                                505,
+                                570
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+                                    "bbox": [
+                                        105,
+                                        556,
+                                        505,
+                                        570
+                                    ],
+                                    "score": 1.0,
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+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                569,
+                                191,
+                                580
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        569,
+                                        191,
+                                        580
+                                    ],
+                                    "score": 1.0,
+                                    "content": "sion. ICLR, 2017.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        }
+                    ],
+                    "index": 33.5,
+                    "bbox_fs": [
+                        105,
+                        556,
+                        505,
+                        580
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        586,
+                        504,
+                        609
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                586,
+                                504,
+                                599
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        586,
+                                        504,
+                                        599
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Andreas S Weigend, David E Rumelhart, and Bernardo A Huberman. Generalization by weight-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                597,
+                                344,
+                                609
+                            ],
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+                                    "bbox": [
+                                        116,
+                                        597,
+                                        344,
+                                        609
+                                    ],
+                                    "score": 1.0,
+                                    "content": "elimination with application to forecasting. NIPS, 1991.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        }
+                    ],
+                    "index": 35.5,
+                    "bbox_fs": [
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+                        504,
+                        638
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+                                613,
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+                                        105,
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+                                        506,
+                                        628
+                                    ],
+                                    "score": 1.0,
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+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                117,
+                                626,
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+                                639
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+                                    "bbox": [
+                                        117,
+                                        626,
+                                        259,
+                                        639
+                                    ],
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+                                    "type": "text"
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+                            ],
+                            "index": 38
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+                        643,
+                        376,
+                        655
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+                                642,
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+                                    "bbox": [
+                                        105,
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+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        186,
+                                        644,
+                                        218,
+                                        654
+                                    ],
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+                                    "content": "9 2 . 4 5 \\%",
+                                    "type": "inline_equation"
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+                                        218,
+                                        642,
+                                        376,
+                                        657
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+                            "index": 39
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+                    ],
+                    "index": 39,
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+                        433,
+                        673
+                    ],
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+                                660,
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+                                        105,
+                                        660,
+                                        435,
+                                        674
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+                                    "content": "Sergey Zagoruyko and Nikos Komodakis. Wide residual networks. BMVC, 2016.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        }
+                    ],
+                    "index": 40,
+                    "bbox_fs": [
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+                        702
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+                                        504,
+                                        691
+                                    ],
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+                            ],
+                            "index": 41
+                        },
+                        {
+                            "bbox": [
+                                115,
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index 0000000000000000000000000000000000000000..f17c04c9437a00bc56c78cee9f4cde0eea80955b
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diff --git a/parse/train/BkVsEMYel/BkVsEMYel.md b/parse/train/BkVsEMYel/BkVsEMYel.md
new file mode 100644
index 0000000000000000000000000000000000000000..c8b3bbff323c6215af4ac8239b721c2830c4a317
--- /dev/null
+++ b/parse/train/BkVsEMYel/BkVsEMYel.md
@@ -0,0 +1,719 @@
+# INDUCTIVE BIAS OF DEEP CONVOLUTIONAL NETWORKS THROUGH POOLING GEOMETRY
+
+Nadav Cohen & Amnon Shashua {cohennadav,shashua}@cs.huji.ac.il
+
+# ABSTRACT
+
+Our formal understanding of the inductive bias that drives the success of convolutional networks on computer vision tasks is limited. In particular, it is unclear what makes hypotheses spaces born from convolution and pooling operations so suitable for natural images. In this paper we study the ability of convolutional networks to model correlations among regions of their input. We theoretically analyze convolutional arithmetic circuits, and empirically validate our findings on other types of convolutional networks as well. Correlations are formalized through the notion of separation rank, which for a given partition of the input, measures how far a function is from being separable. We show that a polynomially sized deep network supports exponentially high separation ranks for certain input partitions, while being limited to polynomial separation ranks for others. The network’s pooling geometry effectively determines which input partitions are favored, thus serves as a means for controlling the inductive bias. Contiguous pooling windows as commonly employed in practice favor interleaved partitions over coarse ones, orienting the inductive bias towards the statistics of natural images. Other pooling schemes lead to different preferences, and this allows tailoring the network to data that departs from the usual domain of natural imagery. In addition to analyzing deep networks, we show that shallow ones support only linear separation ranks, and by this gain insight into the benefit of functions brought forth by depth – they are able to efficiently model strong correlation under favored partitions of the input.
+
+# 1 INTRODUCTION
+
+A central factor in the application of machine learning to a given task is the inductive bias, i.e. the choice of hypotheses space from which learned functions are taken. The restriction posed by the inductive bias is necessary for practical learning, and reflects prior knowledge regarding the task at hand. Perhaps the most successful exemplar of inductive bias to date manifests itself in the use of convolutional networks (LeCun and Bengio (1995)) for computer vision tasks. These hypotheses spaces are delivering unprecedented visual recognition results (e.g. Krizhevsky et al. (2012); Szegedy et al. (2015); Simonyan and Zisserman (2014); He et al. (2015)), largely responsible for the resurgence of deep learning (LeCun et al. (2015)). Unfortunately, our formal understanding of the inductive bias behind convolutional networks is limited – the assumptions encoded into these models, which seem to form an excellent prior knowledge for imagery data, are for the most part a mystery.
+
+Existing works studying the inductive bias of deep networks (not necessarily convolutional) do so in the context of depth efficiency, essentially arguing that for a given amount of resources, more layers result in higher expressiveness. More precisely, depth efficiency refers to a situation where a function realized by a deep network of polynomial size, requires super-polynomial size in order to be realized (or approximated) by a shallower network. In recent years, a large body of research was devoted to proving existence of depth efficiency under different types of architectures (see for example Delalleau and Bengio (2011); Pascanu et al. (2013); Montufar et al. (2014); Telgarsky (2015); Eldan and Shamir (2015); Poggio et al. (2015); Mhaskar et al. (2016)). Nonetheless, despite the wide attention it is receiving, depth efficiency does not convey the complete story behind the inductive bias of deep networks. While it does suggest that depth brings forth functions that are otherwise unattainable, it does not explain why these functions are useful. Loosely speaking, the hypotheses space of a polynomially sized deep network covers a small fraction of the space of all functions. We would like to understand why this small fraction is so successful in practice.
+
+A specific family of convolutional networks gaining increased attention is that of convolutional arithmetic circuits. These models follow the standard paradigm of locality, weight sharing and pooling, yet differ from the most conventional convolutional networks in that their point-wise activations are linear, with non-linearity originating from product pooling. Recently, Cohen et al. (2016b) analyzed the depth efficiency of convolutional arithmetic circuits, showing that besides a negligible (zero measure) set, all functions realizable by a deep network require exponential size in order to be realized (or approximated) by a shallow one. This result, termed complete depth efficiency, stands in contrast to previous depth efficiency results, which merely showed existence of functions efficiently realizable by deep networks but not by shallow ones. Besides their analytic advantage, convolutional arithmetic circuits are also showing promising empirical performance. In particular, they are equivalent to SimNets – a deep learning architecture that excels in computationally constrained settings (Cohen and Shashua (2014); Cohen et al. (2016a)), and in addition, have recently been utilized for classification with missing data (Sharir et al. (2016)). Motivated by these theoretical and practical merits, we focus our analysis in this paper on convolutional arithmetic circuits, viewing them as representative of the class of convolutional networks. We empirically validate our conclusions with both convolutional arithmetic circuits and convolutional rectifier networks – convolutional networks with rectified linear (ReLU, Nair and Hinton (2010)) activation and max or average pooling. Adaptation of the formal analysis to networks of the latter type, similarly to the adaptation of the analysis in Cohen et al. (2016b) carried out by Cohen and Shashua (2016), is left for future work.
+
+Our analysis approaches the study of inductive bias from the direction of function inputs. Specifically, we study the ability of convolutional arithmetic circuits to model correlation between regions of their input. To analyze the correlations of a function, we consider different partitions of input regions into disjoint sets, and ask how far the function is from being separable w.r.t. these partitions. Distance from separability is measured through the notion of separation rank (Beylkin and Mohlenkamp (2002)), which can be viewed as a surrogate of the $L ^ { 2 }$ distance from the closest separable function. For a given function and partition of its input, high separation rank implies that the function induces strong correlation between sides of the partition, and vice versa.
+
+We show that a deep network supports exponentially high separation ranks for certain input partitions, while being limited to polynomial or linear (in network size) separation ranks for others. The network’s pooling geometry effectively determines which input partitions are favored in terms of separation rank, i.e. which partitions enjoy the possibility of exponentially high separation rank with polynomial network size, and which require network to be exponentially large. The standard choice of square contiguous pooling windows favors interleaved (entangled) partitions over coarse ones that divide the input into large distinct areas. Other choices lead to different preferences, for example pooling windows that join together nodes with their spatial reflections lead to favoring partitions that split the input symmetrically. We conclude that in terms of modeled correlations, pooling geometry controls the inductive bias, and the particular design commonly employed in practice orients it towards the statistics of natural images (nearby pixels more correlated than ones that are far apart). Moreover, when processing data that departs from the usual domain of natural imagery, prior knowledge regarding its statistics can be used to derive respective pooling schemes, and accordingly tailor the inductive bias.
+
+With regards to depth efficiency, we show that separation ranks under favored input partitions are exponentially high for all but a negligible set of the functions realizable by a deep network. Shallow networks on the other hand, treat all partitions equally, and support only linear (in network size) separation ranks. Therefore, almost all functions that may be realized by a deep network require a replicating shallow network to have exponential size. By this we return to the complete depth efficiency result of Cohen et al. (2016b), but with an added important insight into the benefit of functions brought forth by depth – they are able to efficiently model strong correlation under favored partitions of the input.
+
+The remainder of the paper is organized as follows. Sec. 2 provides a brief presentation of necessary background material from the field of tensor analysis. Sec. 3 describes the convolutional arithmetic circuits we analyze, and their relation to tensor decompositions. In sec. 4 we convey the concept of separation rank, on which we base our analyses in sec. 5 and 6. The conclusions from our analyses are empirically validated in sec. 7. Finally, sec. 8 concludes.
+
+# 2 PRELIMINARIES
+
+The analyses carried out in this paper rely on concepts and results from the field of tensor analysis. In this section we establish the minimal background required in order to follow our arguments 1 , referring the interested reader to Hackbusch (2012) for a broad and comprehensive introduction to the field.
+
+The core concept in tensor analysis is a tensor, which for our purposes may simply be thought of as a multi-dimensional array. The order of a tensor is defined to be the number of indexing entries in the array, which are referred to as modes. The dimension of a tensor in a particular mode is defined as the number of values that may be taken by the index in that mode. For example, a 4-by-3 matrix is a tensor of order 2, i.e. it has two modes, with dimension 4 in mode 1 and dimension 3 in mode 2. If $\mathcal { A }$ is a tensor of order $N$ and dimension $M _ { i }$ in each mode $i \in [ N ] : = \{ 1 , . . . , N \}$ , the space of all configurations it can take is denoted, quite naturally, by $\mathbb { R } ^ { M _ { 1 } \times \cdots \times \bar { M } _ { N } }$ .
+
+A fundamental operator in tensor analysis is the tensor product, which we denote by $\otimes$ . It is an operator that intakes two tensors $\mathcal { A } \in \mathbb { R } ^ { M _ { 1 } \times \cdots \times M _ { P } }$ and $B \in \mathbb { R } ^ { M _ { P + 1 } \times \cdots \times M _ { P + Q } }$ (orders $P$ and $Q$ respectively), and returns a tensor $\mathcal { A } \otimes \mathcal { B } \in \mathbb { R } ^ { M _ { 1 } \times \cdots \times M _ { P + Q } }$ (order $P + Q )$ defined by: $( A \otimes$ $\mathcal { B } ) _ { d _ { 1 } . . . d _ { P + Q } } = \mathcal { A } _ { d _ { 1 } . . . d _ { P } } \cdot \mathcal { B } _ { d _ { P + 1 } . . . d _ { P + Q } }$ . Notice that in the case $P = Q = 1$ , the tensor product reduces to the standard outer product between vectors, i.e. if $\mathbf { u } \in \mathbb { R } ^ { M _ { 1 } }$ and $\mathbf { v } \in \mathbb { R } ^ { M _ { 2 } }$ , then $\mathbf { u } \otimes \mathbf { v }$ is no other than the rank-1 matrix $\mathbf { u } \mathbf { v } ^ { \top } \in \mathbb { R } ^ { M _ { 1 } \times M _ { 2 } }$ .
+
+We now introduce the important concept of matricization, which is essentially the rearrangement of a tensor as a matrix. Suppose $\mathcal { A }$ is a tensor of order $N$ and dimension $M _ { i }$ in each mode $i \in [ N ]$ , and let $( I , J )$ be a partition of $[ N ]$ , i.e. $I$ and $J$ are disjoint subsets of $[ N ]$ whose union gives $[ N ]$ . We may write $I = \{ i _ { 1 } , \dots , i _ { | I | } \}$ where $i _ { 1 } < \cdots < i _ { | I | }$ , and similarly $\dot { J } = \{ j _ { 1 } , \dots , j _ { | J | } \}$ where $j _ { 1 } <$ $\cdots < j _ { | J | }$ . The matricization of $\mathcal { A }$ w.r.t. the partition $( I , J )$ , denoted $\mathbb { I } \mathbb { A } \mathbb { I } _ { I , J }$ , is the $\Pi _ { t = 1 } ^ { | I | } M _ { i _ { t } }$ -by$\textstyle \prod _ { t = 1 } ^ { | J | } M _ { j _ { t } }$ matrix holding the entries of $\mathcal { A }$ such that $\mathcal { A } _ { d _ { 1 } . . . d _ { N } }$ J Kis placed in row index $\begin{array} { r } { 1 + \sum _ { t = 1 } ^ { | I | } ( d _ { i _ { t } } - } \end{array}$ 1) $\begin{array} { r } { { \ u { 1 } } \prod _ { t ^ { \prime } = t + 1 } ^ { | I | } M _ { i _ { t ^ { \prime } } } } \end{array}$ and column index $\begin{array} { r } { 1 + \sum _ { t = 1 } ^ { | J | } ( d _ { j _ { t } } - 1 ) \prod _ { t ^ { \prime } = t + 1 } ^ { | J | } M _ { j _ { t ^ { \prime } } } } \end{array}$ . If $I = \emptyset$ or $J = \emptyset$ , then by definition $\mathbb { I } \mathbb { A } \mathbb { I } _ { I , J }$ is a row or column (respectively) vector of dimension $\textstyle \prod _ { t = 1 } ^ { N } M _ { t }$ holding $\mathcal { A } _ { d _ { 1 } . . . d _ { N } }$ in entry $\begin{array} { r } { 1 + \sum _ { t = 1 } ^ { N } ( d _ { t } - 1 ) \prod _ { t ^ { \prime } = t + 1 } ^ { N } M _ { t ^ { \prime } } } \end{array}$ .
+
+A well known matrix operator is the Kronecker product, which we denote by $\odot$ . For two matrices $A \ \in \ \mathbb { R } ^ { M _ { 1 } \times M _ { 2 } }$ and $\boldsymbol { B } ^ { \star } \in \mathbb { R } ^ { N _ { 1 } \times N _ { 2 } }$ , $A { \odot } B$ is the matrix in $\mathbb { R } ^ { M _ { 1 } N _ { 1 } \times M _ { 2 } N _ { 2 } }$ holding $A _ { i j } B _ { k l }$ in row index $( i - 1 ) N _ { 1 } + k$ and column index $( j - 1 ) N _ { 2 } + l$ . Let $\mathcal { A }$ and $\boldsymbol { B }$ be tensors of orders $P$ and $Q$ respectively, and let $( I , J )$ be a partition of $[ P + Q ]$ . The basic relation that binds together the tensor product, the matricization operator, and the Kronecker product, is:
+
+$$
+[ A \otimes B ] _ { I , J } = [ [ A ] _ { I \cap [ P ] , J \cap [ P ] } \odot [ [ B ] _ { ( I - P ) \cap [ Q ] , ( J - P ) \cap [ Q ] }
+$$
+
+where $I - P$ and $J - P$ are simply the sets obtained by subtracting $P$ from each of the elements in $I$ and $J$ respectively. In words, eq. 1 implies that the matricization of the tensor product between $\mathcal { A }$ and $\boldsymbol { B }$ w.r.t. the partition $( I , J )$ of $[ P ^ { - } + Q ]$ , is equal to the Kronecker product between two matricizations: that of $\mathcal { A }$ w.r.t. the partition of $[ P ]$ induced by the lower values of $( I , J )$ , and that of $\boldsymbol { B }$ w.r.t. the partition of $[ Q ]$ induced by the higher values of $( I , J )$ .
+
+# 3 CONVOLUTIONAL ARITHMETIC CIRCUITS
+
+The convolutional arithmetic circuit architecture on which we focus in this paper is the one considered in Cohen et al. (2016b), portrayed in fig. 1(a). Instances processed by a network are represented as $N$ -tuples of $s$ -dimensional vectors. They are generally thought of as images, with the $s$ -dimensional vectors corresponding to local patches. For example, instances could be 32-by-32 RGB images, with local patches being $5 \times 5$ regions crossing the three color bands. In this case, assuming a patch is taken around every pixel in an image (boundaries padded), we have $N = 1 0 2 4$ and $s \ = \ 7 5$ . Throughout the paper, we denote a general instance by $X = ( \mathbf { x } _ { 1 } , \ldots , \mathbf { x } _ { N } )$ , with $\mathbf { x } _ { 1 } \ldots \mathbf { x } _ { N } \in \mathbb { R } ^ { s }$ standing for its patches.
+
+![](images/f82db9947b5d7317663714f7caba841ef01195b93260f3948f8fb4026e42f1e5.jpg)  
+Figure 1: Best viewed in color. (a) Convolutional arithmetic circuit architecture analyzed in this paper (see description in sec. 3). $( b )$ Shallow network with global pooling in its single hidden layer. $( c )$ Illustration of input patch ordering for deep network with $2 \times 2$ pooling windows, along with patterns induced by the partitions $( I ^ { o d d } , J ^ { e v e n } ) ^ { { \bf \Phi } }$ and $( I ^ { l o w } , J ^ { h i g h } )$ (eq. 8 and 9 respectively).
+
+The first layer in a network is referred to as representation. It consists of applying $M$ representation functions $f _ { \theta _ { 1 } } \cdot \cdot \cdot f _ { \theta _ { M } } : \mathbb { R } ^ { s } \to \mathbb { R }$ to all patches, thereby creating $M$ feature maps. In the case where representation functions are chosen as $f _ { \boldsymbol { \theta } _ { d } } ( \mathbf { x } ) = \mathbf { \bar { \sigma } } \sigma ( \mathbf { w } _ { d } ^ { \top } \mathbf { x } + b _ { d } )$ , with parameters $\mathbf { \theta } _ { d } = ( \mathbf { w } _ { d } , b _ { d } ) \in \mathbf { \bar { \mathbb { R } } } ^ { s } \times \mathbb { R }$ and some point-wise activation $\sigma ( \cdot )$ , the representation layer reduces to a standard convolutional layer. More elaborate settings are also possible, for example modeling the representation as a cascade of convolutional layers with pooling in-between. Following the representation, a network includes $L$ hidden layers indexed by $l = 0 . . . L - 1$ . Each hidden layer $l$ begins with a $1 \times 1$ conv operator, which is simply a three-dimensional convolution with $r _ { l }$ channels and filters of spatial dimensions 1-by-1. 2 This is followed by spatial pooling, that decimates feature maps by taking products of non-overlapping two-dimensional windows that cover the spatial extent. The last of the $L$ hidden layers $( l = L - 1 )$ ) reduces feature maps to singletons (its pooling operator is global), creating a vector of dimension $r _ { L - 1 }$ . This vector is mapped into $Y$ network outputs through a final dense linear layer.
+
+Altogether, the architectural parameters of a network are the type of representation functions $( f _ { \theta _ { d } } )$ , the pooling window shapes and sizes (which in turn determine the number of hidden layers $L$ ), and the number of channels in each layer ( $M$ for representation, $r _ { 0 } . . . r _ { L - 1 }$ for hidden layers, $Y$ for output). Given these architectural parameters, the learnable parameters of a network are the representation weights $\theta _ { d }$ for channel $d$ ), the conv weights ( $\mathbf { \bar { a } } ^ { l , \gamma }$ for channel $\gamma$ of hidden layer $l$ ), and the output weights $\scriptstyle ( \mathbf { a } ^ { L , y }$ for output node $y$ ).
+
+For a particular setting of weights, every node (neuron) in a given network realizes a function from $( \mathbf { \bar { \mathbb { R } } } ^ { s } ) ^ { N }$ to $\mathbb { R }$ . The receptive field of a node refers to the indexes of input patches on which its function may depend. For example, the receptive field of node $j$ in channel $\gamma$ of conv operator at hidden layer 0 is $\{ j \}$ , and that of an output node is $[ N ]$ , corresponding to the entire input. Denote by $h _ { ( l , \gamma , j ) }$ the function realized by node $j$ of channel $\gamma$ in conv operator at hidden layer $l$ , and let $I ^ { ( l , \gamma , j ) } \subset [ N ]$ be its receptive field. By the structure of the network it is evident that $I ^ { ( l , \gamma , j ) }$ does not depend on $\gamma .$ , so we may write $I ^ { ( l , j ) }$ instead. Moreover, assuming pooling windows are uniform across channels (as customary with convolutional networks), and taking into account the fact that they do not overlap, we conclude that $I ^ { ( l , j _ { 1 } ) }$ and $I ^ { ( l , j _ { 2 } ) }$ are necessarily disjoias $j _ { 1 } \neq j _ { 2 }$ $l = 0 . . . L - 1$ ows tha, where $h _ { ( l , \gamma , j ) }$ be expressedstands for the $\begin{array} { r } { h _ { ( l , \gamma , j ) } ( \mathbf { x } _ { i _ { 1 } } , \ldots , \mathbf { x } _ { i _ { T } } ) = \sum _ { d _ { 1 } \ldots d _ { T } = 1 } ^ { M } { \cal A } _ { d _ { 1 } \ldots d _ { T } } ^ { ( l , \gamma , j ) } \prod _ { t = 1 } ^ { T } f _ { \theta _ { d _ { t } } } ( \mathbf { x } _ { i _ { t } } ) } \end{array}$ $\{ i _ { 1 } , \dots , i _ { T } \}$ receptive field $I ^ { ( l , j ) }$ , and $\mathcal { A } ^ { ( l , \gamma , j ) }$ is a tensor of order $T = | I ^ { ( l , j ) } |$ and dimension $M$ with entries given by polynomials in the network’s conv weights $\{ \mathbf { a } ^ { l , \gamma } \} _ { l , \gamma }$ . Taking the induction one step further (from last hidden layer to network output), we obtain the following expression for functions realized by network outputs:
+
+$$
+h _ { y } \left( \mathbf { x } _ { 1 } , \ldots , \mathbf { x } _ { N } \right) = \sum _ { d _ { 1 } \ldots d _ { N } = 1 } ^ { M } { \mathcal { A } } _ { d _ { 1 } \ldots d _ { N } } ^ { y } \prod _ { i = 1 } ^ { N } f _ { \theta _ { d _ { i } } } ( \mathbf { x } _ { i } )
+$$
+
+$y \in [ Y ]$ here is an output node index, and $h _ { y }$ is the function realized by that node. $\mathcal { A } ^ { y }$ is a tensor of order $N$ and dimension $M$ in each mode, with entries given by polynomials in the network’s conv weights $\{ \mathbf { a } ^ { l , \gamma } \} _ { l , \gamma }$ and output weights $\mathbf { a } ^ { L , y }$ . Hereafter, terms such as function realized by a network or coefficient tensor realized by a network, are to be understood as referring to $h _ { y }$ or $\mathcal { A } ^ { y }$ respectively. Next, we present explicit expressions for $\mathcal { A } ^ { y }$ under two canonical networks – deep and shallow.
+
+Deep network. Consider a network as in fig. 1(a), with pooling windows set to cover four entries each, resulting in $L = \log _ { 4 } N$ hidden layers. The linear weights of such a network are $\{ \mathbf { a } ^ { 0 , \gamma } \in$ $\mathbb { R } ^ { M } \} _ { \gamma \in [ r _ { 0 } ] }$ for conv operator in hidden layer 0, $\{ \mathbf { a } ^ { l , \gamma } \in \mathbb { R } ^ { r _ { l - 1 } } \} _ { \gamma \in [ r _ { l } ] }$ for conv operator in hidden layer $l = 1 . . . L - 1$ , and $\{ \mathbf { a } ^ { L , y } \in \mathbb { R } ^ { r _ { L - 1 } } \} _ { y \in [ Y ] }$ for dense output operator. They determine the coefficient tensor $\mathcal { A } ^ { y }$ (eq. 2) through the following recursive decomposition:
+
+$$
+\begin{array} { r l r l } { \underbrace { \phi ^ { 1 , \gamma } } _ { \mathrm { o r d e r } 4 } } & { = } & { \sum _ { \alpha = 1 } ^ { r _ { 0 } } a _ { \alpha } ^ { 1 , \gamma } \cdot \otimes ^ { 4 } \mathbf { a } ^ { 0 , \alpha } } & & { , \gamma \in [ r _ { 1 } ] } \\ { \mathrm { ~ } } & { \dots } & & { } \\ { \underbrace { \phi ^ { l , \gamma } } _ { \mathrm { o r d e r } 4 ^ { l } } } & { = } & { \sum _ { \alpha = 1 } ^ { r _ { l - 1 } } a _ { \alpha } ^ { l , \gamma } \cdot \otimes ^ { 4 } \phi ^ { l - 1 , \alpha } } & & { , l \in \{ 2 , \dots L - 1 \} , \gamma \in [ r _ { l } ] } \\ & { \dots } & \\ { \underbrace { \mathcal { A } ^ { y } } _ { \mathrm { o r d e r } 4 ^ { L } } } & { = } & { \sum _ { \alpha = 1 } ^ { r _ { L - 1 } } a _ { \alpha } ^ { L , y } \cdot \otimes ^ { 4 } \phi ^ { L - 1 , \alpha } } \end{array}
+$$
+
+$a _ { \alpha } ^ { l , \gamma }$ and $a _ { \alpha } ^ { L , y }$ here are scalars representing entry $\alpha$ in the vectors $\mathbf { a } ^ { l , \gamma }$ and $\mathbf { a } ^ { L , y }$ respectively, and the symbol $\otimes$ with a superscript stands for a repeated tensor product, e.g. $\otimes ^ { 4 } \mathbf { a } ^ { 0 , \alpha } : = \mathbf { a } ^ { 0 , \alpha } \otimes \mathbf { a } ^ { 0 , \bar { \alpha } } \otimes \mathbf { a } ^ { 0 , \alpha } \otimes$ $\mathbf { a } ^ { 0 , \alpha }$ . To verify that under pooling windows of size four $\mathcal { A } ^ { y }$ is indeed given by eq. 3, simply plug the rows of the decomposition into eq. 2, starting from bottom and continuing upwards. For context, eq. 3 describes what is known as a hierarchical tensor decomposition (see chapter 11 in Hackbusch (2012)), with underlying tree over modes being a full quad-tree (corresponding to the fact that the network’s pooling windows cover four entries each).
+
+Shallow network. The second network we pay special attention to is shallow, comprising a single hidden layer with global pooling – see illustration in fig. 1(b). The linear weights of such a network are $\{ \mathbf { a } ^ { 0 , \gamma } \in \mathbb { R } ^ { M } \} _ { \gamma \in [ r _ { 0 } ] }$ for hidden conv operator and $\{ \mathbf { a } ^ { 1 , y } \in \mathbb { R } ^ { r _ { 0 } } \} _ { y \in [ Y ] }$ for dense output operator. They determine the coefficient tensor $\mathcal { A } ^ { y }$ (eq. 2) as follows:
+
+$$
+\mathcal { A } ^ { y } = \sum _ { \gamma = 1 } ^ { r _ { 0 } } a _ { \gamma } ^ { 1 , y } \cdot \otimes ^ { N } \mathbf { a } ^ { 0 , \gamma }
+$$
+
+where $a _ { \gamma } ^ { 1 , y }$ stands for entry $\gamma$ of $\mathbf { a } ^ { 1 , y }$ , and again, the symbol $\otimes$ with a superscript represents a repeated tensor product. The tensor decomposition in eq. 4 is an instance of the classic CP decomposition, also known as rank-1 decomposition (see Kolda and Bader (2009) for a historic survey).
+
+To conclude this section, we relate the background material above, as well as our contribution described in the upcoming sections, to the work of Cohen et al. (2016b). The latter shows that with arbitrary coefficient tensors $\mathcal { A } ^ { y }$ , functions $h _ { y }$ as in eq. 2 form a universal hypotheses space. It is then shown that convolutional arithmetic circuits as in fig. 1(a) realize such functions by applying tensor decompositions to $\mathcal { A } ^ { y }$ , with the type of decomposition determined by the structure of a network (number of layers, number of channels in each layer etc.). The deep network (fig. 1(a) with size-4 pooling windows and $L = \log _ { 4 } N$ hidden layers) and the shallow network (fig. 1(b)) presented hereinabove are two special cases, whose corresponding tensor decompositions are given in eq. 3 and 4 respectively. The central result in Cohen et al. (2016b) relates to inductive bias through the notion of depth efficiency – it is shown that in the parameter space of a deep network, all weight settings but a set of (Lebesgue) measure zero give rise to functions that can only be realized (or approximated) by a shallow network if the latter has exponential size. This result does not relate to the characteristics of instances $X = ( \mathbf { x } _ { 1 } , \ldots , \mathbf { x } _ { N } )$ , it only treats the ability of shallow networks to replicate functions realized by deep networks.
+
+In this paper we draw a line connecting the inductive bias to the nature of $X$ , by studying the relation between a network’s architecture and its ability to model correlation among patches $\mathbf { x } _ { i }$ . Specifically, in sec. 4 we consider partitions $( I , J )$ of $[ N ]$ $\mathbf { \Psi } _ { I \cup J } = \left[ N \right]$ , where $\left\lfloor \cdot \right\rfloor$ stands for disjoint union), and present the notion of separation rank as a measure of the correlation modeled between the patches indexed by $I$ and those indexed by $J$ . In sec. 5.1 the separation rank of a network’s function $h _ { y }$ w.r.t. a partition $( I , J )$ is proven to be equal to the rank of $\mathbb { I } \boldsymbol { \mathcal { A } } ^ { y } \mathbb { I } _ { I , J }$ – the matricization of the coefficient tensor $\mathcal { A } ^ { y }$ w.r.t. $( I , J )$ J K. Sec. 5.2 derives lower and upper bounds on this rank for a deep network, showing that it supports exponential separation ranks with polynomial size for certain partitions, whereas for others it is required to be exponentially large. Subsequently, sec. 5.3 establishes an upper bound on $r a n k \ [ \mathcal { A } ^ { y } ] ] _ { I , J }$ for shallow networks, implying that these J Kmust be exponentially large in order to model exponential separation rank under any partition, and thus cannot efficiently replicate a deep network’s correlations. Our analysis concludes in sec. 6, where we discuss the pooling geometry of a deep network as a means for controlling the inductive bias by determining a correspondence between partitions $( I , J )$ and spatial partitions of the input. Finally, we demonstrate experimentally in sec. 7 how different pooling geometries lead to superior performance in different tasks. Our experiments include not only convolutional arithmetic circuits, but also convolutional rectifier networks, i.e. convolutional networks with ReLU activation and max or average pooling.
+
+# 4 SEPARATION RANK
+
+In this section we define the concept of separation rank for functions realized by convolutional arithmetic circuits (sec. 3), i.e. real functions that take as input $X = ( \mathbf { x } _ { 1 } , \ldots , \mathbf { x } _ { N } ) { \overset { } { \in } } ( \mathbb { R } ^ { s } ) ^ { N }$ . The separation rank serves as a measure of the correlations such functions induce between different sets of input patches, i.e. different subsets of the variable set $\left\{ \mathbf { x } _ { 1 } , \dotsc , \mathbf { x } _ { N } \right\}$ .
+
+Let $( I , J )$ be a partition of input indexes, i.e. $I$ and $J$ are disjoint subsets of $[ N ]$ whose union gives $[ N ]$ . We may write $I = \{ i _ { 1 } , \ldots , i _ { | I | } \}$ where $i _ { 1 } < \cdots < i _ { | I | }$ , and similarly $\bar { J } = \{ j _ { 1 } , \dotsc , j _ { | J | } \}$ where $j _ { 1 } < \cdots < j _ { | J | }$ . For a function $h : ( \mathbb { R } ^ { s } ) ^ { N } \to \mathbb { R }$ , the separation rank w.r.t. the partition $( I , J )$ is defined as follows: 3
+
+$$
+\begin{array} { c } { { s e p ( h ; I , J ) : = \operatorname* { m i n } \Big \{ R \in { \mathbb { N } \cup \{ 0 \} : \exists g _ { 1 } . . . g _ { R } : ( { \mathbb { R } ^ { s } } ) ^ { | I | }  { \mathbb { R } } , g _ { 1 } ^ { \prime } . . . g _ { R } ^ { \prime } : ( { \mathbb { R } ^ { s } } ) ^ { | J | }  { \mathbb { R } } \ s . t . } } } \\ { { h ( { \mathbf x } _ { 1 } , . . . \ , { \mathbf x } _ { N } ) = \sum _ { \nu = 1 } ^ { R } g _ { \nu } ( { \mathbf x } _ { i _ { 1 } } , . . . , { \mathbf x } _ { i _ { | I | } } ) g _ { \nu } ^ { \prime } ( { \mathbf x } _ { j _ { 1 } } , . . . , { \mathbf x } _ { j _ { | J | } } ) \Big \} } } \end{array}
+$$
+
+In words, it is the minimal number of summands that together give $h$ , where each summand is separable w.r.t. $( I , J )$ , i.e. is equal to a product of two functions – one that intakes only patches indexed by $I$ , and another that intakes only patches indexed by $J$ . One may wonder if it is at all possible to express $h$ through such summands, i.e. if the separation rank of $h$ is finite. From the theory of tensor products between $L ^ { 2 }$ spaces (see Hackbusch (2012) for a comprehensive coverage), we know that any $h { \in } L ^ { 2 } ( ( \mathbb { R } ^ { s } ) ^ { N } )$ , i.e. any $h$ that is measurable and square-integrable, may be approximated arbitrarily well by summations of the form $\begin{array} { r } { \sum _ { \nu = 1 } ^ { R } g _ { \nu } ( \mathbf { x } _ { i _ { 1 } } , \dots , \mathbf { x } _ { i _ { | I | } } ) g _ { \nu } ^ { \prime } ( \mathbf { x } _ { j _ { 1 } } , \dots , \mathbf { x } _ { j _ { | J | } } ) } \end{array}$ . Exact realization however is only guaranteed at the limit $R \to \infty$ , thus in general the separation rank of $h$ need not be finite. Nonetheless, as we show in sec. 5, for the class of functions we are interested in, namely functions realizable by convolutional arithmetic circuits, separation ranks are always finite.
+
+The concept of separation rank was introduced in Beylkin and Mohlenkamp (2002) for numerical treatment of high-dimensional functions, and has since been employed for various applications, e.g. quantum chemistry (Harrison et al. (2003)), particle engineering (Hackbusch (2006)) and machine learning (Beylkin et al. (2009)). If the separation rank of a function w.r.t. a partition of its input is equal to 1, the function is separable, meaning it does not model any interaction between the sets of variables. Specifically, if $s e p ( h ; I , J ) ~ = ~ 1$ then there exist $g : ( \mathbb { R } ^ { s } ) ^ { | I | } \  \ \mathbb { R }$ and $g ^ { \prime } : ( \mathbb { R } ^ { s } ) ^ { | J | } \to \mathbb { R }$ such that $h ( { \bf x } _ { 1 } , \ldots , { \bf x } _ { N } ) = g ( { \bf x } _ { i _ { 1 } } , \ldots , { \bf x } _ { i _ { | I | } } ) g ^ { \prime } ( { \bf x } _ { j _ { 1 } } , \ldots , { \bf x } _ { j _ { | J | } } )$ , and the function $h$ cannot take into account consistency between the values of $\{ \mathbf { x } _ { i _ { 1 } } , \dotsc , \mathbf { x } _ { i _ { | I | } } \}$ and those of $\{ \mathbf { x } _ { j _ { 1 } } , \dotsc , \mathbf { x } _ { j _ { | J | } } \}$ . In a statistical setting, if $h$ is a probability density function, this would mean that $\{ \mathbf { x } _ { i _ { 1 } } , \dotsc , \mathbf { x } _ { i _ { | I | } } \}$ and $\{ \mathbf { x } _ { j _ { 1 } } , \dotsc , \mathbf { x } _ { j _ { | J | } } \}$ are statistically independent. The higher $s e p  ( h ; I , J )$ is, the farther $h$ is from this situation, i.e. the more it models dependency between $\{ \mathbf { x } _ { i _ { 1 } } , \dotsc , \mathbf { x } _ { i _ { | I | } } \}$ and $\left\{ \mathbf { x } _ { j _ { \frac { 1 } { 2 } } } , \dotsc , \mathbf { x } _ { j _ { | J | } } \right\}$ , or equivalently, the stronger the correlation it induces between the patches indexed by $I$ and those indexed by $J$ .
+
+The interpretation of separation rank as a measure of deviation from separability is formalized in app. B, where it is shown that $s e p  ( h ; I , J )$ is closely related to the $L ^ { 2 }$ distance of $h$ from the set of separable functions w.r.t. $( I , J )$ . Specifically, we define $D ( h ; I , J )$ as the latter distance divided by the $L ^ { 2 }$ norm of $h ^ { \ 4 }$ , and show that $s e p  ( h ; I , J )$ provides an upper bound on $D ( h ; I , J )$ . While it is not possible to lay out a general lower bound on $D ( h ; I , J )$ in terms of $s e p  ( h ; I , J )$ , we show that the specific lower bounds on $s e p  ( h ; I , J )$ underlying our analyses can be translated into lower bounds on $D ( h ; I , J )$ . This implies that our results, facilitated by upper and lower bounds on separation ranks of convolutional arithmetic circuits, may equivalently be framed in terms of $L ^ { 2 }$ distances from separable functions.
+
+# 5 CORRELATION ANALYSIS
+
+In this section we analyze convolutional arithmetic circuits (sec. 3) in terms of the correlations they can model between sides of different input partitions, i.e. in terms of the separation ranks (sec. 4) they support under different partitions $( I , J )$ of $[ N ]$ . We begin in sec. 5.1, establishing a correspondence between separation ranks and coefficient tensor matricization ranks. This correspondence is then used in sec. 5.2 and 5.3 to analyze the deep and shallow networks (respectively) presented in sec. 3. We note that we focus on these particular networks merely for simplicity of presentation – the analysis can easily be adapted to account for alternative networks with different depths and pooling schemes.
+
+# 5.1 FROM SEPARATION RANK TO MATRICIZATION RANK
+
+Let $h _ { y }$ be a function realized by a convolutional arithmetic circuit, with corresponding coefficient tensor $\mathcal { A } ^ { y }$ (eq. 2). Denote by $( I , J )$ an arbitrary partition of $[ N ]$ , i.e. $I { \uplus } J = { \bf \bar { \rho } } [ N ]$ . We are interested in studying $s e p ( h _ { y } ; I , J ) \ .$ – the separation rank of $h _ { y }$ w.r.t. $( I , J )$ (eq. 5). As claim 1 below states, assuming representation functions $\{ f _ { \theta _ { d } } \} _ { d \in [ M ] }$ are linearly independent (if they are not, we drop dependent functions and modify $\mathcal { A } ^ { y }$ accordingly 5 ), this separation rank is equal to the rank of $\mathbb { [ } \boldsymbol { A } ^ { y } \mathbb { ] } _ { I , J } ^ { - }$ – the matricization of the coefficient tensor $\mathcal { A } ^ { y }$ w.r.t. the partition $( I , J )$ . Our problem J Kthus translates to studying ranks of matricized coefficient tensors.
+
+Claim 1. Let $h _ { y }$ be a function realized by a convolutional arithmetic circuit (fig. 1(a)), with corresponding coefficient tensor $\mathcal { A } ^ { y }$ (eq. 2). Assume that the network’s representation functions $f _ { \theta _ { d } }$ are linearly independent, and that they, as well as the functions $g _ { \nu } , g _ { \nu } ^ { \prime }$ in the definition of separation rank (eq. 5), are measurable and square-integrable. 6 Then, for any partition $( I , J )$ of $[ N ]$ , it holds that $s e p ( h _ { y } ; I , J ) = r a n k \big [ \boldsymbol { \mathcal { A } } ^ { y } \big ] | _ { I , J }$ .
+
+Proof. See app. A.1.
+
+As the linear weights of a network vary, so do the coefficient tensors $( \mathcal { A } ^ { y } )$ it gives rise to. Accordingly, for a particular partition $( I , J )$ , a network does not correspond to a single value of $r a n k \ [ \boldsymbol { \mathcal { A } } ^ { y } ] ] _ { I , J }$ , but rather supports a range of values. We analyze this range by quantifying its maxiJ Kmum, which reflects the strongest correlation that the network can model between the input patches indexed by $I$ and those indexed by $J$ . One may wonder if the maximal value of $r a n k \ [ \mathcal { A } ^ { y } ] ] _ { I , J }$ is the appropriate statistic to measure, as a-priori, it may be that $r a n k \ [ \mathcal { A } ^ { y } ] ] _ { I , J }$ J Kis maximal for very few of J Kthe network’s weight settings, and much lower for all the rest. Apparently, as claim 2 below states, this is not the case, and in fact ra $n k \mathbb { I } A ^ { y } \mathbb { I } _ { I , J }$ is maximal under almost all of the network’s weight settings.
+
+Claim 2. Consider a convolutional arithmetic circuit (fig. $I ( a ) ,$ ) with corresponding coefficient tensor $\mathcal { A } ^ { y }$ (eq. 2). $\mathcal { A } ^ { y }$ depends on the network’s linear weights – $\{ \mathbf { a } ^ { l , \gamma } \} _ { l , \gamma }$ and $\mathbf { a } ^ { L , y }$ , thus for a given partition $( I , J )$ of $[ N ]$ , rank $\mathbb { I } \boldsymbol { \mathcal { A } } ^ { y } \mathbb { I } _ { I , J }$ is a function of these weights. This function obtains its maximum almost everywhere (w.r.t. Lebesgue measure).
+
+Proof. See app. A.2.
+
+# 5.2 DEEP NETWORK
+
+In this subsection we study correlations modeled by the deep network presented in sec. 3 (fig. 1(a) with size-4 pooling windows and $L = \log _ { 4 } N$ hidden layers). In accordance with sec. 5.1, we do so by characterizing the maximal ranks of coefficient tensor matricizations under different partitions.
+
+Recall from eq. 3 the hierarchical decomposition expressing a coefficient tensor $\mathcal { A } ^ { y }$ realized by the deep network. We are interested in matricizations of this tensor under different partitions of $[ N ]$ . Let $( I , J )$ be an arbitrary partition, i.e. $I { \uplus } J = [ N ]$ . Matricizing the last level of eq. 3 w.r.t. $( I , J )$ , while applying the relation in eq. 1, gives:
+
+$$
+\begin{array} { r c l } { { [ [ } A ^ { y } ] ] _ { I , J } }  & { { = } } & { { \sum _ { \alpha = 1 } ^ { r _ { L - 1 } } a _ { \alpha } ^ { L , y } \cdot \left[ [ \phi ^ { L - 1 , \alpha } \otimes \phi ^ { L - 1 , \alpha } \otimes \phi ^ { L - 1 , \alpha } \otimes \phi ^ { L - 1 , \alpha } ] _ { I , J } \right. } } \\ { { } } & { { = } } & { { \sum _ { \alpha = 1 } ^ { r _ { L - 1 } } a _ { \alpha } ^ { L , y } \cdot [ \phi ^ { L - 1 , \alpha } \otimes \phi ^ { L - 1 , \alpha } ] _ { I \cap [ 2 \cdot 4 ^ { L - 1 } ] , J \cap [ 2 \cdot 4 ^ { L - 1 } ] } } } \\ { { } } & { { } } & { { \odot \left[ \phi ^ { L - 1 , \alpha } \otimes \phi ^ { L - 1 , \alpha } \right] _ { ( I - 2 \cdot 4 ^ { L - 1 } ) \cap [ 2 \cdot 4 ^ { L - 1 } ] , ( J - 2 \cdot 4 ^ { L - 1 } ) \cap [ 2 \cdot 4 ^ { L - 1 } ] } } } \end{array}
+$$
+
+Applying eq. 1 again, this time to matricizations of the tensor $\phi ^ { L - 1 , \alpha } \otimes \phi ^ { L - 1 , \alpha }$ , we obtain:
+
+$$
+\begin{array} { l l l l } { { [ \mathcal { A } ^ { y } ] _ { I , J } } } & { { = } } & { { \sum _ { \alpha = 1 } ^ { r _ { L - 1 } } a _ { \alpha } ^ { L , y } \cdot \left[ \left. \phi ^ { L - 1 , \alpha } \right. _ { I \cap [ 4 ^ { L - 1 } ] , J \cap [ 4 ^ { L - 1 } ] } \right. } } \\ { { } } & { { } } & { { \odot \left[ \phi ^ { L - 1 , \alpha } \right] _ { \left( I - 4 ^ { L - 1 } \right) \cap [ 4 ^ { L - 1 } ] , \left( J - 4 ^ { L - 1 } \right) \cap [ 4 ^ { L - 1 } ] } } } \\ { { } } & { { } } & { { \odot \left[ \phi ^ { L - 1 , \alpha } \right] _ { \left( I - 2 \cdot 4 ^ { L - 1 } \right) \cap [ 4 ^ { L - 1 } ] , \left( J - 2 \cdot 4 ^ { L - 1 } \right) \cap [ 4 ^ { L - 1 } ] } } } \\ { { } } & { { } } & { { \odot \left[ \phi ^ { L - 1 , \alpha } \right] _ { \left( I - 3 \cdot 4 ^ { L - 1 } \right) \cap [ 4 ^ { L - 1 } ] , \left( J - 3 \cdot 4 ^ { L - 1 } \right) \cap [ 4 ^ { L - 1 } ] } } } \end{array}
+$$
+
+For every $k \in [ 4 ]$ define $I _ { L - 1 , k } : = ( I - ( k - 1 ) \cdot 4 ^ { L - 1 } ) \cap [ 4 ^ { L - 1 } ]$ and $J _ { L - 1 , k } : = ( J - ( k - 1 ) \cdot 4 ^ { L - 1 } ) \cap$ $[ 4 ^ { L - 1 } ]$ . In words, $\left( I _ { L - 1 , k } , J _ { L - 1 , k } \right)$ represents the partition induced by $( I , J )$ on the $k$ ’th quadrant of $[ N ]$ , i.e. on the $k$ ’th size- $\cdot 4 ^ { L - 1 }$ group of input patches. We now have the following matricized version of the last level in eq. 3:
+
+$$
+\begin{array} { r } { \mathbb { [ } A ^ { y } ] _ { I , J } = \sum _ { \alpha = 1 } ^ { r _ { L - 1 } } a _ { \alpha } ^ { L , y } \cdot \underset { t = 1 } { \overset { 4 } { \odot } } \mathbb { [ } \phi ^ { L - 1 , \alpha } \mathbb { ] } _ { I _ { L - 1 , t } , J _ { L - 1 , t } } } \end{array}
+$$
+
+where the symbol $\odot$ with a running index stands for an iterative Kronecker product. To derive analogous matricized versions for the upper levels of eq. 3, we define for $l \in \{ 0 . . . L - 1 \} , k \in$ $[ N / 4 ^ { \widetilde { l } } ]$ :
+
+$$
+I _ { l , k } : = ( I - ( k - 1 ) \cdot 4 ^ { l } ) \cap [ 4 ^ { l } ] \qquad J _ { l , k } : = ( J - ( k - 1 ) \cdot 4 ^ { l } ) \cap [ 4 ^ { l } ]
+$$
+
+That is to say, $\left( { { I } _ { l , k } } , { { J } _ { l , k } } \right)$ represents the partition induced by $( I , J )$ on the set of indexes $\{ ( k -$ $1 ) \cdot 4 ^ { l } + 1 , \ldots , k \cdot 4 ^ { l } \}$ , i.e. on the $k ^ { \mathrm { { \prime } } }$ ’th size- $. 4 ^ { l }$ group of input patches. With this notation in hand, traversing upwards through the levels of eq. 3, with repeated application of the relation in eq. 1, one arrives at the following matrix decomposition for $\mathbb { I } ^ { \boldsymbol { A } ^ { y } } \mathbb { I } _ { \boldsymbol { I } , \boldsymbol { J } }$ :
+
+$$
+\begin{array}{c} \begin{array} { r l } { \underbrace { \left[ \phi ^ { 1 , \gamma } \right] I _ { 1 , k , \cdot } J _ { 1 , k , \cdot } } _ { \begin{array} { l } { 1 } \\ { M ^ { | I _ { 1 , k } | }  { \mathrm { l o p } } \mathcal { M } ^ { | J _ { 1 , k } | } } \end{array} } } & { = \begin{array} { r l } { \sum _ { \alpha = 1 } ^ { r _ { 0 } } a _ { \alpha } ^ { 1 , \gamma } \cdot \underbrace { \overset { 4 } { \varepsilon } } \left[ \mathbf { a } ^ { 0 , \alpha } \right] I _ { 0 , 4 ( k - 1 ) + \varepsilon } J _ { 0 , 4 ( k - 1 ) + \varepsilon } } \end{array} } \\ { \underbrace { \qquad } } & { \dots } \end{array}  \\ { \underbrace { \left[ \phi ^ { i , \gamma } \right] I _ { l , k , \cdot } J _ { l , k , \cdot } } _ { \begin{array} { l } { 1 } \\ { M ^ { | I _ { 1 , k , \cdot } | }  { \mathrm { l o p } } \mathcal { M } ^ { | J _ { 1 , k } | } } \end{array} } } & { = \begin{array} { r l } { \sum _ { \alpha = 1 } ^ { r _ { l - 1 } } a _ { \alpha } ^ { l , \gamma } \cdot \underbrace { \overset { 4 } { \varepsilon } } \left[ \phi ^ { i - 1 , \alpha } \right] I _ { l - 1 , 4 ( k - 1 ) + \varepsilon } J _ { l - 1 , 4 ( k - 1 ) + \varepsilon } \ , l \in \{ 2 , \dots { L - 1 } \} , \gamma \in } \\ { \dots } \end{array} } \\ { \underbrace { \left[ \phi ^ { i , \gamma } \right] I _ { l , k , \cdot } J _ { 1 , k , \cdot } } _ { \begin{array} { l } { 1 } \\ { M ^ { | I _ { 1 , k , \cdot } | }  { \mathrm { l o p } } \mathcal { M } ^ { | J _ { 1 , l } | } } \end{array} } } & { = \begin{array} { r l } { \sum _ { \alpha = 1 } ^ { r _ { L - 1 } } a _ { \alpha } ^ { L , y } \cdot \underbrace { \overset { 4 } { \varepsilon } } \left[ \phi ^ { L - 1 , \alpha } \right] I _ { L - 1 , \varepsilon } J _ { L - 1 , t } } \end{array} } \end{array}
+$$
+
+Eq. 7 expresses $\mathbb { I } \boldsymbol { \mathcal { A } } ^ { y } \mathbb { I } _ { I , J }$ – the matricization w.r.t. the partition $( I , J )$ of a coefficient tensor $\mathcal { A } ^ { y }$ realJ Kized by the deep network, in terms of the network’s conv weights $\{ \mathbf { a } ^ { l , \gamma } \} _ { l , \gamma }$ and output weights $\mathbf { a } ^ { L , y }$ . As discussed above, our interest lies in the maximal rank that this matricization can take. Theorem 1 below provides lower and upper bounds on this maximal rank, by making use of eq. 7, and of the rank-multiplicative property of the Kronecker product $( r a n k ( A { \odot } B ) = r a n k ( A ) { \cdot } r a n k ( B ) )$ .
+
+Theorem 1. Let $( I , J )$ be a partition of $[ N ]$ , and $\mathbb { I } \boldsymbol { \mathcal { A } } ^ { y } \mathbb { I } _ { I , J }$ be the matricization w.r.t. $( I , J )$ of $a$ coefficient tensor $\mathcal { A } ^ { y }$ J K(eq. 2) realized by the deep network (fig. $\boldsymbol { l } ( \boldsymbol { a } )$ with size-4 pooling windows). For every $l \in \{ 0 . . . L - 1 \}$ and $k \in [ N \dot { / } 4 ^ { l } ]$ , define $I _ { l , k }$ and $J _ { l , k }$ as in eq. 6. Then, the maximal rank that $\mathbb { I } \boldsymbol { \mathcal { A } } ^ { y } \mathbb { I } _ { I , J }$ can take (when network weights vary) is:
+
+• No greater than $\begin{array} { r } { \operatorname* { m i n } \{ M ^ { \mathrm { m i n } } \{ | I | , | J | \} , r _ { L - 1 } \prod _ { t = 1 } ^ { 4 } c ^ { L - 1 , t } \} } \end{array}$ , where $c ^ { 0 , k } : = 1$ for $k \in [ N ]$ , and $\begin{array} { r } { c ^ { l , k } : = \operatorname* { m i n } \{ M ^ { \operatorname* { m i n } \{ | I _ { l , k } | , | J _ { l , k } | \} } , r _ { l - 1 } \prod _ { t = 1 } ^ { 4 } c ^ { l - 1 , 4 ( k - 1 ) + t } \} f o r l \in [ L - 1 ] , k \in [ 0 , T ] \times [ 0 , 1 ] \} , } \end{array}$ .
+
+Proof. See app. A.3.
+
+The lower bound in theorem 1 is exponential in $S$ , the latter defined to be the number of size-4 patch groups that are split by the partition $( I , J )$ , i.e. whose indexes are divided between $I$ and $J$ . Partitions that split many of the size-4 patch groups will thus lead to a large lower bound. For example, consider the partition $( I ^ { o d d } , J ^ { e v e n } )$ defined as follows:
+
+$$
+I ^ { o d d } = \{ 1 , 3 , . . . , N - 1 \} \qquad J ^ { e v e n } = \{ 2 , 4 , . . . , N \}
+$$
+
+This partition splits all size-4 patch groups $\mathit { S } = { N } / { 4 } $ ), leading to a lower bound that is exponential in the number of patches $( N )$ .
+
+The upper bound in theorem 1 is expressed via constants $c ^ { l , k }$ , defined recursively over levels $l = 0 . . . L - 1$ , with $k$ ranging over $\dot { 1 } . . . N / 4 ^ { l }$ for each level $l$ . What prevents $c ^ { l , \tilde { k } }$ from growing double-exponentially fast (w.r.t. $l ,$ ) is the minimization with $M ^ { \operatorname* { m i n } \{ | I _ { l , k } | , | J _ { l , k } | \} }$ . Specifically, if $\mathrm { m i n } \{ | I _ { l , k } | , | \bar { J _ { l , k } } | \}$ is small, i.e. if the partition induced by $( I , J )$ on the $k$ ’th size- $4 ^ { l }$ group of patches is unbalanced (most of the patches belong to one side of the partition, and only a few belong to the other), $c ^ { l , k }$ will be of reasonable size. The higher this takes place in the hierarchy (i.e. the larger $l$ is), the lower our eventual upper bound will be. In other words, if partitions induced by $( I , J )$ on size- $. 4 ^ { l }$ patch groups are unbalanced for large values of $l$ , the upper bound in theorem 1 will be small. For example, consider the partition $( I ^ { l o w } , \mathsf { \bar { J } } ^ { h i g h } )$ defined by:
+
+$$
+I ^ { l o w } = \{ 1 , \ldots , N / 2 \} \qquad J ^ { h i g h } = \{ N / 2 + 1 , \ldots , N \}
+$$
+
+Under $( I ^ { l o w } , J ^ { h i g h } )$ , all partitions induced on size- $\cdot 4 ^ { L - 1 }$ patch groups (quadrants of $[ N ] )$ are completely one-sided $( \operatorname* { m i n } \{ | I _ { L - 1 , k } | , | J _ { L - 1 , k } | \} = 0$ for all $k \in [ 4 ] \cdot$ ), resulting in the upper bound being no greater than $r _ { L - 1 }$ – linear in network size.
+
+To summarize this discussion, theorem 1 states that with the deep network, the maximal rank of a coefficient tensor matricization w.r.t. $( I , J )$ , highly depends on the nature of the partition $( I , J ) - \mathrm { i t }$ will be exponentially high for partitions such as $( \bar { I } ^ { o d \bar { d } } , J ^ { e v e n } )$ , that split many size-4 patch groups, while being only polynomial (or linear) for partitions like $( I ^ { \mathit { l o w } } , J ^ { h i \mathit { \hat { g } } h } )$ , under which size- $\breve { 4 ^ { l } }$ patch groups are unevenly divided for large values of $l$ . Since the rank of a coefficient tensor matricization w.r.t. $( I , J )$ corresponds to the strength of correlation modeled between input patches indexed by $I$ and those indexed by $J$ (sec. 5.1), we conclude that the ability of a polynomially sized deep network to model correlation between sets of input patches highly depends on the nature of these sets.
+
+# 5.3 SHALLOW NETWORK
+
+We now turn to study correlations modeled by the shallow network presented in sec. 3 (fig. 1(b)). In line with sec. 5.1, this is achieved by characterizing the maximal ranks of coefficient tensor matricizations under different partitions.
+
+Recall from eq. 4 the CP decomposition expressing a coefficient tensor $\mathcal { A } ^ { y }$ realized by the shallow network. For an arbitrary partition $( I , J )$ of $[ N ]$ , i.e. $I { \uplus } J = [ N ]$ , matricizing this decomposition with repeated application of the relation in eq. 1, gives the following expression for $[ \mathcal { A } ^ { y } ] _ { I , J }$ – the matricization w.r.t. $( I , J )$ of a coefficient tensor realized by the shallow network:
+
+$$
+\mathbb { L } \boldsymbol { A } ^ { y } \mathbb { I } _ { I , J } = \sum _ { \gamma = 1 } ^ { r _ { 0 } } a _ { \gamma } ^ { 1 , y } \cdot \left( \odot ^ { | I | } \mathbf { a } ^ { 0 , \gamma } \right) \left( \odot ^ { | J | } \mathbf { a } ^ { 0 , \gamma } \right) ^ { \top }
+$$
+
+$\mathbf { \Theta } ^ { \mathrm { ( 0 } \mathrm { I } I \vert } \mathbf { a } ^ { 0 , \gamma }$ and $\odot ^ { | J | } \mathbf { a } ^ { 0 , \gamma }$ here are column vectors of dimensions $M ^ { | I | }$ and $M ^ { | J | }$ respectively, standing for the Kronecker products of $\mathbf { a } ^ { 0 , \gamma } \in \mathbb { R } ^ { M }$ with itself $| I |$ and $| J |$ times (respectively). Eq. 10 immediately leads to two observations regarding the ranks that may be taken by $\mathbb { I } ^ { \boldsymbol { A } ^ { y } } \mathbb { I } _ { \boldsymbol { I } , \boldsymbol { J } }$ . First, they depend on the partition $( I , J )$ only through its division size, i.e. through $| I |$ J and $| J |$ . Second, they are no greater than $\operatorname* { m i n } \{ M ^ { \mathrm { m i n } \{ | I | , | J | \} } , r _ { 0 } \}$ , meaning that the maximal rank is linear (or less) in network size. In light of sec. 5.1 and 5.2, these findings imply that in contrast to the deep network, which with polynomial size supports exponential separation ranks under favored partitions, the shallow network treats all partitions (of a given division size) equally, and can only give rise to an exponential separation rank if its size is exponential.
+
+Suppose now that we would like to use the shallow network to replicate a function realized by a polynomially sized deep network. So long as the deep network’s function admits an exponential separation rank under at least one of the favored partitions (e.g. $( I ^ { o d d } , J ^ { e v e n } ) - { \bf e q . \ 8 } )$ , the shallow network would have to be exponentially large in order to replicate it, i.e. depth efficiency takes place. 7 Since all but a negligible set of the functions realizable by the deep network give rise to maximal separation ranks (sec 5.1), we obtain the complete depth efficiency result of Cohen et al. (2016b). However, unlike Cohen et al. (2016b), which did not provide any explanation for the usefulness of functions brought forth by depth, we obtain an insight into their utility – they are able to efficiently model strong correlation under favored partitions of the input.
+
+# 6 INDUCTIVE BIAS THROUGH POOLING GEOMETRY
+
+The deep network presented in sec. 3, whose correlations we analyzed in sec. 5.2, was defined as having size-4 pooling windows, i.e. pooling windows covering four entries each. We have yet to specify the shapes of these windows, or equivalently, the spatial (two-dimensional) locations of nodes grouped together in the process of pooling. In compliance with standard convolutional network design, we now assume that the network’s (size-4) pooling windows are contiguous square blocks, i.e. have shape $2 \times 2$ . Under this configuration, the network’s functional description (eq. 2 with $\mathcal { A } ^ { y }$ given by eq. 3) induces a spatial ordering of input patches 8 , which may be described by the following recursive process:
+
+• Set the index of the top-left patch to 1.   
+• For $l = 1 , . . . , L = l o g _ { 4 } N$ : Replicate the already-assigned top-left $2 ^ { l - 1 }$ -by- $2 ^ { l - 1 }$ block of indexes, and place copies on its right, bottom-right and bottom. Then, add a $4 ^ { l - 1 }$ offset to all indexes in the right copy, a $2 \cdot 4 ^ { l - 1 }$ offset to all indexes in the bottom-right copy, and a $3 \cdot 4 ^ { l - 1 }$ offset to all indexes in the bottom copy.
+
+With this spatial ordering (illustrated in fig. 1(c)), partitions $( I , J )$ of $[ N ]$ convey a spatial pattern. For example, the partition $( I _ { \cdot } ^ { o d d } , J ^ { e v e n } )$ (eq. 8) corresponds to the pattern illustrated on the left of fig. 1(c), whereas $( I ^ { l o w } , J ^ { h i g h } )$ (eq. 9) corresponds to the pattern illustrated on the right. Our analysis (sec. 5.2) shows that the deep network is able to model strong correlation under $\mathsf { \bar { ( } } I ^ { o d d } , J ^ { e v e n } )$ , while being inefficient for modeling correlation under $( I ^ { l o w } , J ^ { h i \breve { g h } } )$ . More generally, partitions for which $S$ , defined in theorem 1, is high, convey patterns that split many $2 \times 2$ patch blocks, i.e. are highly entangled. These partitions enjoy the possibility of strong correlation. On the other hand, partitions for which $\operatorname* { m i n } \{ \left| I _ { l , k } \right| , \left| J _ { l , k } \right| \}$ is small for large values of $l$ (see eq. 6 for definition of $I _ { l , k }$ and ${ { J } _ { l , k } } .$ ) convey patterns that divide large $2 ^ { l } \times 2 ^ { l }$ patch blocks unevenly, i.e. separate the input to distinct contiguous regions. These partitions, as we have seen, suffer from limited low correlations.
+
+We conclude that with $2 \times 2$ pooling, the deep network is able to model strong correlation between input regions that are highly entangled, at the expense of being inefficient for modeling correlation between input regions that are far apart. Had we selected a different pooling regime, the preference of input partition patterns in terms of modeled correlation would change. For example, if pooling windows were set to group nodes with their spatial reflections (horizontal, vertical and horizontalvertical), coarse patterns that divide the input symmetrically, such as the one illustrated on the right of fig. 1(c), would enjoy the possibility of strong correlation, whereas many entangled patterns would now suffer from limited low correlation. The choice of pooling shapes thus serves as a means for controlling the inductive bias in terms of correlations modeled between input regions. Square contiguous windows, as commonly employed in practice, lead to a preference that complies with our intuition regarding the statistics of natural images (nearby pixels more correlated than distant ones). Other pooling schemes lead to different preferences, and this allows tailoring a network to data that departs from the usual domain of natural imagery. We demonstrate this experimentally in the next section, where it is shown how different pooling geometries lead to superior performance in different tasks.
+
+# 7 EXPERIMENTS
+
+The main conclusion from our analyses (sec. 5 and 6) is that the pooling geometry of a deep convolutional network controls its inductive bias by determining which correlations between input regions can be modeled efficiently. We have also seen that shallow networks cannot model correlations efficiently, regardless of the considered input regions. In this section we validate these assertions empirically, not only with convolutional arithmetic circuits (subject of our analyses), but also with convolutional rectifier networks – convolutional networks with ReLU activation and max or average pooling. For conciseness, we defer to app. C some details regarding our implementation. The latter is fully available online at https://github.com/HUJI-Deep/inductive-pooling.
+
+![](images/ec1691f27312d623cb5e3c98cef35c7d72c68d58943ab148f85e159f956ea567.jpg)  
+Figure 2: Sample of images from our synthetic classification benchmark. Each image displays a random blob with holes, whose morphological closure and left-right symmetry about its center are measured. Two classification tasks are defined – one for closedness and one for symmetry. In each task, the objective is to distinguish between blobs whose respective property (closedness/symmetry) is high, and ones for which it is low. The tasks differ in nature – closedness requires modeling correlations between neighboring pixels, whereas symmetry requires modeling correlations between pixels and their reflections.
+
+Our experiments are based on a synthetic classification benchmark inspired by medical imaging tasks. Instances to be classified are 32-by-32 binary images, each displaying a random distorted oval shape $( b l o b )$ with missing pixels in its interior (holes). For each image, two continuous scores in range $[ 0 , 1 ]$ are computed. The first, referred to as closedness, reflects how morphologically closed a blob is, and is defined to be the ratio between the number of pixels in the blob, and the number of pixels in its closure (see app. D for exact definition of the latter). The second score, named symmetry, reflects the degree to which a blob is left-right symmetric about its center. It is measured by cropping the bounding box around a blob, applying a left-right flip to the latter, and computing the ratio between the number of pixels in the intersection of the blob and its reflection, and the number of pixels in the blob. To generate labeled sets for classification (train and test), we render multiple images, sort them according to their closedness and symmetry, and for each of the two scores, assign the label “high” to the top $40 \%$ and the label “low” to the bottom $40 \%$ (the mid $20 \%$ are considered ill-defined). This creates two binary (two-class) classification tasks – one for closedness and one for symmetry (see fig. 2 for a sample of images participating in both tasks). Given that closedness is a property of a local nature, we expect its classification task to require a predictor to be able to model strong correlations between neighboring pixels. Symmetry on the other hand is a property that relates pixels to their reflections, thus we expect its classification task to demand that a predictor be able to model correlations across distances.
+
+We evaluated the deep convolutional arithmetic circuit considered throughout the paper (fig. 1(a) with size-4 pooling windows) under two different pooling geometries. The first, referred to as square, comprises standard $2 \times 2$ pooling windows. The second, dubbed mirror, pools together nodes with their horizontal, vertical and horizontal-vertical reflections. In both cases, input patches $\left( \mathbf { x } _ { i } \right)$ were set as individual pixels, resulting in $N = 1 0 2 4$ patches and $L = \log _ { 4 } N = 5$ hidden layers. $M = 2$ representation functions $( f _ { \theta _ { d } } )$ were fixed, the first realizing the identity on binary inputs $( f _ { \boldsymbol { \theta } _ { 1 } } ( b ) = b$ for $b \in \{ 0 , 1 \} ,$ ), and the second realizing negation $( f _ { \theta _ { 2 } } ( b ) = 1 - b$ for $\dot { b } \in \{ 0 , 1 \}$ ). Classification was realized through $Y = 2$ network outputs, with prediction following the stronger activation. The number of channels across all hidden layers was uniform, and varied between 8 and 128. Fig. 3 shows the results of applying the deep network with both square and mirror pooling, to both closedness and symmetry tasks, where each of the latter has 20000 images for training and 4000 images for testing. As can be seen in the figure, square pooling significantly outperforms mirror pooling in closedness classification, whereas the opposite occurs in symmetry classification. This complies with our discussion in sec. 6, according to which square pooling supports modeling correlations between entangled (neighboring) regions of the input, whereas mirror pooling puts focus on correlations between input regions that are symmetric w.r.t. one another. We thus obtain a demonstration of how prior knowledge regarding a task at hand may be used to tailor the inductive bias of a deep convolutional network by designing an appropriate pooling geometry.
+
+In addition to the deep network, we also evaluated the shallow convolutional arithmetic circuit analyzed in the paper (fig. 1(b)). The architectural choices for this network were the same as those described above for the deep network besides the number of hidden channels, which in this case applied to the network’s single hidden layer, and varied between 64 and 4096. The highest train and test accuracies delivered by this network (with 4096 hidden channels) were roughly $6 \hat { 2 } \%$ on closedness task, and $7 7 \%$ on symmetry task. The fact that these accuracies are inferior to those of the deep network, even when the latter’s pooling geometry is not optimal for the task at hand, complies with our analysis in sec. 5. Namely, it complies with the observation that separation ranks (correlations) are sometimes exponential and sometimes polynomial with the deep network, whereas with the shallow one they are never more than linear in network size.
+
+![](images/2dce20371cae06c31ed9d495bc3afd7a52a1dbcf10a3544fc77e664d88aed1bf.jpg)  
+Figure 3: Results of applying a deep convolutional arithmetic circuit to closedness and symmetry classification tasks. Two pooling geometries were evaluated – square, which supports modeling correlations between neighboring input regions, and mirror, which puts focus on correlations between regions that are symmetric w.r.t. one another. Each pooling geometry outperforms the other on the task for which its correlations are important, demonstrating how prior knowledge regarding a task at hand may be used to tailor the inductive bias through proper pooling design.
+
+Finally, to assess the validity of our findings for convolutional networks in general, not just convolutional arithmetic circuits, we repeated the above experiments with convolutional rectifier networks. Namely, we placed ReLU activations after every conv operator, switched the pooling operation from product to average, and re-evaluated the deep (square and mirror pooling geometries) and shallow networks. We then reiterated this process once more, with pooling operation set to max instead of average. The results obtained by the deep networks are presented in fig. 4. The shallow network with average pooling reached train/test accuracies of roughly $5 8 \%$ on closedness task, and $5 5 \%$ on symmetry task. With max pooling, performance of the shallow network did not exceed chance. Altogether, convolutional rectifier networks exhibit the same phenomena observed with convolutional arithmetic circuits, indicating that the conclusions from our analyses likely apply to such networks as well. Formal adaptation of the analyses to convolutional rectifier networks, similarly to the adaptation of Cohen et al. (2016b) carried out in Cohen and Shashua (2016), is left for future work.
+
+# 8 DISCUSSION
+
+Through the notion of separation rank, we studied the relation between the architecture of a convolutional network, and its ability to model correlations among input regions. For a given input partition, the separation rank quantifies how far a function is from separability, which in a probabilistic setting, corresponds to statistical independence between sides of the partition.
+
+Our analysis shows that a polynomially sized deep convolutional arithmetic circuit supports exponentially high separation ranks for certain input partitions, while being limited to polynomial or linear (in network size) separation ranks for others. The network’s pooling window shapes effectively determine which input partitions are favored in terms of separation rank, i.e. which partitions enjoy the possibility of exponentially high separation ranks with polynomial network size, and which require network to be exponentially large. Pooling geometry thus serves as a means for controlling the inductive bias. The particular pooling scheme commonly employed in practice – square contiguous windows, favors interleaved partitions over ones that divide the input to distinct areas, thus orients the inductive bias towards the statistics of natural images (nearby pixels more correlated than distant ones). Other pooling schemes lead to different preferences, and this allows tailoring the network to data that departs from the usual domain of natural imagery.
+
+![](images/41abe156433db432f05f8e96ebf71df175bef2102d5a6fceaf879f92285c0d8f.jpg)  
+Figure 4: Results of applying deep convolutional rectifier networks to closedness and symmetry classification tasks. The same trends observed with the deep convolutional arithmetic circuit (fig. 3) are apparent here.
+
+As opposed to deep convolutional arithmetic circuits, shallow ones support only linear (in network size) separation ranks. Therefore, in order to replicate a function realized by a deep network (exponential separation rank), a shallow network must be exponentially large. By this we derive the depth efficiency result of Cohen et al. (2016b), but in addition, provide an insight into the benefit of functions brought forth by depth – they are able to efficiently model strong correlation under favored partitions of the input.
+
+We validated our conclusions empirically, with convolutional arithmetic circuits as well as convolutional rectifier networks – convolutional networks with ReLU activation and max or average pooling. Our experiments demonstrate how different pooling geometries lead to superior performance in different tasks. Specifically, we evaluate deep networks in the measurement of shape continuity, a task of a local nature, and show that standard square pooling windows outperform ones that join together nodes with their spatial reflections. In contrast, when measuring shape symmetry, modeling correlations across distances is of vital importance, and the latter pooling geometry is superior to the conventional one. Shallow networks are inefficient at modeling correlations of any kind, and indeed lead to poor performance on both tasks.
+
+Finally, our analyses and results bring forth the possibility of expanding the coverage of correlations efficiently modeled by a deep convolutional network. Specifically, by blending together multiple pooling geometries in the hidden layers of a network, it is possible to facilitate simultaneous support for a wide variety of correlations suiting data of different types. Investigation of this direction, from both theoretical and empirical perspectives, is viewed as a promising avenue for future research.
+
+# ACKNOWLEDGMENTS
+
+This work is supported by Intel grant ICRI-CI #9-2012-6133, by ISF Center grant 1790/12 and by the European Research Council (TheoryDL project). Nadav Cohen is supported by a Google Doctoral Fellowship in Machine Learning.
+
+# REFERENCES
+
+Richard Bellman. Introduction to matrix analysis, volume 960. SIAM, 1970.
+
+Gregory Beylkin and Martin J Mohlenkamp. Numerical operator calculus in higher dimensions. Proceedings of the National Academy of Sciences, 99(16):10246–10251, 2002.
+
+Gregory Beylkin, Jochen Garcke, and Martin J Mohlenkamp. Multivariate regression and machine learning with sums of separable functions. SIAM Journal on Scientific Computing, 31(3):1840–1857, 2009.
+
+Richard Caron and Tim Traynor. The zero set of a polynomial. WSMR Report 05-02, 2005.
+
+Nadav Cohen and Amnon Shashua. Simnets: A generalization of convolutional networks. Advances in Neural Information Processing Systems (NIPS), Deep Learning Workshop, 2014.
+
+Nadav Cohen and Amnon Shashua. Convolutional rectifier networks as generalized tensor decompositions. International Conference on Machine Learning (ICML), 2016.
+
+Nadav Cohen, Or Sharir, and Amnon Shashua. Deep simnets. IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2016a.
+
+Nadav Cohen, Or Sharir, and Amnon Shashua. On the expressive power of deep learning: A tensor analysis. Conference On Learning Theory (COLT), 2016b.
+
+Thomas M Cover and Joy A Thomas. Elements of information theory. John Wiley & Sons, 2012.
+
+Olivier Delalleau and Yoshua Bengio. Shallow vs. deep sum-product networks. In Advances in Neural Information Processing Systems, pages 666–674, 2011.
+
+Carl Eckart and Gale Young. The approximation of one matrix by another of lower rank. Psychometrika, 1(3): 211–218, 1936.
+
+Ronen Eldan and Ohad Shamir. The power of depth for feedforward neural networks. arXiv preprint arXiv:1512.03965, 2015.
+
+G.H. Golub and C.F. Van Loan. Matrix Computations. Johns Hopkins Studies in the Mathematical Sciences. Johns Hopkins University Press, 2013. ISBN 9781421407944. URL https://books.google.co. il/books?id $_ { \cdot } =$ X5YfsuCWpxMC.
+
+Wolfgang Hackbusch. On the efficient evaluation of coalescence integrals in population balance models. Computing, 78(2):145–159, 2006.
+
+Wolfgang Hackbusch. Tensor Spaces and Numerical Tensor Calculus, volume 42 of Springer Series in Computational Mathematics. Springer Science & Business Media, Berlin, Heidelberg, February 2012.
+
+Robert M Haralick, Stanley R Sternberg, and Xinhua Zhuang. Image analysis using mathematical morphology. IEEE transactions on pattern analysis and machine intelligence, (4):532–550, 1987.
+
+Robert J Harrison, George I Fann, Takeshi Yanai, and Gregory Beylkin. Multiresolution quantum chemistry in multiwavelet bases. In Computational Science-ICCS 2003, pages 103–110. Springer, 2003.
+
+Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recognition. arXiv preprint arXiv:1512.03385, 2015.
+
+Yangqing Jia, Evan Shelhamer, Jeff Donahue, Sergey Karayev, Jonathan Long, Ross Girshick, Sergio Guadarrama, and Trevor Darrell. Caffe: Convolutional architecture for fast feature embedding. In Proceedings of the 22nd ACM international conference on Multimedia, pages 675–678. ACM, 2014.
+
+Frank Jones. Lebesgue integration on Euclidean space. Jones & Bartlett Learning, 2001.
+
+Diederik Kingma and Jimmy Ba. Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980, 2014.
+
+Tamara G Kolda and Brett W Bader. Tensor Decompositions and Applications. SIAM Review (), 51(3):455–500, 2009.
+
+Alex Krizhevsky, Ilya Sutskever, and Geoffrey E Hinton. ImageNet Classification with Deep Convolutional Neural Networks. Advances in Neural Information Processing Systems, pages 1106–1114, 2012.
+
+Yann LeCun and Yoshua Bengio. Convolutional networks for images, speech, and time series. The handbook of brain theory and neural networks, 3361(10), 1995.
+
+Yann LeCun, Yoshua Bengio, and Geoffrey Hinton. Deep learning. Nature, 521(7553):436–444, May 2015.
+
+Hrushikesh Mhaskar, Qianli Liao, and Tomaso Poggio. Learning real and boolean functions: When is deep better than shallow. arXiv preprint arXiv:1603.00988, 2016.
+
+Guido F Montufar, Razvan Pascanu, Kyunghyun Cho, and Yoshua Bengio. On the number of linear regions of deep neural networks. In Advances in Neural Information Processing Systems, pages 2924–2932, 2014.
+
+Vinod Nair and Geoffrey E Hinton. Rectified linear units improve restricted boltzmann machines. In Proceedings of the 27th International Conference on Machine Learning (ICML-10), pages 807–814, 2010.
+
+Razvan Pascanu, Guido Montufar, and Yoshua Bengio. On the number of inference regions of deep feed forward networks with piece-wise linear activations. arXiv preprint arXiv, 1312, 2013.
+
+Tomaso Poggio, Fabio Anselmi, and Lorenzo Rosasco. I-theory on depth vs width: hierarchical function composition. Technical report, Center for Brains, Minds and Machines (CBMM), 2015.
+
+Walter Rudin. Functional analysis. international series in pure and applied mathematics, 1991.
+
+Or Sharir, Ronen Tamari, Nadav Cohen, and Amnon Shashua. Tensorial mixture models. arXiv preprint arXiv:1610.04167, 2016.
+
+Karen Simonyan and Andrew Zisserman. Very deep convolutional networks for large-scale image recognition. arXiv preprint arXiv:1409.1556, 2014.
+
+Nitish Srivastava, Geoffrey E Hinton, Alex Krizhevsky, Ilya Sutskever, and Ruslan Salakhutdinov. Dropout: a simple way to prevent neural networks from overfitting. Journal of Machine Learning Research, 15(1): 1929–1958, 2014.
+
+Christian Szegedy, Wei Liu, Yangqing Jia, Pierre Sermanet, Scott Reed, Dragomir Anguelov, Dumitru Erhan, Vincent Vanhoucke, and Andrew Rabinovich. Going Deeper with Convolutions. CVPR, 2015.
+
+Matus Telgarsky. Representation benefits of deep feedforward networks. arXiv preprint arXiv:1509.08101, 2015.
+
+# A DEFERRED PROOFS
+
+# A.1 PROOF OF CLAIM 1
+
+We prove the equality in two steps, first showing that $s e p ( h _ { y } ; I , J ) { \le } r a n k  { \mathbb { [ } } A ^ { y }  { ] } | I , J$ , and then establishing the J Kconverse. The first step is elementary, and does not make use of the representation functions’ $( f _ { \theta _ { d } } )$ linear independence, or of measurability/square-integrability. The second step does rely on these assumptions, and employs slightly more advanced mathematical machinery. Throughout the proof, we assume without loss of generality that the partition $( I , J )$ of $[ N ]$ is such that $I$ takes on lower values, while $J$ takes on higher ones. That is to say, we assume that $I = \{ 1 , \ldots , | I | \}$ and $J = \{ | I | + 1 , \ldots , N \}$ . 9
+
+To prove that $s e p ( h _ { y } ; I , J ) { \le } r a n k  { \mathbb { [ } } A ^ { y }  { ] } | I , J$ , denote by $R$ the rank of $\mathbb { I } A ^ { y } \mathbb { I } _ { I , J }$ . The latter is an $M ^ { | I | }$ -by- $M ^ { | J | }$ J Kmatrix, thus there exist vectors u1. . .uR ∈ RM|I| and $\mathbf { v } _ { 1 \cdot \cdot \cdot \mathbf { v } _ { R } } \in \mathbb { R } ^ { M ^ { | J | } }$ Ksuch that $\begin{array} { r } { \mathbb { I } \boldsymbol { \mathcal { A } } ^ { y } \mathbb { I } _ { I , J } = \sum _ { \nu = 1 } ^ { R } \mathbf { u } _ { \nu } \mathbf { v } _ { \nu } ^ { \top } } \end{array}$ For every $\nu \in [ R ]$ , let $B ^ { \nu }$ be the tensor of order $| I |$ and dimension $M$ J K in each mode whose arrangement as a column vector gives $\mathbf { u } _ { \nu }$ , i.e. whose matricization w.r.t. the partition $( [ | I | ] , \emptyset )$ is equal to $\mathbf { u } _ { \nu }$ . Similarly, let $\mathcal { C } ^ { \nu }$ , $\nu \in [ R ]$ , be the tensor of order $\vert J \vert = N - \vert I \vert$ and dimension $M$ in each mode whose matricization w.r.t. the partition $( \emptyset , [ | J | ] )$ (arrangement as a row vector) is equal to $\mathbf { v } _ { \nu } ^ { \top }$ . It holds that:
+
+$$
+\begin{array} { l l l } { [ A ^ { y } ] _ { I , J } } & { = } & { \sum _ { \nu = 1 } ^ { R } \mathbf { u } _ { \nu } \mathbf { v } _ { \nu } ^ { \top } } \\ & { = } & { \sum _ { \nu = 1 } ^ { R } [ \mathcal { B } ^ { \nu } ] _ { [ [ I ] ] , \theta } \odot [ \mathcal { C } ^ { \nu } ] _ { \emptyset , [ [ J ] ] } } \\ & { = } & { \sum _ { \nu = 1 } ^ { R } [ \mathcal { B } ^ { \nu } ] _ { I \cap [ [ I ] ] , J \cap [ [ I ] ] } \odot [ \mathcal { C } ^ { \nu } ] _ { ( I - | I ] ) \cap [ [ J ] ] , ( J - | I ] ) \cap [ [ J ] ] } } \\ & { = } & { \sum _ { \nu = 1 } ^ { R } [ \mathcal { B } ^ { \nu } \otimes \mathcal { C } ^ { \nu } ] _ { I , J } } \\ & { = } & { \left[ \sum _ { \nu = 1 } ^ { R } \mathcal { B } ^ { \nu } \otimes \mathcal { C } ^ { \nu } \right] _ { I , J } } \end{array}
+$$
+
+where the third equality relies on the assumption $I = \{ 1 , \dots , | I | \} , J = \{ | I | + 1 , \dots , N \}$ , the fourth equality makes use of the relation in eq. 1, and the last equality is based on the linearity of the matricization operator. Since matricizations are merely rearrangements of tensors, the fact that $\begin{array} { r } { \mathcal { A } ^ { y } = \sum _ { \nu = 1 } ^ { R } \mathcal { B } ^ { \nu } \otimes \mathcal { C } ^ { \nu } } \end{array}$ , or equivalently, $\begin{array} { r } { \mathcal { A } _ { d _ { 1 } . . . d _ { N } } ^ { y } = \sum _ { \nu = 1 } ^ { R } \mathcal { B } _ { d _ { 1 } . . . d _ { | I | } } ^ { \nu } \cdot \mathcal { C } _ { d _ { | I | + 1 } . . . d _ { N } } ^ { \nu } } \end{array}$ $\begin{array} { r } { \mathbb { [ } \mathcal { A } ^ { y } ] _ { I , J } = \mathbb { [ } \sum _ { \nu = 1 } ^ { R } \mathcal { B } ^ { \nu } \otimes \mathcal { C } ^ { \nu } \mathbb { ] } _ { I , J } } \end{array}$ ν=1 for every $d _ { 1 } . . . d _ { N } \in [ M ]$ implies Plugging this into eq. 2 gives:
+
+$$
+\begin{array} { l l l } { { { h } _ { y } } \left( { { \bf { x } } _ { 1 } } , \ldots , { { \bf { x } } _ { N } } \right) } & { { = } } & { { \displaystyle \sum _ { { d } _ { 1 } \ldots { d } _ { N } = 1 } ^ { M } { \cal A } _ { { d } _ { 1 } \ldots { d } _ { N } } ^ { y } \prod _ { i = 1 } ^ { N } { f } _ { { \theta } _ { { d } _ { i } } } \left( { { \bf { x } } _ { i } } \right) } } \\ { { } } & { { = } } & { { \displaystyle \sum _ { { d } _ { 1 } \ldots { d } _ { N } = 1 } ^ { M } \sum _ { { \nu = 1 } } ^ { R } { \cal B } _ { { d } _ { 1 } \ldots { d } _ { | I | } } ^ { \nu } \cdot { \cal C } _ { { d } _ { | I | + 1 } \ldots { d } _ { N } } ^ { \nu } \prod _ { i = 1 } ^ { N } { f } _ { { \theta } _ { { d } _ { i } } } \left( { { \bf { x } } _ { i } } \right) } } \\ { { } } & { { = } } & { { \displaystyle \sum _ { { \nu = 1 } } ^ { R } \left( { \displaystyle \sum _ { { d } _ { 1 } \ldots { d } _ { | I | } = 1 } ^ { M } { \cal B } _ { { d } _ { 1 } \ldots { d } _ { | I | } } ^ { \nu } \prod _ { i = 1 } ^ { | I | } { f } _ { { \theta } _ { { d } _ { i } } } \left( { { \bf { x } } _ { i } } \right) } \right) } } \\ { { } } & { { } } & { { \displaystyle \cdot \left( \sum _ { { d } _ { | I | + 1 } \ldots { d } _ { N } = 1 } ^ { M } { \cal C } _ { { d } _ { | I | + 1 } \ldots { d } _ { N } } ^ { \nu } \prod _ { i = | I | + 1 } ^ { N } { f } _ { { \theta } _ { { d } _ { i } } } \left( { { \bf { x } } _ { i } } \right) \right) } } \end{array}
+$$
+
+For every $\nu \in [ R ]$ , define the functions $g _ { \nu } : ( \mathbb { R } ^ { s } ) ^ { | I | } \to \mathbb { R }$ and $g _ { \nu } ^ { \prime } : ( \mathbb { R } ^ { s } ) ^ { | J | } \to \mathbb { R }$ as follows:
+
+$$
+\begin{array} { l c l } { { g _ { \nu } ( { \bf x } _ { 1 } , \ldots , { \bf x } _ { | I | } ) } } & { { : = } } & { { \sum _ { d _ { 1 } \ldots d _ { | I | } = 1 } ^ { M } { \cal B } _ { d _ { 1 } \ldots d _ { | I | } } ^ { \nu } \prod _ { i = 1 } ^ { | I | } f _ { { \theta } _ { d _ { i } } } ( { \bf x } _ { i } ) } } \\ { { g _ { \nu } ^ { \prime } ( { \bf x } _ { 1 } , \ldots , { \bf x } _ { | J | } ) } } & { { : = } } & { { \sum _ { d _ { 1 } \ldots d _ { | J | } = 1 } ^ { M } { \cal C } _ { d _ { 1 } \ldots d _ { | J | } } ^ { \nu } \prod _ { i = 1 } ^ { | J | } f _ { { \theta } _ { d _ { i } } } ( { \bf x } _ { i } ) } } \end{array}
+$$
+
+Substituting these into eq. 11 leads to:
+
+$$
+h _ { y } \left( \mathbf { x } _ { 1 } , \ldots , \mathbf { x } _ { N } \right) = \sum _ { \nu = 1 } ^ { R } g _ { \nu } ( \mathbf { x } _ { 1 } , \ldots , \mathbf { x } _ { | I | } ) g _ { \nu } ^ { \prime } ( \mathbf { x } _ { | I | + 1 } , \ldots , \mathbf { x } _ { N } )
+$$
+
+which by definition of the separation rank (eq. 5), implies $s e p ( h _ { y } ; I , J ) { \le } R$ . By this we have shown that $s e p ( h _ { y } ; I , J ) { \le } r a n k [ [ \boldsymbol { A } ^ { y } ] ] _ { I , J }$ , as required.
+
+For proving the converse inequality, i.e. $s e p ( h _ { y } ; I , J ) \ge r a n k \perp ^ { y } \perp _ { I , J } ^ { }$ , we rely on basic concepts and results Jfrom functional analysis, or more specifically, from the topic of $L ^ { 2 }$ spaces. While a full introduction to this topic is beyond our scope (the interested reader is referred to Rudin (1991)), we briefly lay out here the minimal background required in order to follow our proof. For any $n \in \mathbb N$ , $L ^ { 2 } ( \mathbb { R } ^ { n } )$ is formally defined as the Hilbert space of Lebesgue measurable square-integrable real functions over $\mathbb { R } ^ { n }$ 10 , equipped with standard (pointwise) addition and scalar multiplication, as well as the inner product defined by integration over point-wise multiplication. For our purposes, $L ^ { 2 } ( \mathbb { R } ^ { n } )$ may simply be thought of as the (infinite-dimensional) vector space of functions $g : \mathbb { R } ^ { n }  \mathbb { R }$ satisfying $\textstyle \int g ^ { 2 } < \infty$ , with inner product defined by $\textstyle \left. g _ { 1 } , g _ { 2 } \right. : = \int g _ { 1 } \cdot g _ { 2 }$ . Our proof will make use of the following basic facts related to $L ^ { 2 }$ spaces:
+
+Fact 1. If $V$ is a finite-dimensional subspace of $L ^ { 2 } ( \mathbb { R } ^ { n } )$ , then any $g \in L ^ { 2 } ( \mathbb { R } ^ { n } )$ may be expressed as $g = p + \delta$ , with $p { \in } V$ and $\delta \in V ^ { \perp }$ (i.e. $\delta$ is orthogonal to all elements in $V$ ). Moreover, such a representation is unique, so in the case where $g \in V$ , we necessarily have $p = g$ and $\delta \equiv 0$ .
+
+Fact 2. I $\{ \mathbf { \psi } _ { g \in L ^ { 2 } ( \mathbb { R } ^ { n } ) , g ^ { \prime } \in L ^ { 2 } ( \mathbb { R } ^ { n \prime } ) }$ , then the function $( \mathbf { x } _ { 1 } , \mathbf { x } _ { 2 } ) { \mapsto } g ( \mathbf { x } _ { 1 } ) { \cdot } g ^ { \prime } ( \mathbf { x } _ { 2 } )$ belongs to $L ^ { 2 } ( \mathbb { R } ^ { n } \times \mathbb { R } ^ { n \prime } )$ .
+
+Fact 3. Let $V$ and $V ^ { \prime }$ be finite-dimensional subspaces of $L ^ { 2 } ( \mathbb { R } ^ { n } )$ and $L ^ { 2 } ( \mathbb { R } ^ { n \prime } )$ respectively, and define $U { \subset } L ^ { 2 } ( \mathbb { R } ^ { n } \times \mathbb { R } ^ { n \prime } )$ to be the subspace spanned by $\{ ( \mathbf { x } _ { 1 } , \mathbf { x } _ { 2 } ) {  } p ( \mathbf { x } _ { 1 } ) { \cdot } p ^ { \prime } ( \mathbf { x } _ { 2 } ) : p { \in } V , p ^ { \prime } { \in } V ^ { \prime } \}$ . Given $g { \in } L ^ { 2 } ( \mathbb { R } ^ { n } ) , \mathsf { \Gamma } _ { g } ^ { \prime } { \in } L ^ { 2 } ( \mathbb { R } ^ { n ^ { \prime } } )$ , consider the function $( \mathbf { x } _ { 1 } , \mathbf { x } _ { 2 } ) { \mapsto } g ( \mathbf { x } _ { 1 } ) { \cdot } g ^ { \prime } ( \mathbf { x } _ { 2 } )$ in $L ^ { 2 } ( \mathbb { R } ^ { n } \times \mathbb { R } ^ { n \prime } )$ . This function belongs to $U ^ { \perp }$ if $g { \in } V ^ { \bot }$ or $g ^ { \prime } { \in } V ^ { \prime \bot }$ .
+
+Fact 4. If $g _ { 1 } . . . g _ { m } { \in } L ^ { 2 } ( \mathbb { R } ^ { n } )$ are linearly independent, then for any $k \in \mathbb { N } ,$ , the set of functions $\begin{array} { r } { \{ ( \mathbf { x } _ { 1 } , \ldots , \mathbf { x } _ { k } ) \mapsto \prod _ { i = 1 } ^ { k } g _ { d _ { i } } ( \mathbf { x } _ { i } ) \} _ { d _ { 1 } \ldots d _ { k } \in [ m ] } } \end{array}$ is linearly independent in $L ^ { 2 } ( ( \mathbb { R } ^ { n } ) ^ { k } )$ .
+
+To facilitate application of the theory of $L ^ { 2 }$ spaces, we now make use of the assumption that the network’s representation functions $f _ { \theta _ { d } }$ , as well as the functions $g _ { \nu } , g _ { \nu } ^ { \prime }$ in the definition of separation rank (eq. 5), are measurable and square-integrable. Taking into account the expression given in eq. 2 for $h _ { y }$ , as well as fact 2 above, one readily sees that $f _ { \theta _ { 1 } } . . . f _ { \theta _ { M } } \in L ^ { 2 } ( \mathbb { R } ^ { s } )$ implies $h _ { y } { \in } L ^ { 2 } ( ( \mathbb { R } ^ { s } ) ^ { N } )$ . The separation rank $s e p ( h _ { y } ; I , J )$ will be the minimal non-negative integer $R$ such that there exist $g _ { 1 } . . . g _ { R } { \in } L ^ { 2 } ( ( \mathbb { R } ^ { s } ) ^ { | I | } )$ and $g _ { 1 } ^ { \prime } . . . g _ { R } ^ { \prime } { \in } L ^ { 2 } ( ( \mathbb { R } ^ { s } ) ^ { | J | } )$ for which:
+
+$$
+h _ { \mathcal { Y } } \big ( \mathbf { x } _ { 1 } , \ldots , \mathbf { x } _ { N } \big ) = \sum _ { \nu = 1 } ^ { R } g _ { \nu } \big ( \mathbf { x } _ { 1 } , \ldots , \mathbf { x } _ { | I | } \big ) g _ { \nu } ^ { \prime } \big ( \mathbf { x } _ { | I | + 1 } , \ldots , \mathbf { x } _ { N } \big )
+$$
+
+We would like to show that $s e p ( h _ { y } ; I , J ) \ge r a n k \perp ^ { y } \perp ^ { } I , J$ . Our strategy for achieving this will be to start from eq. 12, and derive an expression for $\mathbb { I } A ^ { y } \mathbb { I } _ { I , J }$ J Kcomprising a sum of $R$ rank-1 matrices. As an initial step along J Kthis path, define the following finite-dimensional subspaces:
+
+$$
+\begin{array} { l l l l } { V } & { : = } & { s p a n \left\{ ( \mathbf { x } _ { 1 } , \dots , \mathbf { x } _ { | I | } ) \mapsto \prod _ { i = 1 } ^ { | I | } f _ { \theta _ { d _ { i } } } ( \mathbf { x } _ { i } ) \right\} _ { d _ { 1 } \dots d _ { | I | } \in [ M ] } \subset L ^ { 2 } \left( ( \mathbb { R } ^ { s } ) ^ { | I | } \right) } \\ { V ^ { \prime } } & { : = } & { s p a n \left\{ ( \mathbf { x } _ { 1 } , \dots , \mathbf { x } _ { | J | } ) \mapsto \prod _ { i = 1 } ^ { | J | } f _ { \theta _ { d _ { i } } } ( \mathbf { x } _ { i } ) \right\} _ { d _ { 1 } \dots d _ { | J | } \in [ M ] } \subset L ^ { 2 } \left( ( \mathbb { R } ^ { s } ) ^ { | J | } \right) } \\ { U } & { : = } & { s p a n \left\{ ( \mathbf { x } _ { 1 } , \dots , \mathbf { x } _ { N } ) \mapsto \prod _ { i = 1 } ^ { N } f _ { \theta _ { d _ { i } } } ( \mathbf { x } _ { i } ) \right\} _ { d _ { 1 } \dots d _ { N } \in [ M ] } \subset L ^ { 2 } \left( ( \mathbb { R } ^ { s } ) ^ { N } \right) } \end{array}
+$$
+
+Notice that $h _ { y } { \in } U$ (eq. 2), and that $U$ is the span of products from $V$ and $V ^ { \prime }$ , i.e.:
+
+$$
+U = s p a n \{ ( \mathbf { x } _ { 1 } , \ldots , \mathbf { x } _ { N } ) { \overset {  } { \to } } p ( \mathbf { x } _ { 1 } , \ldots , \mathbf { x } _ { | I | } ) \cdot p ^ { \prime } ( \mathbf { x } _ { | I | + 1 } , \ldots , \mathbf { x } _ { N } ) : p { \in } V , p ^ { \prime } { \in } V ^ { \prime } \}
+$$
+
+Returning to eq. 12, we apply fact 1 to obtain orthogonal decompositions of $g 1 . . . g _ { R }$ w.r.t. $V$ , and of $g _ { 1 } ^ { \prime } . . . g _ { R } ^ { \prime }$ w.r.t. $V ^ { \prime }$ . This gives $p _ { 1 } . . . p _ { R } { \in } V$ , $\delta _ { 1 } . . . \delta _ { R } \in V ^ { \perp }$ , ${ p _ { 1 } ^ { \prime } . . . p _ { R } ^ { \prime } } { \in } V ^ { \prime }$ and $\delta _ { 1 } ^ { \prime } . . . \delta _ { R } ^ { \prime } \in V ^ { \prime \perp }$ , such that $g _ { \nu } = p _ { \nu } + \delta _ { \nu }$ an d
+
+$g _ { \nu } ^ { \prime } = p _ { \nu } ^ { \prime } + \delta _ { \nu } ^ { \prime }$ for every $\nu \in [ R ]$ . Plug this into eq. 12:
+
+$$
+\begin{array} { r c l } { { h _ { y } ( { \bf x } { \bf x } _ { 1 } , \ldots , { \bf x } { \bf x } ) } } & { { = } } & { { \sum _ { \nu = 1 } ^ { R } g _ { \nu } ( { \bf x } { \bf _ { 1 } } , \ldots , { \bf x } _ { | I | } ) \cdot g _ { \nu } ^ { \prime } ( { \bf x } | _ { I | + 1 } , \ldots , { \bf x } , { \bf x } ) } } \\ { { } } & { { = } } & { { \displaystyle \sum _ { \nu = 1 } ^ { R } \left( p _ { \nu } ( { \bf x } _ { 1 } , \ldots , { \bf x } _ { | I | } ) + \delta _ { \nu } ( { \bf x } _ { 1 } , \ldots , { \bf x } _ { | I | } ) \right) } } \\ { { } } & { { } } & { { \displaystyle \cdot \left( p _ { \nu } ^ { \prime } ( { \bf x } _ { | I | + 1 } , \ldots , { \bf x } _ { N } ) + \delta _ { \nu } ^ { \prime } ( { \bf x } _ { | I | + 1 } , \ldots , { \bf x } _ { N } ) \right) } } \\ { { } } & { { = } } & { { \displaystyle \sum _ { \nu = 1 } ^ { R } p _ { \nu } ( { \bf x } _ { 1 } , \ldots , { \bf x } _ { | I | } ) \cdot p _ { \nu } ^ { \prime } ( { \bf x } _ { | I | + 1 } , \ldots , { \bf x } _ { N } ) } } \\ { { } } & { { } } & { { \displaystyle + \sum _ { \nu = 1 } ^ { R } p _ { \nu } ( { \bf x } _ { 1 } , \ldots , { \bf x } _ { | I | } ) \cdot \delta _ { \nu } ^ { \prime } ( { \bf x } _ { | I | + 1 } , \ldots , { \bf x } _ { N } ) } } \\ { { } } & { { } } & { { \displaystyle + \sum _ { \nu = 1 } ^ { R } \delta _ { \nu } ( { \bf x } _ { 1 } , \ldots , { \bf x } _ { | I | } ) \cdot p _ { \nu } ^ { \prime } ( { \bf x } _ { | I | + 1 } , \ldots , { \bf x } _ { N } ) } } \\ { { } } & { { } } &   \displaystyle + \sum _ { \nu = 1 } ^ { R } \delta _ { \nu } ( { \bf x } _ { 1 } , \ldots , { \bf x } _ { | I | } ) \cdot p _ { \nu } ^ { \prime } ( { \bf x } _  | I | + 1 \end{array}
+$$
+
+Given that $U$ is the span of products from $V$ and $V ^ { \prime }$ (eq. 16), and that $p _ { \nu } { \in } V , { \delta } _ { \nu } { \in } V ^ { \perp } , p _ { \nu } ^ { \prime } { \in } V ^ { \prime } , { \delta } _ { \nu } ^ { \prime } { \in } V ^ { \prime \perp }$ , one readily sees that the first term in the latter expression belongs to $U$ , while, according to fact 3, the second, third and fourth terms are orthogonal to $U$ . We thus obtained an orthogonal decomposition of $h _ { y }$ w.r.t. $U$ . Since $h _ { y }$ is contained in $U$ , the orthogonal component must vanish (fact 1), and we amount at:
+
+$$
+h _ { y } ( \mathbf { x } _ { 1 } , \ldots , \mathbf { x } _ { N } ) = \sum _ { \nu = 1 } ^ { R } p _ { \nu } ( \mathbf { x } _ { 1 } , \ldots , \mathbf { x } _ { | I | } ) { \cdot } p _ { \nu } ^ { \prime } ( \mathbf { x } _ { | I | + 1 } , \ldots , \mathbf { x } _ { N } )
+$$
+
+For every $\nu \in [ R ]$ , let $B ^ { \nu }$ and $\mathcal { C } ^ { \nu }$ be coefficient tensors of $p _ { \nu }$ and $p _ { \nu } ^ { \prime }$ w.r.t. the functions that span $V$ and $V ^ { \prime }$ (eq. 13 and 14), respectively. Put formally, $B ^ { \nu }$ and $\mathcal { C } ^ { \nu }$ are tensors of orders $| I |$ and $| J |$ (respectively), with dimension $M$ in each mode, meeting:
+
+$$
+\begin{array} { r c l } { { p _ { \nu } ( { \bf x } _ { 1 } , \ldots , { \bf x } _ { | I | } ) } } & { { = } } & { { \sum _ { d _ { 1 } \ldots d _ { | I | } = 1 } ^ { M } { \mathcal B } _ { d _ { 1 } \ldots d _ { | I | } } ^ { \nu } \prod _ { i = 1 } ^ { | I | } f _ { \theta _ { d _ { i } } } ( { \bf x } _ { i } ) } } \\ { { p _ { \nu } ^ { \prime } ( { \bf x } _ { 1 } , \ldots , { \bf x } _ { | J | } ) } } & { { = } } & { { \sum _ { d _ { 1 } \ldots d _ { | J | } = 1 } ^ { M } { \mathcal C } _ { d _ { 1 } \ldots d _ { | J | } } ^ { \nu } \prod _ { i = 1 } ^ { | J | } f _ { \theta _ { d _ { i } } } ( { \bf x } _ { i } ) } } \end{array}
+$$
+
+Substitute into eq. 17:
+
+$$
+\begin{array} { r c l } { { h _ { y } \left( { \bf x } _ { 1 } , \ldots , { \bf x } _ { N } \right) } } & { { = } } & { { \displaystyle \sum _ { \nu = 1 } ^ { R } \left( \sum _ { d _ { 1 } \ldots d _ { | I | } = 1 } ^ { M } \mathcal { B } _ { d _ { 1 } \ldots d _ { | I | } } ^ { \nu } \prod _ { i = 1 } ^ { | I | } f _ { \theta _ { d _ { i } } \left( { \bf x } _ { i } \right) } \right) } } \\ { { } } & { { } } & { { \displaystyle \cdot \left( \sum _ { d _ { | I | + 1 } \ldots d _ { N } = 1 } ^ { M } \mathcal { C } _ { d _ { | I | + 1 } \ldots d _ { N } } ^ { \nu } \prod _ { i = | I | + 1 } ^ { N } f _ { \theta _ { d _ { i } } \left( { \bf x } _ { i } \right) } \right) } } \\ { { } } & { { = } } & { { \displaystyle \sum _ { \nu = 1 } ^ { R } \sum _ { d _ { 1 } \ldots d _ { N } = 1 } ^ { M } \mathcal { B } _ { d _ { 1 } \ldots d _ { | I | } } ^ { \nu } \cdot \mathcal { C } _ { d _ { | I | + 1 } \ldots d _ { N } } ^ { \nu } \prod _ { i = 1 } ^ { N } f _ { \theta _ { d _ { i } } \left( { \bf x } _ { i } \right) } } } \\ { { } } & { { = } } & { { \displaystyle \sum _ { d _ { 1 } \ldots d _ { N } = 1 } ^ { M } \left( \sum _ { \nu = 1 } ^ { R } \mathcal { B } _ { d _ { 1 } \ldots d _ { | I | } } ^ { \nu } \cdot \mathcal { C } _ { d _ { | I | + 1 } \ldots d _ { N } } ^ { \nu } \right) \prod _ { i = 1 } ^ { N } f _ { \theta _ { d _ { i } } \left( { \bf x } _ { i } \right) } } } \end{array}
+$$
+
+Compare this expression for $h _ { y }$ to that given in eq. 2:
+
+$$
+\sum _ { d _ { 1 } . . . d _ { N } = 1 } ^ { M } \left( \sum _ { \nu = 1 } ^ { R } \mathcal { B } _ { d _ { 1 } . . . d _ { | I | } } ^ { \nu } \cdot \mathcal { C } _ { d _ { | I | + 1 } . . . d _ { N } } ^ { \nu } \right) \prod _ { i = 1 } ^ { N } f _ { \theta _ { d _ { i } } } ( \mathbf { x } _ { i } ) = \sum _ { d _ { 1 } . . . d _ { N } = 1 } ^ { M } \mathcal { A } _ { d _ { 1 } . . . d _ { N } } ^ { y } \prod _ { i = 1 } ^ { N } f _ { \theta _ { d _ { i } } } ( \mathbf { x } _ { i } )
+$$
+
+At this point we utilize the given linear independence of $f _ { \theta _ { 1 } } . . . f _ { \theta _ { M } } \in L ^ { 2 } ( \mathbb { R } ^ { s } )$ , from which it follows (fact 4) that the functions spanning $U$ (eq. 15) are linearly independent in $L ^ { 2 } ( ( \mathbb { R } ^ { s } ) ^ { N } )$ . Both sides of eq. 18 are linear combinations of these functions, thus their coefficients must coincide:
+
+$$
+\mathcal { A } _ { d _ { 1 } . . . d _ { N } } ^ { y } = \sum _ { \nu = 1 } ^ { R } \mathcal { B } _ { d _ { 1 } . . . d _ { | I | } } ^ { \nu } \cdot \mathcal { C } _ { d _ { | I | + 1 } . . . d _ { N } } ^ { \nu } , \forall d _ { 1 } . . . d _ { N } \in [ M ] \iff \mathcal { A } ^ { y } = \sum _ { \nu = 1 } ^ { R } \mathcal { B } ^ { \nu } \otimes \mathcal { C } ^ { \nu }
+$$
+
+Matricizing the tensor equation on the right w.r.t. $( I , J )$ gives:
+
+$$
+\begin{array} { l l l } { [ A ^ { y } ] _ { I , J } } & { = } & { \left[ \sum _ { \nu = 1 } ^ { R } B ^ { \nu } \otimes { \mathcal C } ^ { \nu } \right] _ { I , J } } \\ & { = } & { \sum _ { \nu = 1 } ^ { R } [ | B ^ { \nu } \otimes { \mathcal C } ^ { \nu } ] _ { I , J } } \\ & { = } & { \sum _ { \nu = 1 } ^ { R } [ | B ^ { \nu } | ] _ { I \cap [ | I | ] , J \cap [ | I | ] } \odot [ { \mathcal C } ^ { \nu } ] _ { ( I - | I | ) \cap [ | J | ] , ( J - | I | ) \cap [ | J | ] } } \\ & { = } & { \sum _ { \nu = 1 } ^ { R } [ | B ^ { \nu } ] _ { [ | I | ] , \emptyset } \odot [ | { \mathcal C } ^ { \nu } ] _ { \mathcal { \theta } , [ | J | ] } } \end{array}
+$$
+
+where the second equality is based on the linearity of the matricization operator, the third equality relies on the relation in eq. 1, and the last equality makes use of the assumption $I = \stackrel { \cdot } { \{ 1 , \dotsc , | I | \} } , J = \stackrel { \cdot } { \{ | I | \stackrel { \cdot } { + } 1 , \dotsc , N \} }$ .
+
+For every $\nu \in [ R ]$ , $\mathbb { [ } B ^ { \nu } \mathbb { ] } _ { [ | I | ] , \emptyset }$ is a column vector of dimension $M ^ { | I | }$ and $\mathbb { [ } \mathcal { C } ^ { \nu } ] _ { \| , [ | J | ] }$ is a row vector of dimension $M ^ { | J | }$ J K. Denoting these by $\mathbf { u } _ { \nu }$ and $\mathbf { v } _ { \nu } ^ { \top }$ respectively, we may write:
+
+$$
+\mathbb { I } \boldsymbol { \mathcal { A } } ^ { y } \mathbb { I } _ { I , J } = \sum _ { \nu = 1 } ^ { R } \mathbf { u } _ { \nu } \mathbf { v } _ { \nu } ^ { \top }
+$$
+
+This shows that $r a n k \mathbb { [ } \mathbf { \mathcal { A } } ^ { y } \mathbb { ] } _ { I , J \leq R }$ . Since $R$ is a general non-negative integer that admits eq. 12, we may take J Kit to be minimal, i.e. to be equal to $s e p ( h _ { y } ; I , J )$ – the separation rank of $h _ { y }$ w.r.t. $( I , J )$ . By this we obtain $r a n k \ [ \mathcal { A } ^ { y } \ ] _ { I , J } \leq s e p ( h _ { y } ; I , J )$ , which is what we set out to prove.
+
+# A.2 PROOF OF CLAIM 2
+
+The claim is framed in measure theoretical terms, and in accordance, so will its proof be. While a complete introduction to measure theory is beyond our scope (the interested reader is referred to Jones (2001)), we briefly convey here the intuition behind the concepts we will be using, as well as facts we rely upon. The Lebesgue measure is defined over sets in a Euclidean space, and may be interpreted as quantifying their “volume”. For example, the Lebesgue measure of a unit hypercube is one, of the entire space is infinity, and of a finite set of points is zero. In this context, when a phenomenon is said to occur almost everywhere, it means that the set of points in which it does not occur has Lebesgue measure zero, i.e. is negligible. An important result we will make use of (proven in Caron and Traynor (2005) for example) is the following. Given a polynomial defined over $_ n$ real variables, the set of points in $\mathbb { R } ^ { n }$ on which it vanishes is either the entire space (when the polynomial in question is the zero polynomial), or it must have Lebesgue measure zero. In other words, if a polynomial is not identically zero, it must be different from zero almost everywhere.
+
+Heading on to the proof, we recall from sec. 3 that the entries of the coefficient tensor $\mathcal { A } ^ { y }$ (eq. 2) are given by polynomials in the network’s conv weights $\{ \mathbf { a } ^ { l , \gamma } \} _ { l , \gamma }$ and output weights $\mathbf { a } ^ { L , y }$ . Since $\mathbb { I } A ^ { y } \mathbb { I } _ { I , J }$ – the matricization of $\mathcal { A } ^ { y }$ w.r.t. the partition $( I , J )$ J K, is merely a rearrangement of the tensor as a matrix, this matrix too has entries given by polynomials in the network’s linear weights. Now, denote by $r$ the maximal rank taken by $\mathbb { I } A ^ { y } \mathbb { I } _ { I , J }$ as network weights vary, and consider a specific setting of weights for which this rank is J Kattained. We may assume without loss of generality that under this setting, the top-left $r$ -by- $\mathbfit { \nabla } \cdot \mathbfit { r }$ block of $\mathbb { I } A ^ { y } \mathbb { I } _ { I , J }$ is non-singular. The corresponding minor, i.e. the determinant of the sub-matrix $( \mathbb { I } \boldsymbol { \mathcal { A } } ^ { y } \mathbb { \bar { I } } _ { I , J } ) _ { 1 : r , 1 : r }$ J K, is thus a polynomial defined over $\{ \mathbf { a } ^ { l , \gamma } \} _ { l , \gamma }$ and $\mathbf { a } ^ { L , y }$ which is not identically zero. In light of the above, this polynomial is different from zero almost everywhere, implying that $r a n k ( \mathbb { [ } \mathcal { A ^ { y } ] ] } _ { I , J } ) _ { 1 : r , 1 : r } = r$ almost everywhere. Since $r a n k \mathbb { [ } \mathcal { A } ^ { y } ] \rvert _ { I , J } \ge r a n k ( \mathbb { [ } \mathcal { A } ^ { y } \mathbb { ] } \rvert _ { I , J } ) _ { 1 : r , 1 : r }$ , and since by definition $r$ J K is the maximal rank that $\mathbb { I } \boldsymbol { \mathcal { A } } ^ { y } \mathbb { I } _ { I , J }$ can take, we Jhave that $r a n k \ [ \boldsymbol { \mathcal { A } } ^ { y } ] ] _ { I , J }$ Kis maximal almost everywhere.
+
+# A.3 PROOF OF THEOREM 1
+
+The matrix decomposition in eq. 7 expresses $\mathbb { I } \mathbb { A } \mathbb { I } _ { I , J }$ in terms of the network’s linear weights – $\{ \mathbf { a } ^ { 0 , \gamma } ~ \in$ $\mathbb { R } ^ { M } \} _ { \gamma \in [ r _ { 0 } ] }$ Jfor conv operator in hidden layer 0, $\{ \mathbf { a } ^ { l , \gamma } \ \in \ \mathbb { R } ^ { r _ { l - 1 } } \} _ { \gamma \in [ r _ { l } ] }$ for conv operator in hidden layer $l = 1 . . . L - 1$ , and $\mathbf { a } ^ { L , y } \in \mathbb { R } ^ { r _ { L - 1 } }$ for node $y$ of dense output operator. We prove lower and upper bounds on the maximal rank that $\mathbb { I } A \mathbb { I } _ { I , J }$ can take as these weights vary. Our proof relies on the rank-multiplicative property J Kof the Kronecker product $( r a n k ( A @ B ) = r a n k ( A ) { \cdot } r a n k ( B )$ for any real matrices $A$ and $B -$ see Bellman (1970) for proof), but is otherwise elementary.
+
+Beginning with the lower bound, consider the following weight setting $\scriptstyle ( \mathbf { e } _ { \gamma }$ here stands for a vector holding 1 in entry $\gamma$ and 0 at all other entries, 0 stands for a vector holding 0 at all entries, and 1 stands for a vector holding 1 at all entries, with the dimension of a vector to be understood by context):
+
+$$
+\begin{array} { r c l } { { \mathbf a ^ { 0 , \gamma } } } & { { = } } & { { \left\{ \begin{array} { l l } { { \mathbf e _ { \gamma } } } & { { , \gamma \leq \operatorname* { m i n } \{ r _ { 0 } , M \} } } \\ { { \mathbf 0 } } & { { , \mathrm { o t h e r w i s e } } } \end{array} \right. } } \\ { { \mathbf a ^ { 1 , \gamma } } } & { { = } } & { { \left\{ \begin{array} { l l } { { \mathbf 1 } } & { { , \gamma = 1 } } \\ { { \mathbf 0 } } & { { , \mathrm { o t h e r w i s e } } } \end{array} \right. } } \\ { { \mathbf a ^ { l , \gamma } } } & { { = } } & { { \left\{ \begin{array} { l l } { { \mathbf e _ { 1 } } } & { { , \gamma = 1 } } \\ { { \mathbf 0 } } & { { , \mathrm { o t h e r w i s e } } } \end{array} \right. \mathrm { f o r } \ l = 2 . . . L - 1 } } \\ { { \mathbf a ^ { L , y } } } & { { = } } & { { \mathbf e _ { 1 } } } \end{array}
+$$
+
+Let $n \in [ N / 4 ]$ . Recalling the definition of $I _ { l , k }$ and $J _ { l , k }$ from eq. 6, consider the sets $I _ { 1 , n }$ and $J _ { 1 , n }$ , as well as $I _ { 0 , 4 ( n - 1 ) + t }$ and $J _ { 0 , 4 ( n - 1 ) + t }$ for $t \in [ 4 ]$ . $\left( I _ { 1 , n } , J _ { 1 , n } \right)$ is a partition of [4], i.e. $I _ { 1 , n } \cup J _ { 1 , n } = [ 4 ]$ , and for every $t \in$ [4] we have $I _ { 0 , 4 ( n - 1 ) + t } = \{ 1 \}$ and $J _ { 0 , 4 ( n - 1 ) + t } = \emptyset$ if $t$ belongs to $I _ { 1 , n }$ , and otherwise $\mathbf { \tilde { \Gamma } } _ { I _ { 0 , 4 ( n - 1 ) + t } } = \tilde { \varnothing }$
+
+and $J _ { 0 , 4 ( n - 1 ) + t } = \{ 1 \}$ if $t$ belongs to $J _ { 1 , n }$ . This implies that for an arbitrary vector $\mathbf { v }$ , the matricization $\left[ \left[ \mathbf { v } \right] \right] I _ { 0 , 4 ( n - 1 ) + t } , J _ { 0 , 4 ( n - 1 ) + t }$ is equal to $\mathbf { v }$ if $t \in { \cal I } _ { 1 , n }$ , and to $\mathbf { v } ^ { \top }$ if $t \in J _ { 1 , n }$ . Accordingly, for any $\gamma \in [ r _ { 0 } ]$ :
+
+$$
+\underset { t = 1 } { \overset { ( \ b { \Omega } ) } { \subset } } \Vert \mathbf { a } ^ { 0 , \gamma } \Vert _ { I _ { 0 , 4 ( n - 1 ) + t } , J _ { 0 , 4 ( n - 1 ) + t } } = \left\{ \begin{array} { l l } { \left( \mathbf { a } ^ { 0 , \gamma } \odot \mathbf { a } ^ { 0 , \gamma } \odot \mathbf { a } ^ { 0 , \gamma } \odot \mathbf { a } ^ { 0 , \gamma } \odot \mathbf { a } ^ { 0 , \gamma } \right) } & { , | I _ { 1 , n } | = 4 \mid J _ { 1 , n } | = 0 } \\ { \left( \mathbf { a } ^ { 0 , \gamma } \odot \mathbf { a } ^ { 0 , \gamma } \odot \mathbf { a } ^ { 0 , \gamma } \right) ( \mathbf { a } ^ { 0 , \gamma } ) ^ { \top } } & { , | I _ { 1 , n } | = 3 \mid J _ { 1 , n } | = 1 } \\ { \left( \mathbf { a } ^ { 0 , \gamma } \odot \mathbf { a } ^ { 0 , \gamma } \right) \left( \mathbf { a } ^ { 0 , \gamma } \odot \mathbf { a } ^ { 0 , \gamma } \right) ^ { \top } } & { , | I _ { 1 , n } | = 2 \mid J _ { 1 , n } | = 2 } \\ { \left( \mathbf { a } ^ { 0 , \gamma } \right) \left( \mathbf { a } ^ { 0 , \gamma } \odot \mathbf { a } ^ { 0 , \gamma } \odot \mathbf { a } ^ { 0 , \gamma } \right) ^ { \top } } & { , | I _ { 1 , n } | = 1 \mid J _ { 1 , n } | = 3 } \\ { \left( \mathbf { a } ^ { 0 , \gamma } \odot \mathbf { a } ^ { 0 , \gamma } \odot \mathbf { a } ^ { 0 , \gamma } \odot \mathbf { a } ^ { 0 , \gamma } \right) ^ { \top } } & { , | I _ { 1 , n } | = 0 \mid J _ { 1 , n } | = 4 } \end{array} \right.
+$$
+
+Assume that $\gamma \leq \operatorname* { m i n } \{ r _ { 0 } , M \}$ . By our setting $ { \mathbf { a } } ^ { 0 , \gamma } =  { \mathbf { e } } _ { \gamma }$ , so the above matrix holds 1 in a single entry and 0 in all the rest. Moreover, if the matrix is not a row or column vector, i.e. if both $I _ { 1 , n }$ and $J _ { 1 , n }$ are non-empty, the column index and row index of the entry holding 1 are both unique w.r.t. $\gamma$ , i.e. they do not repeat as $\gamma$ ranges over $1 \ldots \operatorname* { m i n } \{ r _ { 0 } , M \}$ . We thus have:
+
+$$
+r a n k \left( \sum _ { \gamma = 1 } ^ { \operatorname* { m i n } \{ r _ { 0 } , M \} } \underset { t = 1 } { \overset { 4 } { \odot } } \mathbb { I } \mathbf { a } ^ { 0 , \gamma } \mathbb { I } _ { I _ { 0 , 4 ( n - 1 ) + t } , J _ { 0 , 4 ( n - 1 ) + t } } \right) = \left\{ \begin{array} { l l } { \operatorname* { m i n } \{ r _ { 0 } , M \} } & { , I _ { 1 , n } \neq \emptyset \land J _ { 1 , n } \neq \emptyset } \\ { 1 } & { , I _ { 1 , n } = \emptyset \lor J _ { 1 , n } = \emptyset } \end{array} \right.
+$$
+
+Since we set $\mathbf { a } ^ { 1 , 1 } = \mathbf { 1 }$ and $\mathbf { a } ^ { 0 , \gamma } = \mathbf { 0 }$ for $\gamma > \mathrm { m i n } \{ r _ { 0 } , M \}$ , we may write:
+
+$$
+r a n k \left( \sum _ { \gamma = 1 } ^ { r _ { 0 } } a _ { \gamma } ^ { 1 , 1 } \cdot \underbrace { \stackrel { 4 } { \longleftrightarrow } } _ { t = 1 } [ \mathbf { a ^ { 0 , \gamma } } ] I _ { 0 , 4 ( n - 1 ) + t } , J _ { 0 , 4 ( n - 1 ) + t } \right) = \left\{ \begin{array} { l l } { \operatorname* { m i n } \{ r _ { 0 } , M \} } & { , I _ { 1 , n } \neq \emptyset \wedge J _ { 1 , n } \neq \emptyset } \\ { 1 } & { , I _ { 1 , n } = \emptyset \vee J _ { 1 , n } = \emptyset } \end{array} \right.
+$$
+
+The latter matrix is by definition equal to $\mathbb { [ } \boldsymbol { \phi } ^ { 1 , 1 } ] _ { I _ { 1 , n } , J _ { 1 , n } }$ (see top row of eq. 7), and so for every $n \in [ N / 4 ]$ :
+
+$$
+r a n k \left[ \phi ^ { 1 , 1 } \right] _ { I _ { 1 , n } , J _ { 1 , n } } = \left\{ \begin{array} { l l } { \operatorname* { m i n } \{ r _ { 0 } , M \} } & { , I _ { 1 , n } \neq \emptyset \land J _ { 1 , n } \neq \emptyset } \\ { 1 } & { , I _ { 1 , n } = \emptyset \lor J _ { 1 , n } = \emptyset } \end{array} \right.
+$$
+
+Now, the fact that we set $\mathbf { a } ^ { L , y } = \mathbf { e } _ { 1 }$ and $\mathbf { a } ^ { l , 1 } = \mathbf { e } _ { 1 }$ for $l = 2 . . . L - 1$ , implies that the second to last levels of the decomposition in eq. 7 collapse to:
+
+$$
+[ \mathcal { A } ^ { y } ] ] _ { I , J } = \underset { t = 1 } { \overset { N / 4 } { \odot } } [ \left[ \phi ^ { 1 , 1 } \right] ] _ { I _ { 1 , t } , J _ { 1 , t } }
+$$
+
+Applying the rank-multiplicative property of the Kronecker product, and plugging in eq. 20, we obtain:
+
+$$
+r a n k \ [ \boldsymbol { A } ^ { y } \ ] _ { I , J } = \prod _ { t = 1 } ^ { N / 4 } r a n k \bigl [ \boldsymbol { \phi } ^ { 1 , 1 } \bigr ] \bigr | _ { I _ { 1 , t } , J _ { 1 , t } } = \operatorname* { m i n } \bigl \{ r _ { 0 } , M \bigr \} ^ { S }
+$$
+
+where $S : = | \{ t \in [ N / 4 ] : I _ { 1 , t } \neq \emptyset \land J _ { 1 , t } \neq \emptyset \} |$ . This equality holds for the specific weight setting we defined in eq. 19. Maximizing over all weight settings gives the sought after lower bound:
+
+$$
+\operatorname* { m a x } _ { \{ \mathbf { a } ^ { l , \gamma } \} _ { l , \gamma } , \mathbf { a } ^ { L , y } } r a n k \ [ \mathcal { A } ^ { y } ] _ { I , J } \ge \operatorname* { m i n } \{ r _ { 0 } , M \} ^ { S }
+$$
+
+Moving on to the upper bound, we show by induction over $l = 1 . . . L - 1$ that for any $k \in [ N / 4 ^ { l } ]$ and $\gamma \in [ r _ { l } ]$ , the rank of $\mathbb { [ } \phi ^ { l , \gamma } \ ] _ { I _ { l , k } , J _ { l , k } }$ is no greater than $c ^ { l , k }$ , regardless of the chosen weight setting. For the base case $l = 1$ Jwe have:
+
+$$
+\begin{array} { r } { \big [ \phi ^ { { 1 } , \gamma } \big ] _ { I _ { 1 , k } , J _ { 1 , k } } = \sum _ { \alpha = 1 } ^ { r _ { 0 } } a _ { \alpha } ^ { 1 , \gamma } \cdot \underset { t = 1 } { \overset { 4 } { \odot } } \big [ \big [ \mathbf { a } ^ { 0 , \alpha } \big ] \big ] _ { I _ { 0 , 4 ( k - 1 ) + t } , J _ { 0 , 4 ( k - 1 ) + t } } } \end{array}
+$$
+
+The $M ^ { | I _ { 1 , k } | }$ -by- $M ^ { | J _ { 1 , k } | }$ matrix $\mathbb { [ } \phi ^ { 1 , \gamma } \ ] _ { I _ { 1 , k } , J _ { 1 , k } }$ is given here as a sum of $r _ { 0 }$ rank-1 terms, thus obviously its rank is no greater than ${ \operatorname* { m i n } \{ M ^ { \operatorname* { m i n } \{ | I _ { 1 , k } | , | J _ { 1 , k } | \} } , r _ { 0 } \} }$ . Since by definition $c ^ { 0 , t } = 1$ for all $t \in [ N ]$ , we may write:
+
+$$
+r a n k [ \phi ^ { 1 , \gamma } ] _ { I _ { 1 , k } , J _ { 1 , k } } \leq \operatorname* { m i n } \left\{ M ^ { \operatorname* { m i n } \{ | I _ { 1 , k } | , | J _ { 1 , k } | \} } , r _ { 0 } \prod _ { t = 1 } ^ { 4 } c ^ { 0 , 4 ( k - 1 ) + t } \right\}
+$$
+
+$c ^ { 1 , k }$ is defined by the right hand side of this inequality, so our inductive hypotheses holds for $l = 1$ . For $l > 1$
+
+$$
+\begin{array} { r } { \mathbb { [ } \phi ^ { l , \gamma } ] _ { I _ { l , k } , J _ { l , k } } = \sum _ { \alpha = 1 } ^ { r _ { l - 1 } } a _ { \alpha } ^ { l , \gamma } \cdot \underset { t = 1 } { \overset { 4 } { \odot } } \mathbb { [ } \phi ^ { l - 1 , \alpha } ] _ { I _ { l - 1 , 4 ( k - 1 ) + t } , J _ { l - 1 , 4 ( k - 1 ) + t } } } \end{array}
+$$
+
+Taking ranks:
+
+$$
+\begin{array} { l c l } { r a n k [ \phi ^ { l , \gamma } ] _ { I _ { l , k } , J _ { l , k } } } & { = } & { r a n k \left( \sum _ { \alpha = 1 } ^ { r _ { l - 1 } } a _ { \alpha } ^ { l , \gamma } \cdot \underset { t = 1 } { \overset { \ll } { \prod } } [ \phi ^ { l - 1 , \alpha } ] _ { I _ { l - 1 , 4 ( k - 1 ) + t } , J _ { l - 1 , 4 ( k - 1 ) + t } } \right) } \\ & { \leq } & { \sum _ { \alpha = 1 } ^ { r _ { l - 1 } } r a n k \left( \underset { t = 1 } { \overset { \ll } { \longrightarrow } } [ \phi ^ { l - 1 , \alpha } ] _ { I _ { l - 1 , 4 ( k - 1 ) + t } , J _ { l - 1 , 4 ( k - 1 ) + t } } \right) } \\ & { = } & { \sum _ { \alpha = 1 } ^ { r _ { l - 1 } } \prod _ { t = 1 } ^ { 4 } r a n k [ \phi ^ { l - 1 , \alpha } ] _ { I _ { l - 1 , 4 ( k - 1 ) + t } , J _ { l - 1 , 4 ( k - 1 ) + t } } } \\ & { \leq } & { \sum _ { \alpha = 1 } ^ { r _ { l - 1 } } \prod _ { t = 1 } ^ { 4 } c ^ { l - 1 , 4 ( k - 1 ) + t } } \\ & { = } & { r _ { l - 1 } \prod _ { t = 1 } ^ { 4 } c ^ { l - 1 , 4 ( k - 1 ) + t } } \end{array}
+$$
+
+where we used rank sub-additivity in the second line, the rank-multiplicative property of the Kronecker product in the third line, and our inductive hypotheses for $l - 1$ in the fourth line. Since the number rows and columns in $\mathbb { [ } \boldsymbol { \phi } ^ { l , \gamma } \ ] _ { I _ { l , k } , J _ { l , k } }$ is $M ^ { | I _ { l , k } | }$ and $M ^ { | J _ { l , k } | }$ respectively, we may incorporate these terms into the inequality, obJtaining:
+
+$$
+r a n k [ \phi ^ { l , \gamma } ] _ { I _ { l , k } , J _ { l , k } } \leq \operatorname* { m i n } \left\{ M ^ { \operatorname* { m i n } \{ | I _ { l , k } | , | J _ { l , k } | \} } , r _ { l - 1 } \prod _ { t = 1 } ^ { 4 } c ^ { l - 1 , 4 ( k - 1 ) + t } \right\}
+$$
+
+The right hand side here is equal to $c ^ { l , k }$ by definition, so our inductive hypotheses indeed holds for all $l =$ $1 \ldots L - 1$ . To establish the sought after upper bound on the rank of $\mathbb { I } A ^ { y } \mathbb { I } _ { I , J }$ , we recall that the latter is given by:
+
+$$
+\ [ \mathcal { A } ^ { y } ] _ { I , J } = \sum _ { \alpha = 1 } ^ { r _ { L - 1 } } a _ { \alpha } ^ { L , y } \cdot \underset { t = 1 } { \overset { 4 } { \odot } } [ [ \phi ^ { L - 1 , \alpha } ] ] _ { I _ { L - 1 , t } , J _ { L - 1 , t } }
+$$
+
+Carry out a series of steps similar to before, while making use of our inductive hypotheses for $l = L - 1$
+
+$$
+\begin{array} { l l l } { r a n k \| A ^ { y } \| _ { I , J } } & { = } & { r a n k \left( \sum _ { \alpha = 1 } ^ { r _ { L - 1 } } a _ { \alpha } ^ { L , y } \cdot \underset { i = 1 } { \overset { \llangle } { \langle } } \| \phi ^ { L - 1 , \alpha } \| _ { I _ { L - 1 , t } , J _ { L - 1 , t } } \right) } \\ & { \leq } & { \sum _ { \alpha = 1 } ^ { r _ { L - 1 } } r a n k \left( \underset { i = 1 } { \overset { \llangle } { \langle } } \| \phi ^ { L - 1 , \alpha } \| _ { I _ { L - 1 , t } , J _ { L - 1 , t } } \right) } \\ & { = } & { \sum _ { \alpha = 1 } ^ { r _ { L - 1 } } \prod _ { t = 1 } ^ { 4 } r a n k \| \phi ^ { L - 1 , \alpha } \| _ { I _ { L - 1 , t } , J _ { L - 1 , t } } } \\ & { \leq } & { \sum _ { \alpha = 1 } ^ { r _ { L - 1 } } \prod _ { t = 1 } ^ { 4 } c ^ { L - 1 , t } } \\ & { = } & { r L - 1 \prod _ { t = 1 } ^ { 4 } c ^ { L - 1 , t } } \end{array}
+$$
+
+Since $\mathbb { I } A ^ { y } \mathbb { I } _ { I , J }$ has $M ^ { \left| I \right| }$ rows and $M ^ { | J | }$ columns, we may include these terms in the inequality, thus reaching J Kthe upper bound we set out to prove.
+
+# B SEPARATION RANK AND THE $L ^ { 2 }$ DISTANCE FROM SEPARABLE FUNCTIONS
+
+Our analysis of correlations modeled by convolutional networks is based on the concept of separation rank, conveyed in sec. 4. When the separation rank of a function w.r.t. a partition of its input is equal to 1, the function is separable, meaning it does not model any interaction between sides of the partition. We argued that the higher the separation rank, the farther the function is from this situation, i.e. the stronger the correlation it induces between sides of the partition. In the current appendix we formalize this argument, by relating separation rank to the $L ^ { 2 }$ distance from the set of separable functions. We begin by defining and characterizing a normalized (scale invariant) version of this distance (app. B.1). It is then shown (app. B.2) that separation rank provides an upper bound on the normalized distance. Finally, a lower bound that applies to deep convolutional arithmetic circuits is derived (app. B.3), based on the lower bound for their separation ranks established in sec. 5.2. Together, these steps imply that our entire analysis, facilitated by upper and lower bounds on separation ranks of convolutional arithmetic circuits, can be interpreted as based on upper and lower bounds on (normalized) $L ^ { 2 }$ distances from separable functions.
+
+In the text hereafter, we assume familiarity of the reader with the contents of sec. 2, 3, 4, 5 and the proofs given in app. A. We also rely on basic knowledge in the topic of $L ^ { 2 }$ spaces (see discussion in app. A.1 for minimal background required in order to follow our arguments), as well as several results concerning singular values of matrices. In line with sec. 5, an assumption throughout this appendix is that all functions in question are measurable and square-integrable (i.e. belong to $L ^ { 2 }$ over the respective Euclidean space), and in app. B.3, we also make use of the fact that representation functions $( f _ { \theta _ { d } } )$ of a convolutional arithmetic circuit can be regarded as linearly independent (see sec. 5.1). Finally, for convenience, we now fix $( I , J ) - \mathrm { a n }$ arbitrary partition of $[ N ]$ . Specifically, $I$ and $J$ are disjoint subsets of $[ N ]$ whose union gives $[ N ]$ , denoted by $I = \{ i _ { 1 } , \ldots , i _ { | I | } \}$ with $i _ { 1 } < \cdots < i _ { | I | }$ , and $J = \{ j _ { 1 } , \dots , j _ { | J | } \}$ with $j _ { 1 } < \cdots < j _ { | J | }$ .
+
+# B.1 NORMALIZED $L ^ { 2 }$ DISTANCE FROM SEPARABLE FUNCTIONS
+
+For a function $h { \in } L ^ { 2 } ( ( \mathbb { R } ^ { s } ) ^ { N } )$ (which is not identically zero), the normalized $L ^ { 2 }$ distance from the set of separable functions w.r.t. $( I , J )$ , is defined as follows:
+
+$$
+D ( h ; I , J ) : = \frac { 1 } { | | h | | } \cdot \operatorname* { i n f } _ { g \in L ^ { 2 } ( ( \mathbb { R } ^ { \delta } ) ^ { \lfloor J \rfloor } ) } \left| \left| h ( \mathbf { x } _ { 1 } , \dots , \mathbf { x } _ { N } ) - g ( \mathbf { x } _ { i _ { 1 } } , \dots , \mathbf { x } _ { i _ { | I | } } ) g ^ { \prime } ( \mathbf { x } _ { j _ { 1 } } , \dots , \mathbf { x } _ { j _ { | J | } } ) \right| \right|
+$$
+
+where $\left\| \cdot \right\|$ refers to the norm of $L ^ { 2 }$ space, e.g. $\textstyle \| h \| : = ( \int _ { ( \mathbb { R } ^ { s } ) ^ { N } } h ^ { 2 } ) ^ { 1 / 2 }$ . In words, $D ( h ; I , J )$ is defined as the minimal $L ^ { 2 }$ distance between $h$ and a function that is separable w.r.t. $( I , J )$ , divided by the norm of $h$ . The normalization (division by $\| h \| )$ admits scale invariance to $D ( h ; I , J )$ , and is of critical importance – without it, rescaling $h$ would accordingly rescale the distance measure, rendering the latter uninformative in terms of deviation from separability.
+
+It is worthwhile noting the resemblance between $D ( h ; I , J )$ and the concept of mutual information (see Cover and Thomas (2012) for a comprehensive introduction). Both measures quantify the interaction that a normalized function 11 induces between input variables, by measuring distance from separable functions. The difference between the measures is threefold. First, mutual information considers probability density functions (non-negative and in $L ^ { 1 }$ ), while $D ( h ; I , J )$ applies to functions in $L ^ { 2 }$ . Second, the notion of distance in mutual information is quantified through the Kullback-Leibler divergence, whereas in $D ( h ; I , J )$ it is simply the $L ^ { 2 }$ metric. Third, while mutual information evaluates the distance from a specific separable function – product of marginal distributions, $D ( h ; I , J )$ evaluates the minimal distance across all separable functions.
+
+We now turn to establish a spectral characterization of $D ( h ; I , J )$ , which will be used in app. B.2 and B.3 for deriving upper and lower bounds (respectively). Assume we have the following expression for $h$ :
+
+$$
+h ( { \bf x } _ { 1 } , \ldots , { \bf x } _ { N } ) = \sum _ { \mu = 1 } ^ { m } \sum _ { \mu ^ { \prime } = 1 } ^ { m ^ { \prime } } A _ { \mu , \mu ^ { \prime } } \cdot \phi _ { \mu } ( { \bf x } _ { i _ { 1 } } , \ldots , { \bf x } _ { i _ { | I | } } ) \phi _ { \mu ^ { \prime } } ^ { \prime } ( { \bf x } _ { j _ { 1 } } , \ldots , { \bf x } _ { j _ { | J | } } )
+$$
+
+where $m$ and $m ^ { \prime }$ are positive integers, $A$ is an $m$ -by- $m ^ { \prime }$ real matrix, and $\{ \phi _ { \mu } \} _ { \mu = 1 } ^ { m } , \{ \phi _ { \mu ^ { \prime } } ^ { \prime } \} _ { \mu ^ { \prime } = 1 } ^ { m ^ { \prime } }$ are orthonormal sets of functions in $L ^ { 2 } ( ( \mathbb { R } ^ { s } ) ^ { | I | } ) , L ^ { 2 } ( ( \mathbb { R } ^ { s } ) ^ { | J | } )$ respectively. We refer to such expression as an orthonormal separable decomposition of $h$ , with $A$ being its coefficient matrix. We will show that for any orthonormal separable decomposition, $D ( h ; I , J )$ is given by the following formula:
+
+$$
+D ( h ; I , J ) = { \sqrt { 1 - { \frac { \sigma _ { 1 } ^ { 2 } ( A ) } { \sigma _ { 1 } ^ { 2 } ( A ) + \cdots + \sigma _ { \operatorname* { m i n } \{ m , m ^ { \prime } \} } } } ( A ) } }
+$$
+
+where $\sigma _ { 1 } ( A ) \geq \cdot \cdot \cdot \geq \sigma _ { \operatorname* { m i n } \{ m , m ^ { \prime } \} } ( A ) \geq 0$ are the singular values of the coefficient matrix $A$ . This implies that if the largest singular value of $A$ accounts for a significant portion of the spectral energy, the normalized $L ^ { 2 }$ distance of $h$ from separable functions is small. On the other hand, if all but a fraction of the spectral energy is attributed to trailing singular values, $h$ is far from being separable $( D ( h ; I , J )$ is close to 1).
+
+As a first step in deriving eq. 23, we show that $\| h \| ^ { 2 } = \sigma _ { 1 } ^ { 2 } ( A ) + \cdot \cdot \cdot + \sigma _ { \operatorname* { m i n } \{ m , m ^ { \prime } \} } ^ { 2 } ( A ) \colon$
+
+$$
+\begin{array} { r l r } { \mathrm { d } t ^ { 2 } } & { = } & { \int \boldsymbol { \mu } ^ { \nu } ( \mathbf { S } _ { \mu \nu } - \mathbf { S } _ { \nu \mu } ) \mathrm { d } \mathbf { S } _ { \nu \mu } \mathrm { d } t ^ { 2 } , } \\ & { \in \int \left( \sum _ { s ^ { \prime } = - 1 } ^ { \infty } \sum _ { \nu ^ { \prime } = 1 } ^ { \infty } A _ { \mu \nu } - \boldsymbol { S } _ { \nu \mu } \right) \mathrm { d } s , } \\ & { \in \mathbb { R } ^ { 3 } \sum _ { \nu \in \mathcal { S } _ { \mu \nu } } \sum _ { \nu ^ { \prime } = 1 } ^ { \infty } A _ { \mu \nu } - \boldsymbol { S } _ { \nu \mu } \mathrm { d } s , } \\ & { \in \mathbb { R } ^ { 3 } \sum _ { \nu \in \mathcal { S } _ { \mu \nu } } \sum _ { \nu ^ { \prime } = 1 } ^ { \infty } A _ { \mu \nu } \mathrm { d } s , } \\ & { \in \mathbb { R } ^ { 3 } \sum _ { \nu \in \mathcal { S } _ { \mu \nu } } \sum _ { \nu ^ { \prime } = 1 } ^ { \infty } A _ { \mu \nu } \mathrm { d } s , } \\ & { \in \mathbb { R } ^ { 3 } \sum _ { \nu \in \mathcal { S } _ { \mu \nu } } \sum _ { \nu ^ { \prime } = 1 } ^ { \infty } A _ { \mu \nu } \mathrm { d } s , } \\ & { = } & { \int \mathrm { e } ^ { \mathrm { i } ( s ) } , } \\ &  \frac { \sum _ { s ^ { \prime } = 1 } ^ { \infty } \sum _ { \nu ^ { \prime } = 1 } ^ { \infty } \sum _ { \nu ^ { \prime } = 1 } ^ { \infty } A _ { \mu \nu ^ { \prime } } \mathrm { d } s , } \\ & { } & { \mathrm { e } ^ { \mathrm { i } ( s ) } , } \\ &  \frac  \sum _ { s ^ { \prime } = 1 } ^ { \infty } \sum _ { \nu ^ { \prime } = 1 } ^ { \infty } \sum _ { \nu ^ { \prime } = 1 } ^ { \infty } \sum _ { \nu ^ { \prime } = 1 } ^ { \infty } \sum _ { \nu ^ { \prime } = 1 } ^ { \infty } \sum _ { \nu ^ { \prime } = 1 } ^ { \infty } \sum _ { \nu ^ { \prime } = 1 } ^ { \infty } \sum _ { \nu ^ { \prime } = 1 } ^ { \infty } A _ { \mu \nu ^ { \prime } } \mathrm \end{array}
+$$
+
+Equality (1) here originates from the definition of $L ^ { 2 }$ norm. (2) is obtained by plugging in the expression in eq. 22. (3) is merely an arithmetic manipulation. (4) follows from the linearity of integration. (5) makes use of Fubini’s theorem (see Jones (2001)). (6) results from the orthonormality of $\{ \phi _ { \mu } \} _ { \mu = 1 } ^ { m }$ and $\{ \phi _ { \mu ^ { \prime } } ^ { \prime } \} _ { \mu ^ { \prime } = 1 } ^ { m ^ { \prime } }$ . (7) is a trivial computation. Finally, (8) is an outcome of the fact that the squared Frobenius norm of a matrix, i.e. the sum of squares over its entries, is equal to the sum of squares over its singular values (see Golub and Van Loan (2013) for proof).
+
+Let $g { \in } L ^ { 2 } ( ( \mathbb { R } ^ { s } ) ^ { | I | } )$ . By fact 1 in app. A.1, there exist scalars $\alpha _ { 1 } \ldots \alpha _ { m } \in \mathbb { R }$ , and a function $\delta { \in } L ^ { 2 } ( ( \mathbb { R } ^ { s } ) ^ { | I | } )$ orthogonal to sp $i n \{ \phi _ { 1 } \ldots \phi _ { m } \}$ , such that $\begin{array} { r } { g = \sum _ { \mu = 1 } ^ { m } \alpha _ { \mu } \cdot \phi _ { \mu } + \delta . } \end{array}$ . Similarly, for any $g ^ { \prime } { \in } L ^ { 2 } ( ( \mathbb { R } ^ { s } ) ^ { | J | } )$ there exist $\alpha _ { 1 } ^ { \prime } \ldots \alpha _ { m ^ { \prime } } ^ { \prime } \in \mathbb { R }$ and $\delta ^ { \prime } \in s p a n \{ \phi _ { 1 } ^ { \prime } \ldots \phi _ { m ^ { \prime } } ^ { \prime } \} ^ { \perp }$ such that $\begin{array} { r } { g ^ { \prime } = \sum _ { \mu ^ { \prime } = 1 } ^ { m ^ { \prime } } \alpha _ { \mu ^ { \prime } } ^ { \prime } \cdot \phi _ { \mu ^ { \prime } } ^ { \prime } + \delta ^ { \prime } } \end{array}$ . Fact 2 in app. A.1 indicates that the function given by $( \mathbf { x } _ { 1 } , \ldots , \mathbf { x } _ { N } ) { \mapsto } g ( \mathbf { x } _ { i _ { 1 } } , \ldots , \mathbf { x } _ { i _ { | I | } } ) g ^ { \prime } ( \mathbf { x } _ { j _ { 1 } } , \ldots , \mathbf { x } _ { j _ { | J | } } )$ belongs to $L ^ { 2 } ( ( \mathbb { R } ^ { s } ) ^ { N } )$ . We may express it as follows:
+
+$$
+\begin{array} { r l r } { g ( { \bf x } _ { i _ { 1 } } , \ldots , { \bf x } _ { i _ { | I | } } ) g ^ { \prime } ( { \bf x } _ { j _ { 1 } } , \ldots , { \bf x } _ { j _ { | J | } } ) } & { = } & { \sum _ { \mu = 1 } ^ { m } \sum _ { \mu ^ { \prime } = 1 } ^ { m ^ { \prime } } \alpha _ { \mu } \alpha _ { \mu ^ { \prime } } ^ { \prime } \cdot \phi _ { \mu } ( { \bf x } _ { i _ { 1 } } , \ldots , { \bf x } _ { i _ { | I | } } ) \phi _ { \mu ^ { \prime } } ^ { \prime } ( { \bf x } _ { j _ { 1 } } , \ldots , { \bf x } _ { j _ { | J | } } ) } \\ & { } & { + \left( \sum _ { \mu = 1 } ^ { m } \alpha _ { \mu } \cdot \phi _ { \mu } ( { \bf x } _ { i _ { 1 } } , \ldots , { \bf x } _ { i _ { | I | } } ) \right) \cdot \delta ^ { \prime } ( { \bf x } _ { j _ { 1 } } , \ldots , { \bf x } _ { j _ { | J | } } ) } \\ & { } & { + \delta ( { \bf x } _ { i _ { 1 } } , \ldots , { \bf x } _ { i _ { | I | } } ) \cdot \left( \sum _ { \mu ^ { \prime } = 1 } ^ { m ^ { \prime } } \alpha _ { \mu ^ { \prime } } ^ { \prime } \cdot \phi _ { \mu ^ { \prime } } ^ { \prime } ( { \bf x } _ { j _ { 1 } } , \ldots , { \bf x } _ { j _ { | J | } } ) \right) } \\ & { } & { + \delta ( { \bf x } _ { i _ { 1 } } , \ldots , { \bf x } _ { i _ { | I | } } ) \delta ^ { \prime } ( { \bf x } _ { j _ { 1 } } , \ldots , { \bf x } _ { j _ { | J | } } ) } \end{array}
+$$
+
+According to fact 3 in app. A.1, the second, third and fourth terms on the right hand side of the above are orthogonal to $s \bar { p } a n \{ ( { \bf x } _ { 1 } , \ldots , \hat { \bf x } _ { N } ) { \mapsto } { \phi } _ { \mu } ( { \bf x } _ { i _ { 1 } } , \ldots , { \bf x } _ { i _ { | I | } } ) { \phi } _ { \mu ^ { \prime } } ^ { \prime } ( { \bf x } _ { j _ { 1 } } , \ldots , { \bf x } _ { j _ { | J | } } ) \} _ { \mu \in [ m ] , \mu ^ { \prime } \in [ m ^ { \prime } ] } ,$ . Denote their summation by $\mathcal { E } ( \mathbf { x } _ { 1 } , \ldots , \mathbf { x } _ { N } )$ , and subtract the overall function from $h$ (given by eq. 22):
+
+$$
+\begin{array} { r l } & { h ( { \mathbf x } _ { 1 } , \ldots , { \mathbf x } _ { N } ) - g ( { \mathbf x } _ { i _ { 1 } } , \ldots , { \mathbf x } _ { i _ { | I | } } ) g ^ { \prime } ( { \mathbf x } _ { j _ { 1 } } , \ldots , { \mathbf x } _ { j _ { | J | } } ) } \\ & { \qquad = \sum _ { \mu = 1 } ^ { m } \sum _ { \mu ^ { \prime } = 1 } ^ { m ^ { \prime } } A _ { \mu , \mu ^ { \prime } } \cdot \phi _ { \mu } ( { \mathbf x } _ { i _ { 1 } } , \ldots , { \mathbf x } _ { i _ { | I | } } ) \phi _ { \mu ^ { \prime } } ^ { \prime } ( { \mathbf x } _ { j _ { 1 } } , \ldots , { \mathbf x } _ { j _ { | J | } } ) } \\ & { \qquad - \sum _ { \mu = 1 } ^ { m } \sum _ { \mu ^ { \prime } = 1 } ^ { m ^ { \prime } } \alpha _ { \mu } \alpha _ { \mu ^ { \prime } } ^ { \prime } \cdot \phi _ { \mu } ( { \mathbf x } _ { i _ { 1 } } , \ldots , { \mathbf x } _ { i _ { | I | } } ) \phi _ { \mu ^ { \prime } } ^ { \prime } ( { \mathbf x } _ { j _ { 1 } } , \ldots , { \mathbf x } _ { j _ { | J | } } ) - \mathcal { E } ( { \mathbf x } _ { 1 } , \ldots , { \mathbf x } _ { N } ) } \\ & { \qquad = \sum _ { \mu = 1 } ^ { m } \sum _ { \mu ^ { \prime } = 1 } ^ { m ^ { \prime } } ( A _ { \mu , \mu ^ { \prime } } - \alpha _ { \mu } \alpha _ { \mu ^ { \prime } } ^ { \prime } ) \cdot \phi _ { \mu } ( { \mathbf x } _ { i _ { 1 } } , \ldots , { \mathbf x } _ { i _ { | I | } } ) \phi _ { \mu ^ { \prime } } ^ { \prime } ( { \mathbf x } _ { j _ { 1 } } , \ldots , { \mathbf x } _ { j _ { | J | } } ) - \mathcal { E } ( { \mathbf x } _ { 1 } , \ldots , { \mathbf x } _ { N } ) } \end{array}
+$$
+
+Since the two terms in the latter expression are orthogonal to one another, we have:
+
+$$
+\begin{array} { r l } & { \left\| h ( \mathbf x _ { 1 } , \dots , \mathbf x _ { N } ) - g ( \mathbf x _ { i _ { 1 } } , \dots , \mathbf x _ { i _ { | I | } } ) g ^ { \prime } ( \mathbf x _ { j _ { 1 } } , \dots , \mathbf x _ { j _ { | J | } } ) \right\| ^ { 2 } } \\ & { \quad = \left\| \sum _ { \mu = 1 } ^ { m } \sum _ { \mu ^ { \prime } = 1 } ^ { m ^ { \prime } } ( A _ { \mu , \mu ^ { \prime } } - \alpha _ { \mu } \alpha _ { \mu ^ { \prime } } ^ { \prime } ) \cdot \phi _ { \mu } ( \mathbf x _ { i _ { 1 } } , \dots , \mathbf x _ { i _ { | I | } } ) \phi _ { \mu ^ { \prime } } ^ { \prime } ( \mathbf x _ { j _ { 1 } } , \dots , \mathbf x _ { j _ { | J | } } ) \right\| ^ { 2 } + \| \mathcal E ( \mathbf x _ { 1 } , \dots , \mathbf x _ { N } ) \| ^ { 2 } } \end{array}
+$$
+
+Applying a sequence of steps as in eq. 24 to the first term in the second line of the above, we obtain:
+
+$$
+\left| h ( { \bf x } _ { 1 } , \ldots , { \bf x } _ { N } ) - g ( { \bf x } _ { i _ { 1 } } , \ldots , { \bf x } _ { i _ { | I | } } ) g ^ { \prime } ( { \bf x } _ { j _ { 1 } } , \ldots , { \bf x } _ { j _ { | I | } } ) \right| ^ { 2 } = \sum _ { \mu = 1 } ^ { m } \sum _ { \mu ^ { \prime } = 1 } ^ { m ^ { \prime } } ( A _ { \mu , \mu ^ { \prime } } - \alpha _ { \mu } \alpha _ { \mu ^ { \prime } } ^ { \prime } ) ^ { 2 } + \| \mathcal E ( { \bf x } _ { 1 } , \ldots , { \bf x } _ { N } ) \| ^ { 2 }
+$$
+
+$\mathcal { E } ( { \bf x } _ { 1 } , . . . , { \bf x } _ { N } ) = 0$ if $\delta$ and $\delta ^ { \prime }$ are the zero functions, implying that:
+
+$$
+\left\| h ( { \bf x } _ { 1 } , \ldots , { \bf x } _ { N } ) - g ( { \bf x } _ { i _ { 1 } } , \ldots , { \bf x } _ { i _ { | I | } } ) g ^ { \prime } ( { \bf x } _ { j _ { 1 } } , \ldots , { \bf x } _ { j _ { | J | } } ) \right\| ^ { 2 } \geq \sum _ { \mu = 1 } ^ { m } \sum _ { \mu ^ { \prime } = 1 } ^ { m ^ { \prime } } ( A _ { \mu , \mu ^ { \prime } } - \alpha _ { \mu } \alpha _ { \mu ^ { \prime } } ^ { \prime } ) ^ { 2 }
+$$
+
+with equality holding if $\begin{array} { r } { g = \sum _ { \mu = 1 } ^ { m } \alpha _ { \mu } \cdot \phi _ { \mu } } \end{array}$ and $\begin{array} { r } { g ^ { \prime } = \sum _ { \mu ^ { \prime } = 1 } ^ { m ^ { \prime } } \alpha _ { \mu ^ { \prime } } ^ { \prime } \cdot \phi _ { \mu ^ { \prime } } ^ { \prime } } \end{array}$ . Now, $\begin{array} { r } { \sum _ { \mu = 1 } ^ { m } \sum _ { \mu ^ { \prime } = 1 } ^ { m ^ { \prime } } ( A _ { \mu , \mu ^ { \prime } } - \alpha _ { \mu } \alpha _ { \mu ^ { \prime } } ^ { \prime } ) ^ { 2 } } \end{array}$ is the squared Frobenius distance between the matrix $A$ and the rank-1 matrix $\pmb { \alpha } \pmb { \alpha } ^ { \prime \top }$ , where $_ { \pmb { \alpha } }$ and $\mathbf { \Delta } _ { \mathbf { { \alpha } } \mathbf { { \alpha } } } ^ { \prime }$ are column vectors holding $\alpha _ { 1 } \ldots \alpha _ { m }$ and $\alpha _ { 1 } ^ { \prime } \ldots \alpha _ { m ^ { \prime } } ^ { \prime }$ respectively. This squared distance is greater than or equal to the sum of squares over the second to last singular values of $A$ , and moreover, the inequality holds with equality for proper choices of $_ { \pmb { \alpha } }$ and $\mathbf { \Delta } _ { \mathbf { { \alpha } } \mathbf { { \alpha } } } ^ { \prime }$ (Eckart and Young (1936)). From this we conclude that:
+
+$$
+\begin{array} { r } { \left| \left| h ( \mathbf { x } _ { 1 } , \ldots , \mathbf { x } _ { N } ) - g ( \mathbf { x } _ { i _ { 1 } } , \ldots , \mathbf { x } _ { i _ { | I | } } ) g ^ { \prime } ( \mathbf { x } _ { j _ { 1 } } , \ldots , \mathbf { x } _ { j _ { | J | } } ) \right| \right| ^ { 2 } \geq \sigma _ { 2 } ^ { 2 } ( A ) + \cdot \cdot \cdot + \sigma _ { \operatorname* { m i n } \{ m , m ^ { \prime } \} } ^ { 2 } ( A ) } \end{array}
+$$
+
+with equality holding if $g$ and $g ^ { \prime }$ are set to $\scriptstyle \sum _ { \mu = 1 } ^ { m } \alpha _ { \mu } \cdot \phi _ { \mu }$ and $\scriptstyle \sum _ { \mu ^ { \prime } = 1 } ^ { m ^ { \prime } } \alpha _ { \mu ^ { \prime } } ^ { \prime } \cdot \phi _ { \mu ^ { \prime } } ^ { \prime }$ (respectively) for proper choices of $\alpha _ { 1 } \ldots \alpha _ { m }$ and $\alpha _ { 1 } ^ { \prime } \ldots \alpha _ { m ^ { \prime } } ^ { \prime }$ . We thus have the infimum over all possible $g , g ^ { \prime }$ :
+
+$$
+ \underset { g \in L ^ { 2 } ( \mathbb { R } ^ { 3 } ) ^ { | \mathcal { I } | } } { \operatorname* { i n f } } | | h ( \mathbf { x } _ { 1 } , \ldots , \mathbf { x } _ { N } ) - g ( \mathbf { x } _ { i _ { 1 } } , \ldots , \mathbf { x } _ { i _ { | I | } } ) g ^ { \prime } ( \mathbf { x } _ { j _ { 1 } } , \ldots , \mathbf { x } _ { j _ { | J | } } ) | | ^ { 2 } = \sigma _ { 2 } ^ { 2 } ( A ) + \cdot \cdot \cdot + \sigma _ { \operatorname* { m i n } \{ m , m ^ { \prime } \} } ^ { 2 } ( A )
+$$
+
+Recall that we would like to derive the formula in eq. 23 for $D ( h ; I , J )$ , assuming $h$ is given by the orthonormal separable decomposition in eq. 22. Taking square root of the equalities established in eq. 24 and 25, and plugging them into the definition of $D ( h ; I , J )$ (eq. 21), we obtain the sought after result.
+
+# B.2 UPPER BOUND THROUGH SEPARATION RANK
+
+We now relate $D ( h ; I , J )$ – the normalized $L ^ { 2 }$ distance of $h { \in } L ^ { 2 } ( ( \mathbb { R } ^ { s } ) ^ { N } )$ from the set of separable functions w.r.t. $( I , J )$ (eq. 21), to $s e p  ( h ; I , J )$ – the separation rank of $h$ w.r.t. $( I , J )$ (eq. 5). Specifically, we make use of the formula in eq. 23 to derive an upper bound on $D ( h ; I , J )$ in terms of $s e p  ( h ; I , J )$ .
+
+Assuming $h$ has finite separation rank (otherwise the bound we derive is trivial), we may express it as:
+
+$$
+h ( { \bf x } _ { 1 } , \ldots , { \bf x } _ { N } ) = \sum _ { \nu = 1 } ^ { R } g _ { \nu } ( { \bf x } _ { i _ { 1 } } , \ldots , { \bf x } _ { i _ { | I | } } ) g _ { \nu } ^ { \prime } ( { \bf x } _ { j _ { 1 } } , \ldots , { \bf x } _ { j _ { | J | } } )
+$$
+
+where $R$ is some positive integer (necessarily greater than or equal to $s e p ( h ; I , J ) )$ , and $g _ { 1 } . . . g _ { R } { \in } L ^ { 2 } ( ( \mathbb { R } ^ { s } ) ^ { | I | } )$ , $g _ { 1 } ^ { \prime } . . . g _ { R } ^ { \prime } { \in } L ^ { 2 } ( ( \mathbb { R } ^ { s } ) ^ { | J | } )$ . Let $\{ \phi _ { 1 } , . . . , \phi _ { m } \} { \subset } L ^ { 2 } ( ( \mathbb { R } ^ { s } ) ^ { | I | } )$ and $\{ \phi _ { 1 } ^ { \prime } , . . . , \phi _ { m ^ { \prime } } ^ { \prime } \} { \subset } L ^ { 2 } ( ( \mathbb { R } ^ { s } ) ^ { | J | } )$ be two sets of orthery mal functionthere exist $s p a n \{ g _ { 1 } . . . g _ { R } \}$ $s p a n \{ g _ { 1 } ^ { \prime } . . . g _ { R } ^ { \prime } \}$ respectch that r ev-and $\nu { \in } R$ $\alpha _ { \nu , 1 } \ldots \alpha _ { \nu , m } \ \in \mathbb { R }$ $\alpha _ { \nu , 1 } ^ { \prime } \ldots \alpha _ { \nu , m ^ { \prime } } ^ { \prime } \ \in \mathbb { R }$ $\begin{array} { r } { g _ { \nu } = \sum _ { \mu = 1 } ^ { m } \alpha _ { \nu , \mu } \cdot \phi _ { \mu } } \end{array}$ $\begin{array} { r } { g _ { \nu } ^ { \prime } = \sum _ { \mu ^ { \prime } = 1 } ^ { m ^ { \prime } } \alpha _ { \nu , \mu ^ { \prime } } ^ { \prime } \cdot \phi _ { \mu ^ { \prime } } ^ { \prime } } \end{array}$ . Plugging this into eq. 26, we obtain:
+
+$$
+h ( { \bf x } _ { 1 } , . . . , { \bf x } _ { N } ) = \sum _ { \mu = 1 } ^ { m } \sum _ { \mu ^ { \prime } = 1 } ^ { m ^ { \prime } } \left( \sum _ { \nu = 1 } ^ { R } \alpha _ { \nu , \mu } \alpha _ { \nu , \mu ^ { \prime } } ^ { \prime } \right) \cdot \phi _ { \mu } ( { \bf x } _ { i _ { 1 } } , . . . , { \bf x } _ { i _ { | I | } } ) \phi _ { \mu ^ { \prime } } ^ { \prime } ( { \bf x } _ { j _ { 1 } } , . . . , { \bf x } _ { j _ { | J | } } )
+$$
+
+This is an orthonormal separable decomposition of $h$ (eq. 22), with coefficient matrix $\begin{array} { r } { A = \sum _ { \nu = 1 } ^ { R } \pmb { \alpha } _ { \nu } ( \pmb { \alpha } _ { \nu } ^ { \prime } ) ^ { \top } } \end{array}$ , where $\pmb { \alpha } _ { \nu } : = [ \alpha _ { \nu , 1 } \ldots \alpha _ { \nu , m } ] ^ { \top }$ and $\pmb { \alpha } _ { \nu } ^ { \prime } : = [ \alpha _ { \nu , 1 } ^ { \prime } \ldots \alpha _ { \nu , m ^ { \prime } } ^ { \prime } ] ^ { \top }$ for every $\nu { \in } R$ . Obviously the rank of $A$ is no greater than $R$ , implying:
+
+$$
+\frac { \sigma _ { 1 } ^ { 2 } ( A ) } { \sigma _ { 1 } ^ { 2 } ( A ) + \cdots + \sigma _ { \operatorname* { m i n } \{ m , m ^ { \prime } \} } ^ { 2 } ( A ) } \geq \frac { 1 } { R }
+$$
+
+where as in app. B.1, $\sigma _ { 1 } ( A ) \geq \cdot \cdot \cdot \geq \sigma _ { \operatorname* { m i n } \{ m , m ^ { \prime } \} } ( A ) \geq 0$ stand for the singular values of $A$ . Introducing this inequality into eq. 23 gives:
+
+$$
+D ( h ; I , J ) = { \sqrt { 1 - { \frac { \sigma _ { 1 } ^ { 2 } ( A ) } { \sigma _ { 1 } ^ { 2 } ( A ) + \cdots + \sigma _ { \operatorname* { m i n } \{ m , m ^ { \prime } \} } } ^ { ( A ) } } } } \leq { \sqrt { 1 - { \frac { 1 } { R } } } }
+$$
+
+The latter holds for any $R \in \mathbb N$ that admits eq. 26, so in particular we may take it to be minimal, i.e. to be equal to $s e p ( h ; I , J ) ~ ^ { 1 2 }$ , bringing forth the sought after upper bound:
+
+$$
+D ( h ; I , J ) \leq \sqrt { 1 - \frac { 1 } { s e p ( h ; I , J ) } }
+$$
+
+By eq. 27, low separation rank implies proximity (in normalized $L ^ { 2 }$ sense) to a separable function. We may use the inequality to translate the upper bounds on separation ranks established for deep and shallow convolutional arithmetic circuits (sec. 5.2 and 5.3 respectively), into upper bounds on normalized $\cdot ^ { 2 }$ distances from separable functions. To completely frame our analysis in terms of the latter measure, a translation of the lower bound on separation ranks of deep convolutional arithmetic circuits (sec. 5.2) is also required. Eq. 27 does not facilitate such translation, and in fact, it is easy to construct functions $h$ whose separation ranks are high yet are very close (in normalized $L ^ { 2 }$ sense) to separable functions. 13 However, as we show in app. B.3 below, the specific lower bound of interest can indeed be translated, and our analysis may entirely be framed in terms of normalized $L ^ { 2 }$ distance from separable functions.
+
+# B.3 LOWER BOUND FOR DEEP CONVOLUTIONAL ARITHMETIC CIRCUITS
+
+Let $h _ { y } { \in } L ^ { 2 } ( ( \mathbb { R } ^ { s } ) ^ { N } )$ be a function realized by a deep convolutional arithmetic circuit (fig. 1(a) with size-4 pooling windows and $L = \log _ { 4 } N$ hidden layers), i.e. $h _ { y }$ is given by eq. 2, where $f _ { \theta _ { 1 } } . . . f _ { \theta _ { M } } \in L ^ { 2 } ( \mathbb { R } ^ { s } )$ are linearly independent representation functions, and $\mathcal { A } ^ { y }$ is a coefficient tensor of order $N$ and dimension $M$ in each mode, determined by the linear weights of the network $( \{ \mathbf { a } ^ { l , \gamma } \} _ { l , \gamma } , \mathbf { a } ^ { L , y } )$ through the hierarchical decomposition in eq. 3. Rearrange eq. 2 by grouping indexes $d _ { 1 } . . . d _ { N }$ in accordance with the partition $( I , J )$ :
+
+$$
+h _ { y } \left( \mathbf { x } _ { 1 } , . . . , \mathbf { x } _ { N } \right) = \sum _ { d _ { i _ { 1 } } , . . . d _ { i _ { | I | } } = 1 } ^ { M } \sum _ { d _ { j _ { 1 } } . . . d _ { j _ { | J | } } = 1 } ^ { M } \mathcal { A } _ { d _ { 1 } . . . d _ { N } } ^ { y } \cdot \left( \prod _ { t = 1 } ^ { | I | } f _ { \theta _ { d _ { i _ { t } } } } ( \mathbf { x } _ { i _ { t } } ) \right) \left( \prod _ { t = 1 } ^ { | J | } f _ { \theta _ { d _ { j _ { t } } } } ( \mathbf { x } _ { j _ { t } } ) \right)
+$$
+
+Let $m = M ^ { \lvert I \rvert }$ , and define the following mapping:
+
+$$
+\mu : [ M ] ^ { | I | }  [ m ] \quad , \quad \mu ( d _ { i _ { 1 } } , \ldots , d _ { i _ { | I | } } ) = 1 + \sum _ { t = 1 } ^ { | I | } ( d _ { i _ { t } } - 1 ) \cdot M ^ { | I | - t }
+$$
+
+$\mu$ is a one-to-one correspondence between the index sets $[ M ] ^ { | I | }$ and $[ m ]$ . We slightly abuse notation, and denote by $( d _ { i _ { 1 } } ( \mu ) , \ldots , d _ { i _ { | I | } } ( \mu ) )$ the tuple in $[ M ] ^ { | I | }$ that maps to $\mu \in [ m ]$ . Additionally, we denote the function $\prod _ { t = 1 } ^ { \left| I \right| } f _ { \theta _ { d _ { t } ( \mu ) } } \left( \mathbf { x } _ { i _ { t } } \right)$ , which according to fact 2 in app. A.1 belongs to $L ^ { 2 } ( ( R ^ { s } ) ^ { \left| I \right| } )$ , by $\phi _ { \mu } ( \mathbf { x } _ { i _ { 1 } } , \ldots , \mathbf { x } _ { i _ { | I | } } )$ . In the exact same manner, we let $m ^ { \prime } = M ^ { \vert J \vert }$ , and define the bijective mapping:
+
+$$
+\mu ^ { \prime } : [ M ] ^ { | J | }  [ m ^ { \prime } ] \quad , \quad \mu ^ { \prime } ( d _ { j _ { 1 } } , \ldots , d _ { j _ { | J | } } ) = 1 + \sum _ { t = 1 } ^ { | J | } ( d _ { j _ { t } } - 1 ) \cdot M ^ { | J | - t }
+$$
+
+As before, $( d _ { j 1 } ( \mu ^ { \prime } ) , \dots , d _ { j _ { | J | } } ( \mu ^ { \prime } ) )$ stands for the tuple in $[ M ] ^ { | J | }$ that maps to $\mu ^ { \prime } \in [ m ^ { \prime } ]$ , and the function $\begin{array} { r } { \prod _ { t = 1 } ^ { | J | } f _ { \theta _ { d _ { j _ { t } } ( \mu ^ { \prime } ) } } ( \mathbf { x } _ { j _ { t } } ) { \in } L ^ { 2 } ( ( R ^ { s } ) ^ { | J | } ) } \end{array}$ is denoted by $\phi _ { \mu ^ { \prime } } ^ { \prime } ( \mathbf { x } _ { j _ { 1 } } , \ldots , \mathbf { x } _ { j _ { | J | } } )$ . Now, recall the definition of matricization given in sec. 2, and consider $\mathbb { I } A ^ { y } \mathbb { I } _ { I , J }$ – the matricization of the coefficient tensor $A ^ { y }$ w.r.t. $( I , J )$ . This is a matrix of size $m$ -by- $m ^ { \prime }$ , holding $\mathcal { A } _ { d _ { 1 } . . . d _ { N } }$ in row index $\mu ( d _ { i _ { 1 } } , \ldots , d _ { i _ { | I | } } )$ and column index $\mu ^ { \prime } ( d _ { j _ { 1 } } , \dots , d _ { j _ { | J | } } )$ . Rewriting eq. 28 with the indexes $\mu$ and $\mu ^ { \prime }$ instead of $( d _ { i _ { 1 } } , \ldots , d _ { i _ { | I | } } )$ and $( d _ { j _ { 1 } } , \dotsc , d _ { j _ { | J | } } )$ , we obtain:
+
+$$
+h _ { y } \left( { \bf x } _ { 1 } , \ldots , { \bf x } _ { N } \right) = \sum _ { \mu = 1 } ^ { m } \sum _ { \mu ^ { \prime } = 1 } ^ { m ^ { \prime } } \left( \mathbb { I } A ^ { y } \mathbb { I } _ { I , J } \right) _ { \mu , \mu ^ { \prime } } \cdot \phi _ { \mu } ( { \bf x } _ { i 1 } , \ldots , { \bf x } _ { i _ { | I | } } ) \phi _ { \mu ^ { \prime } } ^ { \prime } ( { \bf x } _ { j 1 } , \ldots , { \bf x } _ { j _ { | J | } } ) \mathrm { I } .
+$$
+
+This equation has the form of eq. 22. However, for it to qualify as an orthonormal separable decomposition, the sets of functions $\{ \phi _ { 1 } , . . . , \phi _ { m } \} { \subset } L ^ { 2 } ( ( \mathbb { R } ^ { s } ) ^ { | I | } )$ and $\{ \phi _ { 1 } ^ { \prime } , . . . , \phi _ { m ^ { \prime } } ^ { \prime } \} { \subset } L ^ { 2 } ( ( \mathbb { R } ^ { s } ) ^ { | J | } )$ must be orthonormal. If the latter holds eq. 23 may be applied, giving an expression for $D ( h _ { y } ; I , J ) .$ – the normalized $L ^ { 2 }$ distance of $h _ { y }$ from the set of separable functions w.r.t. $( I , J )$ , in terms of the singular values of $\mathbb { I } ^ { \boldsymbol { A } ^ { y } } \mathbb { I } , \boldsymbol { J }$ .
+
+We now direct our attention to the special case where $f _ { \theta _ { 1 } \cdot \cdot \cdot \cdot f _ { \theta _ { M } } \in L ^ { 2 } ( \mathbb { R } ^ { s } ) - }$ the network’s representation functions, are known to be orthonormal. The general setting, in which only linear independence is known, will be treated thereafter. Orthonormality of representation functions implies that $\phi _ { 1 } \hdots \phi _ { m } { \in } L ^ { 2 } ( ( \mathbb { R } ^ { s } ) ^ { | I | } )$ are orthonormal as well:
+
+$$
+\begin{array} { r l } { \langle \phi _ { n } , \phi _ { n } \rangle } & { \frac { 1 } { ( n ) } ( \begin{array} { l } { \phi _ { n } ( \mathbf { x } _ { i _ { 1 } } , . . . , \mathbf { x } _ { i _ { 1 } / i } ) \phi _ { \theta _ { n } } ( \mathbf { x } _ { i _ { 1 } } , . . . , \mathbf { x } _ { i _ { 1 } / i } ) d \mathbf { x } _ { i _ { 1 } } \cdots d \mathbf { x } _ { i _ { 1 / i } } } \\ { \frac { 1 } { ( n ) } } \end{array} ) } \\ & { \frac { 1 } { ( n ) } ( \begin{array} { l } { \prod _ { i = 1 } ^ { [ n ] } f \phi _ { \varepsilon _ { i _ { 1 } } ( \omega ) } ( \mathbf { x } _ { i _ { 1 } } ) \prod _ { i = 1 } ^ { [ n ] } \beta _ { \phi _ { \varepsilon _ { i _ { 1 } } ( \omega ) } } ( \mathbf { x } _ { i _ { 1 } } ) d \mathbf { x } _ { i _ { 1 } } \cdots d \mathbf { x } _ { i _ { 1 / i } } } \\ { \frac { 1 } { ( n ) } } \end{array}  } \\ & { \frac { 1 } { ( n ) } \prod _ { i = 1 } ^ { [ n ] } \int \beta _ { \phi _ { \varepsilon _ { i _ { 1 } } ( \omega ) } } ( \mathbf { x } _ { i _ { 1 } } ) d \rho _ { \phi _ { \varepsilon _ { i _ { 1 } } ( \omega ) } } ( \mathbf { x } _ { i _ { 1 } } ) d \mathbf { x } _ { i _ { 1 } } } \\ & { \frac { 1 } { ( n ) } \prod _ { i = 1 } ^ { [ n ] }  f \phi _ { \varepsilon _ { i _ { 1 } } ( \omega ) } , f \phi _ { \varepsilon _ { i _ { 1 } } ( \omega ) }  } \\ & { \frac { 1 } { ( n ) } \prod _ { i = 1 } ^ { [ n ] } \{ \begin{array} { l l } { 1 } & { \alpha _ { i } , \beta _ { \phi _ { \varepsilon _ { i } } ( \omega ) } - d _ { i _ { 1 } } ( \mu ) } \\ { 0 } & { \alpha _ { i } \ln \cosh \sinh \sinh \sinh } \end{array} \} } \\ &  \frac { 1 } { ( n ) } \{ \begin{array} { l l } { 1 } & { \alpha _ { j } \leq d _ { i _ { 1 } } ( \mu ) - d _ { i _ { 1 } } ( \mu ) } \\ { 0 } &  \beta _  \phi _ { \varepsilon } \end{array} \end{array}
+$$
+
+(1) and (4) here follow from the definition of inner product in $L ^ { 2 }$ space, (2) replaces $\phi _ { \mu }$ and $\phi _ { \bar { \mu } }$ by their definitions, (3) makes use of Fubini’s theorem (see Jones (2001)), (5) relies on the (temporary) assumption that representation functions are orthonormal, (6) is a trivial step, and (7) owes to the fact that $\mu \mapsto ( d _ { i _ { 1 } } ( \mu ) , \ldots , d _ { i _ { | I | } } ( \mu ) )$ is an injective mapping. A similar sequence of steps (applied to $\langle \phi _ { \mu ^ { \prime } } ^ { \prime } , \phi _ { \bar { \mu } ^ { \prime } } ^ { \prime } \rangle $ ) shows that in addition to $\phi _ { 1 } \ldots \phi _ { m }$ , the functions $\phi _ { 1 } ^ { \prime } \ldots \phi _ { m ^ { \prime } } ^ { \prime } \in L ^ { 2 } ( ( \mathbb { R } ^ { s } ) ^ { | J | } )$ will also be orthonormal if $f _ { \boldsymbol { \theta } _ { 1 } } . . . f _ { \boldsymbol { \theta } _ { M } }$ are. We conclude that if representation functions are orthonormal, eq. 29 indeed provides an orthonormal separable decomposition of $h _ { y }$ , and the formula in eq. 23 may be applied:
+
+$$
+D ( h _ { y } ; I , J ) = \sqrt { 1 - \frac { \sigma _ { 1 } ^ { 2 } ( [ \mathscr { A } ^ { y } ] _ { I , J } ) } { \sigma _ { 1 } ^ { 2 } ( [ \mathscr { A } ^ { y } ] _ { I , J } ) + \cdots + \sigma _ { \operatorname* { m i n } \{ m , m ^ { \prime } \} } ^ { 2 } ( [ \mathscr { A } ^ { y } ] _ { I , J } ) } }
+$$
+
+where $\sigma _ { 1 } ( [ \bar { \jmath } { \cal A } _ { - } ^ { y } ] [ . , . ] ) \geq \dots \geq \sigma _ { \operatorname* { m i n } \{ m , m ^ { \prime } \} } ( [ \bar { \jmath } { \cal A } ^ { y } ] _ { I , J } ) \geq 0$ are the singular values of the coefficient tensor Jmatricization $\mathbb { I } A ^ { y } \mathbb { I } _ { I , J }$ .
+
+In sec. 5.2 we showed that the maximal separation rank realizable by a deep network is greater than or equal to $\operatorname* { m i n } \{ r _ { 0 } , M \} ^ { S }$ , where $M , r _ { 0 }$ are the number of channels in the representation and first hidden layers (respectively), and $S$ stands for the number of index quadruplets (sets of the form $\{ 4 k { - } 3 , 4 k { - } 2 , 4 k { - } 1 , 4 k \}$ for some $k \in$ $[ N / 4 ] )$ that are split by the partition $( I , J )$ . To prove this lower bound, we presented in app. A.3 a specific setting for the linear weights of the network $( \{ \mathbf { a } ^ { l , \gamma } \} _ { l , \gamma } , \mathbf { a } ^ { L , y } )$ under which $r a n k \mathbb { [ } \mathcal { A } ^ { y } ] _ { I , J } = \operatorname* { m i n } \{ r _ { 0 } , M \} ^ { S }$ . J KCareful examination of the proof shows that with this particular weight setting, not only is the rank of $\mathbb { I } A ^ { y } \mathbb { I } _ { I , J }$ equal to $\operatorname* { m i n } \{ r _ { 0 } , M \} ^ { S }$ J K, but also, all of its non-zero singular values are equal to one another. 14 This implies that $\sigma _ { 1 } ^ { 2 } ( [ \mathcal { A } ^ { y } ] _ { I , J } ) / ( \sigma _ { 1 } ^ { 2 } ( [ \mathcal { A } ^ { y } ] _ { I , J } ) + \cdot \cdot \cdot + \sigma _ { \operatorname* { m i n } \{ m , m ^ { \prime } \} } ^ { 2 } ( [ \mathcal { A } ^ { y } ] _ { I , J } ) ) = \operatorname* { m i n } \{ r _ { 0 } , M \} ^ { - S }$ , and since we currently assume that $f _ { \boldsymbol { \theta } _ { 1 } } . . . f _ { \boldsymbol { \theta } _ { M } }$ are orthonormal, eq. 30 applies and we obtain $D ( h _ { y } ; I , J ) = \sqrt { 1 - \operatorname* { m i n } \{ r _ { 0 } , M \} ^ { - S } }$ . Maximizing over all possible weight settings, we arrive at the following lower bound for the normalized $L ^ { 2 }$ distance from separable functions brought forth by a deep convolutional arithmetic circuit:
+
+$$
+\operatorname* { s u p } _ { \{ \mathbf { a } ^ { l , \gamma } \} _ { l , \gamma } , \ \mathbf { a } ^ { L , y } } D \left( h _ { y } | _ { \{ \mathbf { a } ^ { l , \gamma } \} _ { l , \gamma } , \mathbf { a } ^ { L , y } } ; I , J \right) \geq \sqrt { 1 - \frac { 1 } { \operatorname* { m i n } \{ r _ { 0 } , M \} ^ { S } } }
+$$
+
+Turning to the general case, we omit the assumption that representation functions $f _ { \theta _ { 1 } } . . . f _ { \theta _ { M } } \in L ^ { 2 } ( \mathbb { R } ^ { s } )$ are orthonormal, and merely rely on their linear independence. The latter implies that the dimension of $s p a n \{ f _ { \theta _ { 1 } } . . . f _ { \theta _ { M } } \}$ is ionepl $M$ , thus there exist orthonormal functiatrix between the bases – the matrix de the original representation functions $\varphi _ { 1 } . . . \varphi _ { M } \in L ^ { 2 } ( \mathbf { \hat { \mathbb { R } } } ^ { s } )$ p, l $F \in$ $\mathbb { R } ^ { M \times M }$ $\begin{array} { r } { \varphi _ { c } = \sum _ { d = 1 } ^ { M } F _ { c , d } \cdot f _ { \theta _ { d } } } \end{array}$ $\forall c \in [ M ]$ $f _ { \boldsymbol { \theta } _ { 1 } \cdot \cdot \cdot \cdot } f _ { \boldsymbol { \theta } _ { M } }$ $\varphi _ { 1 } . . . \varphi _ { M }$ Using the latter, the lower bound in eq. 31 applies, and there exists a setting for the linear weights of the network – $\{ \mathbf { a } ^ { l , \gamma } \} _ { l , \gamma } , \mathbf { a } ^ { L , y }$ , such that $D ( \bar { h } _ { y } ; I , \bar { J } ) \ge \sqrt { 1 - \operatorname* { m i n } \{ r _ { 0 } , M \} ^ { - S } }$ . Recalling the structure of convolutional arithmetic circuits (fig. 1(a)), one readily sees that if we return to the original representation functions $f _ { \boldsymbol { \theta } _ { 1 } } . . . f _ { \boldsymbol { \theta } _ { M } }$ , while multiplying conv weights in hidden layer 0 by $F ^ { \top }$ (i.e. mapping $\mathbf { a } ^ { 0 , \gamma } { \mapsto } F ^ { \top } \mathbf { a } ^ { 0 , \gamma } ,$ ), the overall function $h _ { y }$ remains unchanged, and in particular $D ( h _ { y } ; I , J ) \ge \sqrt { 1 - \operatorname* { m i n } \{ r _ { 0 } , M \} ^ { - S } }$ still holds. We conclude that the lower bound in eq. 31 applies, even if representation functions are not orthonormal.
+
+To summarize, we translated the lower bound from sec. 5.2 on the maximal separation rank realized by a deep convolutional arithmetic circuit, into a lower bound on the maximal normalized $L ^ { 2 }$ distance from separable functions (eq. 31). This, along with the translation of upper bounds facilitated in app. B.2, implies that the analysis carried out in the paper, which studies correlations modeled by convolutional networks through the notion of separation rank, may equivalently be framed in terms of normalized $L ^ { 2 }$ distance from separable functions. We note however that there is one particular aspect in our original analysis that does not carry through the translation. Namely, in sec. 5.1 it was shown that separation ranks realized by convolutional arithmetic circuits are maximal almost always, i.e. for all linear weight settings but a set of (Lebesgue) measure zero. Put differently, for a given partition $( I , J )$ , the maximal separation rank brought forth by a network characterizes almost all functions realized by it. An equivalent statement does not hold with the continuous measure of normalized $L ^ { 2 }$ distance from separable functions. The behavior of this measure across the hypotheses space of a network is non-trivial, and forms a subject for future research.
+
+# C IMPLEMENTATION DETAILS
+
+In this appendix we provide implementation details omitted from the description of our experiments in sec. 7. Our implementation, available online at https://github.com/HUJI-Deep/inductive-pooling, is based on the SimNets branch (Cohen et al. (2016a)) of Caffe toolbox (Jia et al. (2014)). The latter realizes convolutional arithmetic circuits in log-space for numerical stability.
+
+When training convolutional arithmetic circuits, we followed the hyper-parameter choices made by Sharir et al. (2016). In particular, our objective function was the cross-entropy loss with no $L ^ { 2 }$ regularization (i.e. with weight decay set to 0), optimized using Adam (Kingma and Ba (2014)) with step-size $\alpha = 0 . 0 0 3$ and moment decay rates $\beta _ { 1 } = \beta _ { 2 } = 0 . 9$ . 15000 iterations with batch size 64 (48 epochs) were run, with the step-size $\alpha$ decreasing by a factor of 10 after 12000 iterations (38.4 epochs). We did not use dropout (Srivastava et al. (2014)), as the limiting factor in terms of accuracies was the difficulty of fitting training data (as opposed to overfitting) – see fig. 3.
+
+For training the conventional convolutional rectifier networks, we merely switched the hyper-parameters of Adam to the recommended settings specified in Kingma and Ba (2014) $( \alpha = 0 . 0 0 1 , \beta _ { 1 } = \bar { 0 } . 9 , \bar { \beta } _ { 2 } = 0 . 9 9 9 )$ , and set weight decay to the standard value of 0.0001.
+
+# D MORPHOLOGICAL CLOSURE
+
+The synthetic dataset used in our experiments (sec. 7) consists of binary images displaying different shapes (blobs). One of the tasks facilitated by this dataset is the detection of morphologically closed blobs, i.e. of images that are relatively similar to their morphological closure. The procedure we followed for computing the morphological closure of a binary image is:
+
+1. Pad the given image with background (0 value) pixels   
+2. Morphological dilation: simultaneously turn on (set to 1) all pixels that have a (left, right, top or bottom) neighbor originally active (holding 1)   
+3. Morphological erosion: simultaneously turn off (set to 0) all pixels that have a (left, right, top or bottom) neighbor currently inactive (holding 0)   
+4. Remove pixels introduced in padding
+
+It is not difficult to see that any pixel active in the original image is necessarily active in its closure. Moreover, pixels that are originally inactive yet are surrounded by active ones will also be turned on in the closure, hence the effect of “gap filling”. Finally, we note that the particular sequence of steps described above represents the most basic form of morphological closure. The interested reader is referred to Haralick et al. (1987) for a much more comprehensive introduction.
\ No newline at end of file
diff --git a/parse/train/BkVsEMYel/BkVsEMYel_content_list.json b/parse/train/BkVsEMYel/BkVsEMYel_content_list.json
new file mode 100644
index 0000000000000000000000000000000000000000..1ca760440b18fb9ad5d63fc582f9861c8d5a34be
--- /dev/null
+++ b/parse/train/BkVsEMYel/BkVsEMYel_content_list.json
@@ -0,0 +1,3486 @@
+[
+    {
+        "type": "text",
+        "text": "INDUCTIVE BIAS OF DEEP CONVOLUTIONAL NETWORKS THROUGH POOLING GEOMETRY ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            98,
+            712,
+            147
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Nadav Cohen & Amnon Shashua {cohennadav,shashua}@cs.huji.ac.il ",
+        "bbox": [
+            183,
+            170,
+            513,
+            199
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "ABSTRACT ",
+        "text_level": 1,
+        "bbox": [
+            454,
+            236,
+            544,
+            251
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Our formal understanding of the inductive bias that drives the success of convolutional networks on computer vision tasks is limited. In particular, it is unclear what makes hypotheses spaces born from convolution and pooling operations so suitable for natural images. In this paper we study the ability of convolutional networks to model correlations among regions of their input. We theoretically analyze convolutional arithmetic circuits, and empirically validate our findings on other types of convolutional networks as well. Correlations are formalized through the notion of separation rank, which for a given partition of the input, measures how far a function is from being separable. We show that a polynomially sized deep network supports exponentially high separation ranks for certain input partitions, while being limited to polynomial separation ranks for others. The network’s pooling geometry effectively determines which input partitions are favored, thus serves as a means for controlling the inductive bias. Contiguous pooling windows as commonly employed in practice favor interleaved partitions over coarse ones, orienting the inductive bias towards the statistics of natural images. Other pooling schemes lead to different preferences, and this allows tailoring the network to data that departs from the usual domain of natural imagery. In addition to analyzing deep networks, we show that shallow ones support only linear separation ranks, and by this gain insight into the benefit of functions brought forth by depth – they are able to efficiently model strong correlation under favored partitions of the input. ",
+        "bbox": [
+            233,
+            265,
+            764,
+            556
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            580,
+            336,
+            595
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "A central factor in the application of machine learning to a given task is the inductive bias, i.e. the choice of hypotheses space from which learned functions are taken. The restriction posed by the inductive bias is necessary for practical learning, and reflects prior knowledge regarding the task at hand. Perhaps the most successful exemplar of inductive bias to date manifests itself in the use of convolutional networks (LeCun and Bengio (1995)) for computer vision tasks. These hypotheses spaces are delivering unprecedented visual recognition results (e.g. Krizhevsky et al. (2012); Szegedy et al. (2015); Simonyan and Zisserman (2014); He et al. (2015)), largely responsible for the resurgence of deep learning (LeCun et al. (2015)). Unfortunately, our formal understanding of the inductive bias behind convolutional networks is limited – the assumptions encoded into these models, which seem to form an excellent prior knowledge for imagery data, are for the most part a mystery. ",
+        "bbox": [
+            174,
+            611,
+            825,
+            763
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Existing works studying the inductive bias of deep networks (not necessarily convolutional) do so in the context of depth efficiency, essentially arguing that for a given amount of resources, more layers result in higher expressiveness. More precisely, depth efficiency refers to a situation where a function realized by a deep network of polynomial size, requires super-polynomial size in order to be realized (or approximated) by a shallower network. In recent years, a large body of research was devoted to proving existence of depth efficiency under different types of architectures (see for example Delalleau and Bengio (2011); Pascanu et al. (2013); Montufar et al. (2014); Telgarsky (2015); Eldan and Shamir (2015); Poggio et al. (2015); Mhaskar et al. (2016)). Nonetheless, despite the wide attention it is receiving, depth efficiency does not convey the complete story behind the inductive bias of deep networks. While it does suggest that depth brings forth functions that are otherwise unattainable, it does not explain why these functions are useful. Loosely speaking, the hypotheses space of a polynomially sized deep network covers a small fraction of the space of all functions. We would like to understand why this small fraction is so successful in practice. ",
+        "bbox": [
+            174,
+            771,
+            825,
+            922
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            171,
+            103,
+            821,
+            132
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "A specific family of convolutional networks gaining increased attention is that of convolutional arithmetic circuits. These models follow the standard paradigm of locality, weight sharing and pooling, yet differ from the most conventional convolutional networks in that their point-wise activations are linear, with non-linearity originating from product pooling. Recently, Cohen et al. (2016b) analyzed the depth efficiency of convolutional arithmetic circuits, showing that besides a negligible (zero measure) set, all functions realizable by a deep network require exponential size in order to be realized (or approximated) by a shallow one. This result, termed complete depth efficiency, stands in contrast to previous depth efficiency results, which merely showed existence of functions efficiently realizable by deep networks but not by shallow ones. Besides their analytic advantage, convolutional arithmetic circuits are also showing promising empirical performance. In particular, they are equivalent to SimNets – a deep learning architecture that excels in computationally constrained settings (Cohen and Shashua (2014); Cohen et al. (2016a)), and in addition, have recently been utilized for classification with missing data (Sharir et al. (2016)). Motivated by these theoretical and practical merits, we focus our analysis in this paper on convolutional arithmetic circuits, viewing them as representative of the class of convolutional networks. We empirically validate our conclusions with both convolutional arithmetic circuits and convolutional rectifier networks – convolutional networks with rectified linear (ReLU, Nair and Hinton (2010)) activation and max or average pooling. Adaptation of the formal analysis to networks of the latter type, similarly to the adaptation of the analysis in Cohen et al. (2016b) carried out by Cohen and Shashua (2016), is left for future work. ",
+        "bbox": [
+            174,
+            138,
+            825,
+            402
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Our analysis approaches the study of inductive bias from the direction of function inputs. Specifically, we study the ability of convolutional arithmetic circuits to model correlation between regions of their input. To analyze the correlations of a function, we consider different partitions of input regions into disjoint sets, and ask how far the function is from being separable w.r.t. these partitions. Distance from separability is measured through the notion of separation rank (Beylkin and Mohlenkamp (2002)), which can be viewed as a surrogate of the $L ^ { 2 }$ distance from the closest separable function. For a given function and partition of its input, high separation rank implies that the function induces strong correlation between sides of the partition, and vice versa. ",
+        "bbox": [
+            174,
+            412,
+            825,
+            523
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "We show that a deep network supports exponentially high separation ranks for certain input partitions, while being limited to polynomial or linear (in network size) separation ranks for others. The network’s pooling geometry effectively determines which input partitions are favored in terms of separation rank, i.e. which partitions enjoy the possibility of exponentially high separation rank with polynomial network size, and which require network to be exponentially large. The standard choice of square contiguous pooling windows favors interleaved (entangled) partitions over coarse ones that divide the input into large distinct areas. Other choices lead to different preferences, for example pooling windows that join together nodes with their spatial reflections lead to favoring partitions that split the input symmetrically. We conclude that in terms of modeled correlations, pooling geometry controls the inductive bias, and the particular design commonly employed in practice orients it towards the statistics of natural images (nearby pixels more correlated than ones that are far apart). Moreover, when processing data that departs from the usual domain of natural imagery, prior knowledge regarding its statistics can be used to derive respective pooling schemes, and accordingly tailor the inductive bias. ",
+        "bbox": [
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+        "type": "text",
+        "text": "With regards to depth efficiency, we show that separation ranks under favored input partitions are exponentially high for all but a negligible set of the functions realizable by a deep network. Shallow networks on the other hand, treat all partitions equally, and support only linear (in network size) separation ranks. Therefore, almost all functions that may be realized by a deep network require a replicating shallow network to have exponential size. By this we return to the complete depth efficiency result of Cohen et al. (2016b), but with an added important insight into the benefit of functions brought forth by depth – they are able to efficiently model strong correlation under favored partitions of the input. ",
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+        "text": "The remainder of the paper is organized as follows. Sec. 2 provides a brief presentation of necessary background material from the field of tensor analysis. Sec. 3 describes the convolutional arithmetic circuits we analyze, and their relation to tensor decompositions. In sec. 4 we convey the concept of separation rank, on which we base our analyses in sec. 5 and 6. The conclusions from our analyses are empirically validated in sec. 7. Finally, sec. 8 concludes. ",
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+        "type": "text",
+        "text": "2 PRELIMINARIES ",
+        "text_level": 1,
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+        "text": "The analyses carried out in this paper rely on concepts and results from the field of tensor analysis. In this section we establish the minimal background required in order to follow our arguments 1 , referring the interested reader to Hackbusch (2012) for a broad and comprehensive introduction to the field. ",
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+        "text": "The core concept in tensor analysis is a tensor, which for our purposes may simply be thought of as a multi-dimensional array. The order of a tensor is defined to be the number of indexing entries in the array, which are referred to as modes. The dimension of a tensor in a particular mode is defined as the number of values that may be taken by the index in that mode. For example, a 4-by-3 matrix is a tensor of order 2, i.e. it has two modes, with dimension 4 in mode 1 and dimension 3 in mode 2. If $\\mathcal { A }$ is a tensor of order $N$ and dimension $M _ { i }$ in each mode $i \\in [ N ] : = \\{ 1 , . . . , N \\}$ , the space of all configurations it can take is denoted, quite naturally, by $\\mathbb { R } ^ { M _ { 1 } \\times \\cdots \\times \\bar { M } _ { N } }$ . ",
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+        "type": "text",
+        "text": "A fundamental operator in tensor analysis is the tensor product, which we denote by $\\otimes$ . It is an operator that intakes two tensors $\\mathcal { A } \\in \\mathbb { R } ^ { M _ { 1 } \\times \\cdots \\times M _ { P } }$ and $B \\in \\mathbb { R } ^ { M _ { P + 1 } \\times \\cdots \\times M _ { P + Q } }$ (orders $P$ and $Q$ respectively), and returns a tensor $\\mathcal { A } \\otimes \\mathcal { B } \\in \\mathbb { R } ^ { M _ { 1 } \\times \\cdots \\times M _ { P + Q } }$ (order $P + Q )$ defined by: $( A \\otimes$ $\\mathcal { B } ) _ { d _ { 1 } . . . d _ { P + Q } } = \\mathcal { A } _ { d _ { 1 } . . . d _ { P } } \\cdot \\mathcal { B } _ { d _ { P + 1 } . . . d _ { P + Q } }$ . Notice that in the case $P = Q = 1$ , the tensor product reduces to the standard outer product between vectors, i.e. if $\\mathbf { u } \\in \\mathbb { R } ^ { M _ { 1 } }$ and $\\mathbf { v } \\in \\mathbb { R } ^ { M _ { 2 } }$ , then $\\mathbf { u } \\otimes \\mathbf { v }$ is no other than the rank-1 matrix $\\mathbf { u } \\mathbf { v } ^ { \\top } \\in \\mathbb { R } ^ { M _ { 1 } \\times M _ { 2 } }$ . ",
+        "bbox": [
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+        "type": "text",
+        "text": "We now introduce the important concept of matricization, which is essentially the rearrangement of a tensor as a matrix. Suppose $\\mathcal { A }$ is a tensor of order $N$ and dimension $M _ { i }$ in each mode $i \\in [ N ]$ , and let $( I , J )$ be a partition of $[ N ]$ , i.e. $I$ and $J$ are disjoint subsets of $[ N ]$ whose union gives $[ N ]$ . We may write $I = \\{ i _ { 1 } , \\dots , i _ { | I | } \\}$ where $i _ { 1 } < \\cdots < i _ { | I | }$ , and similarly $\\dot { J } = \\{ j _ { 1 } , \\dots , j _ { | J | } \\}$ where $j _ { 1 } <$ $\\cdots < j _ { | J | }$ . The matricization of $\\mathcal { A }$ w.r.t. the partition $( I , J )$ , denoted $\\mathbb { I } \\mathbb { A } \\mathbb { I } _ { I , J }$ , is the $\\Pi _ { t = 1 } ^ { | I | } M _ { i _ { t } }$ -by$\\textstyle \\prod _ { t = 1 } ^ { | J | } M _ { j _ { t } }$ matrix holding the entries of $\\mathcal { A }$ such that $\\mathcal { A } _ { d _ { 1 } . . . d _ { N } }$ J Kis placed in row index $\\begin{array} { r } { 1 + \\sum _ { t = 1 } ^ { | I | } ( d _ { i _ { t } } - } \\end{array}$ 1) $\\begin{array} { r } { { \\ u { 1 } } \\prod _ { t ^ { \\prime } = t + 1 } ^ { | I | } M _ { i _ { t ^ { \\prime } } } } \\end{array}$ and column index $\\begin{array} { r } { 1 + \\sum _ { t = 1 } ^ { | J | } ( d _ { j _ { t } } - 1 ) \\prod _ { t ^ { \\prime } = t + 1 } ^ { | J | } M _ { j _ { t ^ { \\prime } } } } \\end{array}$ . If $I = \\emptyset$ or $J = \\emptyset$ , then by definition $\\mathbb { I } \\mathbb { A } \\mathbb { I } _ { I , J }$ is a row or column (respectively) vector of dimension $\\textstyle \\prod _ { t = 1 } ^ { N } M _ { t }$ holding $\\mathcal { A } _ { d _ { 1 } . . . d _ { N } }$ in entry $\\begin{array} { r } { 1 + \\sum _ { t = 1 } ^ { N } ( d _ { t } - 1 ) \\prod _ { t ^ { \\prime } = t + 1 } ^ { N } M _ { t ^ { \\prime } } } \\end{array}$ . ",
+        "bbox": [
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+        "type": "text",
+        "text": "A well known matrix operator is the Kronecker product, which we denote by $\\odot$ . For two matrices $A \\ \\in \\ \\mathbb { R } ^ { M _ { 1 } \\times M _ { 2 } }$ and $\\boldsymbol { B } ^ { \\star } \\in \\mathbb { R } ^ { N _ { 1 } \\times N _ { 2 } }$ , $A { \\odot } B$ is the matrix in $\\mathbb { R } ^ { M _ { 1 } N _ { 1 } \\times M _ { 2 } N _ { 2 } }$ holding $A _ { i j } B _ { k l }$ in row index $( i - 1 ) N _ { 1 } + k$ and column index $( j - 1 ) N _ { 2 } + l$ . Let $\\mathcal { A }$ and $\\boldsymbol { B }$ be tensors of orders $P$ and $Q$ respectively, and let $( I , J )$ be a partition of $[ P + Q ]$ . The basic relation that binds together the tensor product, the matricization operator, and the Kronecker product, is: ",
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+    {
+        "type": "equation",
+        "img_path": "images/43e53bf577cfd71675370260018f8909f2a00a3610112dead3598d9fb5d3c68f.jpg",
+        "text": "$$\n[ A \\otimes B ] _ { I , J } = [ [ A ] _ { I \\cap [ P ] , J \\cap [ P ] } \\odot [ [ B ] _ { ( I - P ) \\cap [ Q ] , ( J - P ) \\cap [ Q ] }\n$$",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "where $I - P$ and $J - P$ are simply the sets obtained by subtracting $P$ from each of the elements in $I$ and $J$ respectively. In words, eq. 1 implies that the matricization of the tensor product between $\\mathcal { A }$ and $\\boldsymbol { B }$ w.r.t. the partition $( I , J )$ of $[ P ^ { - } + Q ]$ , is equal to the Kronecker product between two matricizations: that of $\\mathcal { A }$ w.r.t. the partition of $[ P ]$ induced by the lower values of $( I , J )$ , and that of $\\boldsymbol { B }$ w.r.t. the partition of $[ Q ]$ induced by the higher values of $( I , J )$ . ",
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+        "type": "text",
+        "text": "3 CONVOLUTIONAL ARITHMETIC CIRCUITS ",
+        "text_level": 1,
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+        "text": "The convolutional arithmetic circuit architecture on which we focus in this paper is the one considered in Cohen et al. (2016b), portrayed in fig. 1(a). Instances processed by a network are represented as $N$ -tuples of $s$ -dimensional vectors. They are generally thought of as images, with the $s$ -dimensional vectors corresponding to local patches. For example, instances could be 32-by-32 RGB images, with local patches being $5 \\times 5$ regions crossing the three color bands. In this case, assuming a patch is taken around every pixel in an image (boundaries padded), we have $N = 1 0 2 4$ and $s \\ = \\ 7 5$ . Throughout the paper, we denote a general instance by $X = ( \\mathbf { x } _ { 1 } , \\ldots , \\mathbf { x } _ { N } )$ , with $\\mathbf { x } _ { 1 } \\ldots \\mathbf { x } _ { N } \\in \\mathbb { R } ^ { s }$ standing for its patches. ",
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+    {
+        "type": "image",
+        "img_path": "images/f82db9947b5d7317663714f7caba841ef01195b93260f3948f8fb4026e42f1e5.jpg",
+        "image_caption": [
+            "Figure 1: Best viewed in color. (a) Convolutional arithmetic circuit architecture analyzed in this paper (see description in sec. 3). $( b )$ Shallow network with global pooling in its single hidden layer. $( c )$ Illustration of input patch ordering for deep network with $2 \\times 2$ pooling windows, along with patterns induced by the partitions $( I ^ { o d d } , J ^ { e v e n } ) ^ { { \\bf \\Phi } }$ and $( I ^ { l o w } , J ^ { h i g h } )$ (eq. 8 and 9 respectively). "
+        ],
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+        "type": "text",
+        "text": "The first layer in a network is referred to as representation. It consists of applying $M$ representation functions $f _ { \\theta _ { 1 } } \\cdot \\cdot \\cdot f _ { \\theta _ { M } } : \\mathbb { R } ^ { s } \\to \\mathbb { R }$ to all patches, thereby creating $M$ feature maps. In the case where representation functions are chosen as $f _ { \\boldsymbol { \\theta } _ { d } } ( \\mathbf { x } ) = \\mathbf { \\bar { \\sigma } } \\sigma ( \\mathbf { w } _ { d } ^ { \\top } \\mathbf { x } + b _ { d } )$ , with parameters $\\mathbf { \\theta } _ { d } = ( \\mathbf { w } _ { d } , b _ { d } ) \\in \\mathbf { \\bar { \\mathbb { R } } } ^ { s } \\times \\mathbb { R }$ and some point-wise activation $\\sigma ( \\cdot )$ , the representation layer reduces to a standard convolutional layer. More elaborate settings are also possible, for example modeling the representation as a cascade of convolutional layers with pooling in-between. Following the representation, a network includes $L$ hidden layers indexed by $l = 0 . . . L - 1$ . Each hidden layer $l$ begins with a $1 \\times 1$ conv operator, which is simply a three-dimensional convolution with $r _ { l }$ channels and filters of spatial dimensions 1-by-1. 2 This is followed by spatial pooling, that decimates feature maps by taking products of non-overlapping two-dimensional windows that cover the spatial extent. The last of the $L$ hidden layers $( l = L - 1 )$ ) reduces feature maps to singletons (its pooling operator is global), creating a vector of dimension $r _ { L - 1 }$ . This vector is mapped into $Y$ network outputs through a final dense linear layer. ",
+        "bbox": [
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+        "type": "text",
+        "text": "Altogether, the architectural parameters of a network are the type of representation functions $( f _ { \\theta _ { d } } )$ , the pooling window shapes and sizes (which in turn determine the number of hidden layers $L$ ), and the number of channels in each layer ( $M$ for representation, $r _ { 0 } . . . r _ { L - 1 }$ for hidden layers, $Y$ for output). Given these architectural parameters, the learnable parameters of a network are the representation weights $\\theta _ { d }$ for channel $d$ ), the conv weights ( $\\mathbf { \\bar { a } } ^ { l , \\gamma }$ for channel $\\gamma$ of hidden layer $l$ ), and the output weights $\\scriptstyle ( \\mathbf { a } ^ { L , y }$ for output node $y$ ). ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "For a particular setting of weights, every node (neuron) in a given network realizes a function from $( \\mathbf { \\bar { \\mathbb { R } } } ^ { s } ) ^ { N }$ to $\\mathbb { R }$ . The receptive field of a node refers to the indexes of input patches on which its function may depend. For example, the receptive field of node $j$ in channel $\\gamma$ of conv operator at hidden layer 0 is $\\{ j \\}$ , and that of an output node is $[ N ]$ , corresponding to the entire input. Denote by $h _ { ( l , \\gamma , j ) }$ the function realized by node $j$ of channel $\\gamma$ in conv operator at hidden layer $l$ , and let $I ^ { ( l , \\gamma , j ) } \\subset [ N ]$ be its receptive field. By the structure of the network it is evident that $I ^ { ( l , \\gamma , j ) }$ does not depend on $\\gamma .$ , so we may write $I ^ { ( l , j ) }$ instead. Moreover, assuming pooling windows are uniform across channels (as customary with convolutional networks), and taking into account the fact that they do not overlap, we conclude that $I ^ { ( l , j _ { 1 } ) }$ and $I ^ { ( l , j _ { 2 } ) }$ are necessarily disjoias $j _ { 1 } \\neq j _ { 2 }$ $l = 0 . . . L - 1$ ows tha, where $h _ { ( l , \\gamma , j ) }$ be expressedstands for the $\\begin{array} { r } { h _ { ( l , \\gamma , j ) } ( \\mathbf { x } _ { i _ { 1 } } , \\ldots , \\mathbf { x } _ { i _ { T } } ) = \\sum _ { d _ { 1 } \\ldots d _ { T } = 1 } ^ { M } { \\cal A } _ { d _ { 1 } \\ldots d _ { T } } ^ { ( l , \\gamma , j ) } \\prod _ { t = 1 } ^ { T } f _ { \\theta _ { d _ { t } } } ( \\mathbf { x } _ { i _ { t } } ) } \\end{array}$ $\\{ i _ { 1 } , \\dots , i _ { T } \\}$ receptive field $I ^ { ( l , j ) }$ , and $\\mathcal { A } ^ { ( l , \\gamma , j ) }$ is a tensor of order $T = | I ^ { ( l , j ) } |$ and dimension $M$ with entries given by polynomials in the network’s conv weights $\\{ \\mathbf { a } ^ { l , \\gamma } \\} _ { l , \\gamma }$ . Taking the induction one step further (from last hidden layer to network output), we obtain the following expression for functions realized by network outputs: ",
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+        "text": "",
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+        "img_path": "images/27fd262e1c7cfdb6957059dfbb318b38f73dcbc8fc4ce9a86ef0ea26187e17d0.jpg",
+        "text": "$$\nh _ { y } \\left( \\mathbf { x } _ { 1 } , \\ldots , \\mathbf { x } _ { N } \\right) = \\sum _ { d _ { 1 } \\ldots d _ { N } = 1 } ^ { M } { \\mathcal { A } } _ { d _ { 1 } \\ldots d _ { N } } ^ { y } \\prod _ { i = 1 } ^ { N } f _ { \\theta _ { d _ { i } } } ( \\mathbf { x } _ { i } )\n$$",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "$y \\in [ Y ]$ here is an output node index, and $h _ { y }$ is the function realized by that node. $\\mathcal { A } ^ { y }$ is a tensor of order $N$ and dimension $M$ in each mode, with entries given by polynomials in the network’s conv weights $\\{ \\mathbf { a } ^ { l , \\gamma } \\} _ { l , \\gamma }$ and output weights $\\mathbf { a } ^ { L , y }$ . Hereafter, terms such as function realized by a network or coefficient tensor realized by a network, are to be understood as referring to $h _ { y }$ or $\\mathcal { A } ^ { y }$ respectively. Next, we present explicit expressions for $\\mathcal { A } ^ { y }$ under two canonical networks – deep and shallow. ",
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+        "type": "text",
+        "text": "Deep network. Consider a network as in fig. 1(a), with pooling windows set to cover four entries each, resulting in $L = \\log _ { 4 } N$ hidden layers. The linear weights of such a network are $\\{ \\mathbf { a } ^ { 0 , \\gamma } \\in$ $\\mathbb { R } ^ { M } \\} _ { \\gamma \\in [ r _ { 0 } ] }$ for conv operator in hidden layer 0, $\\{ \\mathbf { a } ^ { l , \\gamma } \\in \\mathbb { R } ^ { r _ { l - 1 } } \\} _ { \\gamma \\in [ r _ { l } ] }$ for conv operator in hidden layer $l = 1 . . . L - 1$ , and $\\{ \\mathbf { a } ^ { L , y } \\in \\mathbb { R } ^ { r _ { L - 1 } } \\} _ { y \\in [ Y ] }$ for dense output operator. They determine the coefficient tensor $\\mathcal { A } ^ { y }$ (eq. 2) through the following recursive decomposition: ",
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+        "img_path": "images/a4dbaf5fb24977ad300660dc058e8eed6d61ae4f719219f99a4ba92ad87e0301.jpg",
+        "text": "$$\n\\begin{array} { r l r l } { \\underbrace { \\phi ^ { 1 , \\gamma } } _ { \\mathrm { o r d e r } 4 } } & { = } & { \\sum _ { \\alpha = 1 } ^ { r _ { 0 } } a _ { \\alpha } ^ { 1 , \\gamma } \\cdot \\otimes ^ { 4 } \\mathbf { a } ^ { 0 , \\alpha } } & & { , \\gamma \\in [ r _ { 1 } ] } \\\\ { \\mathrm { ~ } } & { \\dots } & & { } \\\\ { \\underbrace { \\phi ^ { l , \\gamma } } _ { \\mathrm { o r d e r } 4 ^ { l } } } & { = } & { \\sum _ { \\alpha = 1 } ^ { r _ { l - 1 } } a _ { \\alpha } ^ { l , \\gamma } \\cdot \\otimes ^ { 4 } \\phi ^ { l - 1 , \\alpha } } & & { , l \\in \\{ 2 , \\dots L - 1 \\} , \\gamma \\in [ r _ { l } ] } \\\\ & { \\dots } & \\\\ { \\underbrace { \\mathcal { A } ^ { y } } _ { \\mathrm { o r d e r } 4 ^ { L } } } & { = } & { \\sum _ { \\alpha = 1 } ^ { r _ { L - 1 } } a _ { \\alpha } ^ { L , y } \\cdot \\otimes ^ { 4 } \\phi ^ { L - 1 , \\alpha } } \\end{array}\n$$",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "$a _ { \\alpha } ^ { l , \\gamma }$ and $a _ { \\alpha } ^ { L , y }$ here are scalars representing entry $\\alpha$ in the vectors $\\mathbf { a } ^ { l , \\gamma }$ and $\\mathbf { a } ^ { L , y }$ respectively, and the symbol $\\otimes$ with a superscript stands for a repeated tensor product, e.g. $\\otimes ^ { 4 } \\mathbf { a } ^ { 0 , \\alpha } : = \\mathbf { a } ^ { 0 , \\alpha } \\otimes \\mathbf { a } ^ { 0 , \\bar { \\alpha } } \\otimes \\mathbf { a } ^ { 0 , \\alpha } \\otimes$ $\\mathbf { a } ^ { 0 , \\alpha }$ . To verify that under pooling windows of size four $\\mathcal { A } ^ { y }$ is indeed given by eq. 3, simply plug the rows of the decomposition into eq. 2, starting from bottom and continuing upwards. For context, eq. 3 describes what is known as a hierarchical tensor decomposition (see chapter 11 in Hackbusch (2012)), with underlying tree over modes being a full quad-tree (corresponding to the fact that the network’s pooling windows cover four entries each). ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Shallow network. The second network we pay special attention to is shallow, comprising a single hidden layer with global pooling – see illustration in fig. 1(b). The linear weights of such a network are $\\{ \\mathbf { a } ^ { 0 , \\gamma } \\in \\mathbb { R } ^ { M } \\} _ { \\gamma \\in [ r _ { 0 } ] }$ for hidden conv operator and $\\{ \\mathbf { a } ^ { 1 , y } \\in \\mathbb { R } ^ { r _ { 0 } } \\} _ { y \\in [ Y ] }$ for dense output operator. They determine the coefficient tensor $\\mathcal { A } ^ { y }$ (eq. 2) as follows: ",
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+        "type": "equation",
+        "img_path": "images/ef7dd73a2a2cf55d6ba2e05f73b4ce7b34092b42b81030cf755ab4bfaeeb7cd3.jpg",
+        "text": "$$\n\\mathcal { A } ^ { y } = \\sum _ { \\gamma = 1 } ^ { r _ { 0 } } a _ { \\gamma } ^ { 1 , y } \\cdot \\otimes ^ { N } \\mathbf { a } ^ { 0 , \\gamma }\n$$",
+        "text_format": "latex",
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+        "page_idx": 4
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+    {
+        "type": "text",
+        "text": "where $a _ { \\gamma } ^ { 1 , y }$ stands for entry $\\gamma$ of $\\mathbf { a } ^ { 1 , y }$ , and again, the symbol $\\otimes$ with a superscript represents a repeated tensor product. The tensor decomposition in eq. 4 is an instance of the classic CP decomposition, also known as rank-1 decomposition (see Kolda and Bader (2009) for a historic survey). ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "To conclude this section, we relate the background material above, as well as our contribution described in the upcoming sections, to the work of Cohen et al. (2016b). The latter shows that with arbitrary coefficient tensors $\\mathcal { A } ^ { y }$ , functions $h _ { y }$ as in eq. 2 form a universal hypotheses space. It is then shown that convolutional arithmetic circuits as in fig. 1(a) realize such functions by applying tensor decompositions to $\\mathcal { A } ^ { y }$ , with the type of decomposition determined by the structure of a network (number of layers, number of channels in each layer etc.). The deep network (fig. 1(a) with size-4 pooling windows and $L = \\log _ { 4 } N$ hidden layers) and the shallow network (fig. 1(b)) presented hereinabove are two special cases, whose corresponding tensor decompositions are given in eq. 3 and 4 respectively. The central result in Cohen et al. (2016b) relates to inductive bias through the notion of depth efficiency – it is shown that in the parameter space of a deep network, all weight settings but a set of (Lebesgue) measure zero give rise to functions that can only be realized (or approximated) by a shallow network if the latter has exponential size. This result does not relate to the characteristics of instances $X = ( \\mathbf { x } _ { 1 } , \\ldots , \\mathbf { x } _ { N } )$ , it only treats the ability of shallow networks to replicate functions realized by deep networks. ",
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+    {
+        "type": "text",
+        "text": "In this paper we draw a line connecting the inductive bias to the nature of $X$ , by studying the relation between a network’s architecture and its ability to model correlation among patches $\\mathbf { x } _ { i }$ . Specifically, in sec. 4 we consider partitions $( I , J )$ of $[ N ]$ $\\mathbf { \\Psi } _ { I \\cup J } = \\left[ N \\right]$ , where $\\left\\lfloor \\cdot \\right\\rfloor$ stands for disjoint union), and present the notion of separation rank as a measure of the correlation modeled between the patches indexed by $I$ and those indexed by $J$ . In sec. 5.1 the separation rank of a network’s function $h _ { y }$ w.r.t. a partition $( I , J )$ is proven to be equal to the rank of $\\mathbb { I } \\boldsymbol { \\mathcal { A } } ^ { y } \\mathbb { I } _ { I , J }$ – the matricization of the coefficient tensor $\\mathcal { A } ^ { y }$ w.r.t. $( I , J )$ J K. Sec. 5.2 derives lower and upper bounds on this rank for a deep network, showing that it supports exponential separation ranks with polynomial size for certain partitions, whereas for others it is required to be exponentially large. Subsequently, sec. 5.3 establishes an upper bound on $r a n k \\ [ \\mathcal { A } ^ { y } ] ] _ { I , J }$ for shallow networks, implying that these J Kmust be exponentially large in order to model exponential separation rank under any partition, and thus cannot efficiently replicate a deep network’s correlations. Our analysis concludes in sec. 6, where we discuss the pooling geometry of a deep network as a means for controlling the inductive bias by determining a correspondence between partitions $( I , J )$ and spatial partitions of the input. Finally, we demonstrate experimentally in sec. 7 how different pooling geometries lead to superior performance in different tasks. Our experiments include not only convolutional arithmetic circuits, but also convolutional rectifier networks, i.e. convolutional networks with ReLU activation and max or average pooling. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4 SEPARATION RANK ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            549,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "In this section we define the concept of separation rank for functions realized by convolutional arithmetic circuits (sec. 3), i.e. real functions that take as input $X = ( \\mathbf { x } _ { 1 } , \\ldots , \\mathbf { x } _ { N } ) { \\overset { } { \\in } } ( \\mathbb { R } ^ { s } ) ^ { N }$ . The separation rank serves as a measure of the correlations such functions induce between different sets of input patches, i.e. different subsets of the variable set $\\left\\{ \\mathbf { x } _ { 1 } , \\dotsc , \\mathbf { x } _ { N } \\right\\}$ . ",
+        "bbox": [
+            174,
+            582,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Let $( I , J )$ be a partition of input indexes, i.e. $I$ and $J$ are disjoint subsets of $[ N ]$ whose union gives $[ N ]$ . We may write $I = \\{ i _ { 1 } , \\ldots , i _ { | I | } \\}$ where $i _ { 1 } < \\cdots < i _ { | I | }$ , and similarly $\\bar { J } = \\{ j _ { 1 } , \\dotsc , j _ { | J | } \\}$ where $j _ { 1 } < \\cdots < j _ { | J | }$ . For a function $h : ( \\mathbb { R } ^ { s } ) ^ { N } \\to \\mathbb { R }$ , the separation rank w.r.t. the partition $( I , J )$ is defined as follows: 3 ",
+        "bbox": [
+            173,
+            643,
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+            705
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "img_path": "images/7949167671f031914715eb4034967e262e857d51d1a6c619824570d08fd395c8.jpg",
+        "text": "$$\n\\begin{array} { c } { { s e p ( h ; I , J ) : = \\operatorname* { m i n } \\Big \\{ R \\in { \\mathbb { N } \\cup \\{ 0 \\} : \\exists g _ { 1 } . . . g _ { R } : ( { \\mathbb { R } ^ { s } } ) ^ { | I | }  { \\mathbb { R } } , g _ { 1 } ^ { \\prime } . . . g _ { R } ^ { \\prime } : ( { \\mathbb { R } ^ { s } } ) ^ { | J | }  { \\mathbb { R } } \\ s . t . } } } \\\\ { { h ( { \\mathbf x } _ { 1 } , . . . \\ , { \\mathbf x } _ { N } ) = \\sum _ { \\nu = 1 } ^ { R } g _ { \\nu } ( { \\mathbf x } _ { i _ { 1 } } , . . . , { \\mathbf x } _ { i _ { | I | } } ) g _ { \\nu } ^ { \\prime } ( { \\mathbf x } _ { j _ { 1 } } , . . . , { \\mathbf x } _ { j _ { | J | } } ) \\Big \\} } } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            171,
+            710,
+            795,
+            773
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "In words, it is the minimal number of summands that together give $h$ , where each summand is separable w.r.t. $( I , J )$ , i.e. is equal to a product of two functions – one that intakes only patches indexed by $I$ , and another that intakes only patches indexed by $J$ . One may wonder if it is at all possible to express $h$ through such summands, i.e. if the separation rank of $h$ is finite. From the theory of tensor products between $L ^ { 2 }$ spaces (see Hackbusch (2012) for a comprehensive coverage), we know that any $h { \\in } L ^ { 2 } ( ( \\mathbb { R } ^ { s } ) ^ { N } )$ , i.e. any $h$ that is measurable and square-integrable, may be approximated arbitrarily well by summations of the form $\\begin{array} { r } { \\sum _ { \\nu = 1 } ^ { R } g _ { \\nu } ( \\mathbf { x } _ { i _ { 1 } } , \\dots , \\mathbf { x } _ { i _ { | I | } } ) g _ { \\nu } ^ { \\prime } ( \\mathbf { x } _ { j _ { 1 } } , \\dots , \\mathbf { x } _ { j _ { | J | } } ) } \\end{array}$ . Exact realization however is only guaranteed at the limit $R \\to \\infty$ , thus in general the separation rank of $h$ need not be finite. Nonetheless, as we show in sec. 5, for the class of functions we are interested in, namely functions realizable by convolutional arithmetic circuits, separation ranks are always finite. ",
+        "bbox": [
+            173,
+            780,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            173,
+            103,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "The concept of separation rank was introduced in Beylkin and Mohlenkamp (2002) for numerical treatment of high-dimensional functions, and has since been employed for various applications, e.g. quantum chemistry (Harrison et al. (2003)), particle engineering (Hackbusch (2006)) and machine learning (Beylkin et al. (2009)). If the separation rank of a function w.r.t. a partition of its input is equal to 1, the function is separable, meaning it does not model any interaction between the sets of variables. Specifically, if $s e p ( h ; I , J ) ~ = ~ 1$ then there exist $g : ( \\mathbb { R } ^ { s } ) ^ { | I | } \\  \\ \\mathbb { R }$ and $g ^ { \\prime } : ( \\mathbb { R } ^ { s } ) ^ { | J | } \\to \\mathbb { R }$ such that $h ( { \\bf x } _ { 1 } , \\ldots , { \\bf x } _ { N } ) = g ( { \\bf x } _ { i _ { 1 } } , \\ldots , { \\bf x } _ { i _ { | I | } } ) g ^ { \\prime } ( { \\bf x } _ { j _ { 1 } } , \\ldots , { \\bf x } _ { j _ { | J | } } )$ , and the function $h$ cannot take into account consistency between the values of $\\{ \\mathbf { x } _ { i _ { 1 } } , \\dotsc , \\mathbf { x } _ { i _ { | I | } } \\}$ and those of $\\{ \\mathbf { x } _ { j _ { 1 } } , \\dotsc , \\mathbf { x } _ { j _ { | J | } } \\}$ . In a statistical setting, if $h$ is a probability density function, this would mean that $\\{ \\mathbf { x } _ { i _ { 1 } } , \\dotsc , \\mathbf { x } _ { i _ { | I | } } \\}$ and $\\{ \\mathbf { x } _ { j _ { 1 } } , \\dotsc , \\mathbf { x } _ { j _ { | J | } } \\}$ are statistically independent. The higher $s e p  ( h ; I , J )$ is, the farther $h$ is from this situation, i.e. the more it models dependency between $\\{ \\mathbf { x } _ { i _ { 1 } } , \\dotsc , \\mathbf { x } _ { i _ { | I | } } \\}$ and $\\left\\{ \\mathbf { x } _ { j _ { \\frac { 1 } { 2 } } } , \\dotsc , \\mathbf { x } _ { j _ { | J | } } \\right\\}$ , or equivalently, the stronger the correlation it induces between the patches indexed by $I$ and those indexed by $J$ . ",
+        "bbox": [
+            173,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "The interpretation of separation rank as a measure of deviation from separability is formalized in app. B, where it is shown that $s e p  ( h ; I , J )$ is closely related to the $L ^ { 2 }$ distance of $h$ from the set of separable functions w.r.t. $( I , J )$ . Specifically, we define $D ( h ; I , J )$ as the latter distance divided by the $L ^ { 2 }$ norm of $h ^ { \\ 4 }$ , and show that $s e p  ( h ; I , J )$ provides an upper bound on $D ( h ; I , J )$ . While it is not possible to lay out a general lower bound on $D ( h ; I , J )$ in terms of $s e p  ( h ; I , J )$ , we show that the specific lower bounds on $s e p  ( h ; I , J )$ underlying our analyses can be translated into lower bounds on $D ( h ; I , J )$ . This implies that our results, facilitated by upper and lower bounds on separation ranks of convolutional arithmetic circuits, may equivalently be framed in terms of $L ^ { 2 }$ distances from separable functions. ",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "5 CORRELATION ANALYSIS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            488,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "In this section we analyze convolutional arithmetic circuits (sec. 3) in terms of the correlations they can model between sides of different input partitions, i.e. in terms of the separation ranks (sec. 4) they support under different partitions $( I , J )$ of $[ N ]$ . We begin in sec. 5.1, establishing a correspondence between separation ranks and coefficient tensor matricization ranks. This correspondence is then used in sec. 5.2 and 5.3 to analyze the deep and shallow networks (respectively) presented in sec. 3. We note that we focus on these particular networks merely for simplicity of presentation – the analysis can easily be adapted to account for alternative networks with different depths and pooling schemes. ",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "5.1 FROM SEPARATION RANK TO MATRICIZATION RANK ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            654,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Let $h _ { y }$ be a function realized by a convolutional arithmetic circuit, with corresponding coefficient tensor $\\mathcal { A } ^ { y }$ (eq. 2). Denote by $( I , J )$ an arbitrary partition of $[ N ]$ , i.e. $I { \\uplus } J = { \\bf \\bar { \\rho } } [ N ]$ . We are interested in studying $s e p ( h _ { y } ; I , J ) \\ .$ – the separation rank of $h _ { y }$ w.r.t. $( I , J )$ (eq. 5). As claim 1 below states, assuming representation functions $\\{ f _ { \\theta _ { d } } \\} _ { d \\in [ M ] }$ are linearly independent (if they are not, we drop dependent functions and modify $\\mathcal { A } ^ { y }$ accordingly 5 ), this separation rank is equal to the rank of $\\mathbb { [ } \\boldsymbol { A } ^ { y } \\mathbb { ] } _ { I , J } ^ { - }$ – the matricization of the coefficient tensor $\\mathcal { A } ^ { y }$ w.r.t. the partition $( I , J )$ . Our problem J Kthus translates to studying ranks of matricized coefficient tensors. ",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Claim 1. Let $h _ { y }$ be a function realized by a convolutional arithmetic circuit (fig. 1(a)), with corresponding coefficient tensor $\\mathcal { A } ^ { y }$ (eq. 2). Assume that the network’s representation functions $f _ { \\theta _ { d } }$ are linearly independent, and that they, as well as the functions $g _ { \\nu } , g _ { \\nu } ^ { \\prime }$ in the definition of separation rank (eq. 5), are measurable and square-integrable. 6 Then, for any partition $( I , J )$ of $[ N ]$ , it holds that $s e p ( h _ { y } ; I , J ) = r a n k \\big [ \\boldsymbol { \\mathcal { A } } ^ { y } \\big ] | _ { I , J }$ . ",
+        "bbox": [
+            174,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Proof. See app. A.1. ",
+        "bbox": [
+            174,
+            147,
+            310,
+            161
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "As the linear weights of a network vary, so do the coefficient tensors $( \\mathcal { A } ^ { y } )$ it gives rise to. Accordingly, for a particular partition $( I , J )$ , a network does not correspond to a single value of $r a n k \\ [ \\boldsymbol { \\mathcal { A } } ^ { y } ] ] _ { I , J }$ , but rather supports a range of values. We analyze this range by quantifying its maxiJ Kmum, which reflects the strongest correlation that the network can model between the input patches indexed by $I$ and those indexed by $J$ . One may wonder if the maximal value of $r a n k \\ [ \\mathcal { A } ^ { y } ] ] _ { I , J }$ is the appropriate statistic to measure, as a-priori, it may be that $r a n k \\ [ \\mathcal { A } ^ { y } ] ] _ { I , J }$ J Kis maximal for very few of J Kthe network’s weight settings, and much lower for all the rest. Apparently, as claim 2 below states, this is not the case, and in fact ra $n k \\mathbb { I } A ^ { y } \\mathbb { I } _ { I , J }$ is maximal under almost all of the network’s weight settings. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Claim 2. Consider a convolutional arithmetic circuit (fig. $I ( a ) ,$ ) with corresponding coefficient tensor $\\mathcal { A } ^ { y }$ (eq. 2). $\\mathcal { A } ^ { y }$ depends on the network’s linear weights – $\\{ \\mathbf { a } ^ { l , \\gamma } \\} _ { l , \\gamma }$ and $\\mathbf { a } ^ { L , y }$ , thus for a given partition $( I , J )$ of $[ N ]$ , rank $\\mathbb { I } \\boldsymbol { \\mathcal { A } } ^ { y } \\mathbb { I } _ { I , J }$ is a function of these weights. This function obtains its maximum almost everywhere (w.r.t. Lebesgue measure). ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Proof. See app. A.2. ",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "5.2 DEEP NETWORK ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "In this subsection we study correlations modeled by the deep network presented in sec. 3 (fig. 1(a) with size-4 pooling windows and $L = \\log _ { 4 } N$ hidden layers). In accordance with sec. 5.1, we do so by characterizing the maximal ranks of coefficient tensor matricizations under different partitions. ",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Recall from eq. 3 the hierarchical decomposition expressing a coefficient tensor $\\mathcal { A } ^ { y }$ realized by the deep network. We are interested in matricizations of this tensor under different partitions of $[ N ]$ . Let $( I , J )$ be an arbitrary partition, i.e. $I { \\uplus } J = [ N ]$ . Matricizing the last level of eq. 3 w.r.t. $( I , J )$ , while applying the relation in eq. 1, gives: ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "equation",
+        "img_path": "images/4be574003a6ad98e919e47c9bab52edce87f563d77907b3cc01970c64872e37c.jpg",
+        "text": "$$\n\\begin{array} { r c l } { { [ [ } A ^ { y } ] ] _ { I , J } }  & { { = } } & { { \\sum _ { \\alpha = 1 } ^ { r _ { L - 1 } } a _ { \\alpha } ^ { L , y } \\cdot \\left[ [ \\phi ^ { L - 1 , \\alpha } \\otimes \\phi ^ { L - 1 , \\alpha } \\otimes \\phi ^ { L - 1 , \\alpha } \\otimes \\phi ^ { L - 1 , \\alpha } ] _ { I , J } \\right. } } \\\\ { { } } & { { = } } & { { \\sum _ { \\alpha = 1 } ^ { r _ { L - 1 } } a _ { \\alpha } ^ { L , y } \\cdot [ \\phi ^ { L - 1 , \\alpha } \\otimes \\phi ^ { L - 1 , \\alpha } ] _ { I \\cap [ 2 \\cdot 4 ^ { L - 1 } ] , J \\cap [ 2 \\cdot 4 ^ { L - 1 } ] } } } \\\\ { { } } & { { } } & { { \\odot \\left[ \\phi ^ { L - 1 , \\alpha } \\otimes \\phi ^ { L - 1 , \\alpha } \\right] _ { ( I - 2 \\cdot 4 ^ { L - 1 } ) \\cap [ 2 \\cdot 4 ^ { L - 1 } ] , ( J - 2 \\cdot 4 ^ { L - 1 } ) \\cap [ 2 \\cdot 4 ^ { L - 1 } ] } } } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            194,
+            542,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Applying eq. 1 again, this time to matricizations of the tensor $\\phi ^ { L - 1 , \\alpha } \\otimes \\phi ^ { L - 1 , \\alpha }$ , we obtain: ",
+        "bbox": [
+            171,
+            635,
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+        "page_idx": 7
+    },
+    {
+        "type": "equation",
+        "img_path": "images/d09f4b1ec6dcfc05e65fb2e50765c454b87cf2520daebcf29689dc263692abd5.jpg",
+        "text": "$$\n\\begin{array} { l l l l } { { [ \\mathcal { A } ^ { y } ] _ { I , J } } } & { { = } } & { { \\sum _ { \\alpha = 1 } ^ { r _ { L - 1 } } a _ { \\alpha } ^ { L , y } \\cdot \\left[ \\left. \\phi ^ { L - 1 , \\alpha } \\right. _ { I \\cap [ 4 ^ { L - 1 } ] , J \\cap [ 4 ^ { L - 1 } ] } \\right. } } \\\\ { { } } & { { } } & { { \\odot \\left[ \\phi ^ { L - 1 , \\alpha } \\right] _ { \\left( I - 4 ^ { L - 1 } \\right) \\cap [ 4 ^ { L - 1 } ] , \\left( J - 4 ^ { L - 1 } \\right) \\cap [ 4 ^ { L - 1 } ] } } } \\\\ { { } } & { { } } & { { \\odot \\left[ \\phi ^ { L - 1 , \\alpha } \\right] _ { \\left( I - 2 \\cdot 4 ^ { L - 1 } \\right) \\cap [ 4 ^ { L - 1 } ] , \\left( J - 2 \\cdot 4 ^ { L - 1 } \\right) \\cap [ 4 ^ { L - 1 } ] } } } \\\\ { { } } & { { } } & { { \\odot \\left[ \\phi ^ { L - 1 , \\alpha } \\right] _ { \\left( I - 3 \\cdot 4 ^ { L - 1 } \\right) \\cap [ 4 ^ { L - 1 } ] , \\left( J - 3 \\cdot 4 ^ { L - 1 } \\right) \\cap [ 4 ^ { L - 1 } ] } } } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
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+            654,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "For every $k \\in [ 4 ]$ define $I _ { L - 1 , k } : = ( I - ( k - 1 ) \\cdot 4 ^ { L - 1 } ) \\cap [ 4 ^ { L - 1 } ]$ and $J _ { L - 1 , k } : = ( J - ( k - 1 ) \\cdot 4 ^ { L - 1 } ) \\cap$ $[ 4 ^ { L - 1 } ]$ . In words, $\\left( I _ { L - 1 , k } , J _ { L - 1 , k } \\right)$ represents the partition induced by $( I , J )$ on the $k$ ’th quadrant of $[ N ]$ , i.e. on the $k$ ’th size- $\\cdot 4 ^ { L - 1 }$ group of input patches. We now have the following matricized version of the last level in eq. 3: ",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "equation",
+        "img_path": "images/5affee9e89e1fc029d7f5f877d41a4a5d5603ca4a939626188338c9475bbaff1.jpg",
+        "text": "$$\n\\begin{array} { r } { \\mathbb { [ } A ^ { y } ] _ { I , J } = \\sum _ { \\alpha = 1 } ^ { r _ { L - 1 } } a _ { \\alpha } ^ { L , y } \\cdot \\underset { t = 1 } { \\overset { 4 } { \\odot } } \\mathbb { [ } \\phi ^ { L - 1 , \\alpha } \\mathbb { ] } _ { I _ { L - 1 , t } , J _ { L - 1 , t } } } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            328,
+            819,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "where the symbol $\\odot$ with a running index stands for an iterative Kronecker product. To derive analogous matricized versions for the upper levels of eq. 3, we define for $l \\in \\{ 0 . . . L - 1 \\} , k \\in$ $[ N / 4 ^ { \\widetilde { l } } ]$ : ",
+        "bbox": [
+            174,
+            103,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "equation",
+        "img_path": "images/92e25f79eea6cf2e224252796edfd765019ebc251d18637b4feb01d57b4dc442.jpg",
+        "text": "$$\nI _ { l , k } : = ( I - ( k - 1 ) \\cdot 4 ^ { l } ) \\cap [ 4 ^ { l } ] \\qquad J _ { l , k } : = ( J - ( k - 1 ) \\cdot 4 ^ { l } ) \\cap [ 4 ^ { l } ]\n$$",
+        "text_format": "latex",
+        "bbox": [
+            272,
+            143,
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+            162
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "That is to say, $\\left( { { I } _ { l , k } } , { { J } _ { l , k } } \\right)$ represents the partition induced by $( I , J )$ on the set of indexes $\\{ ( k -$ $1 ) \\cdot 4 ^ { l } + 1 , \\ldots , k \\cdot 4 ^ { l } \\}$ , i.e. on the $k ^ { \\mathrm { { \\prime } } }$ ’th size- $. 4 ^ { l }$ group of input patches. With this notation in hand, traversing upwards through the levels of eq. 3, with repeated application of the relation in eq. 1, one arrives at the following matrix decomposition for $\\mathbb { I } ^ { \\boldsymbol { A } ^ { y } } \\mathbb { I } _ { \\boldsymbol { I } , \\boldsymbol { J } }$ : ",
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+        "page_idx": 8
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+    {
+        "type": "equation",
+        "img_path": "images/f122cc4ea51c4f205cdf5bd4e10528fc1294e26225ae9b7603e2b03d6ead2435.jpg",
+        "text": "$$\n\\begin{array}{c} \\begin{array} { r l } { \\underbrace { \\left[ \\phi ^ { 1 , \\gamma } \\right] I _ { 1 , k , \\cdot } J _ { 1 , k , \\cdot } } _ { \\begin{array} { l } { 1 } \\\\ { M ^ { | I _ { 1 , k } | }  { \\mathrm { l o p } } \\mathcal { M } ^ { | J _ { 1 , k } | } } \\end{array} } } & { = \\begin{array} { r l } { \\sum _ { \\alpha = 1 } ^ { r _ { 0 } } a _ { \\alpha } ^ { 1 , \\gamma } \\cdot \\underbrace { \\overset { 4 } { \\varepsilon } } \\left[ \\mathbf { a } ^ { 0 , \\alpha } \\right] I _ { 0 , 4 ( k - 1 ) + \\varepsilon } J _ { 0 , 4 ( k - 1 ) + \\varepsilon } } \\end{array} } \\\\ { \\underbrace { \\qquad } } & { \\dots } \\end{array}  \\\\ { \\underbrace { \\left[ \\phi ^ { i , \\gamma } \\right] I _ { l , k , \\cdot } J _ { l , k , \\cdot } } _ { \\begin{array} { l } { 1 } \\\\ { M ^ { | I _ { 1 , k , \\cdot } | }  { \\mathrm { l o p } } \\mathcal { M } ^ { | J _ { 1 , k } | } } \\end{array} } } & { = \\begin{array} { r l } { \\sum _ { \\alpha = 1 } ^ { r _ { l - 1 } } a _ { \\alpha } ^ { l , \\gamma } \\cdot \\underbrace { \\overset { 4 } { \\varepsilon } } \\left[ \\phi ^ { i - 1 , \\alpha } \\right] I _ { l - 1 , 4 ( k - 1 ) + \\varepsilon } J _ { l - 1 , 4 ( k - 1 ) + \\varepsilon } \\ , l \\in \\{ 2 , \\dots { L - 1 } \\} , \\gamma \\in } \\\\ { \\dots } \\end{array} } \\\\ { \\underbrace { \\left[ \\phi ^ { i , \\gamma } \\right] I _ { l , k , \\cdot } J _ { 1 , k , \\cdot } } _ { \\begin{array} { l } { 1 } \\\\ { M ^ { | I _ { 1 , k , \\cdot } | }  { \\mathrm { l o p } } \\mathcal { M } ^ { | J _ { 1 , l } | } } \\end{array} } } & { = \\begin{array} { r l } { \\sum _ { \\alpha = 1 } ^ { r _ { L - 1 } } a _ { \\alpha } ^ { L , y } \\cdot \\underbrace { \\overset { 4 } { \\varepsilon } } \\left[ \\phi ^ { L - 1 , \\alpha } \\right] I _ { L - 1 , \\varepsilon } J _ { L - 1 , t } } \\end{array} } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Eq. 7 expresses $\\mathbb { I } \\boldsymbol { \\mathcal { A } } ^ { y } \\mathbb { I } _ { I , J }$ – the matricization w.r.t. the partition $( I , J )$ of a coefficient tensor $\\mathcal { A } ^ { y }$ realJ Kized by the deep network, in terms of the network’s conv weights $\\{ \\mathbf { a } ^ { l , \\gamma } \\} _ { l , \\gamma }$ and output weights $\\mathbf { a } ^ { L , y }$ . As discussed above, our interest lies in the maximal rank that this matricization can take. Theorem 1 below provides lower and upper bounds on this maximal rank, by making use of eq. 7, and of the rank-multiplicative property of the Kronecker product $( r a n k ( A { \\odot } B ) = r a n k ( A ) { \\cdot } r a n k ( B ) )$ . ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Theorem 1. Let $( I , J )$ be a partition of $[ N ]$ , and $\\mathbb { I } \\boldsymbol { \\mathcal { A } } ^ { y } \\mathbb { I } _ { I , J }$ be the matricization w.r.t. $( I , J )$ of $a$ coefficient tensor $\\mathcal { A } ^ { y }$ J K(eq. 2) realized by the deep network (fig. $\\boldsymbol { l } ( \\boldsymbol { a } )$ with size-4 pooling windows). For every $l \\in \\{ 0 . . . L - 1 \\}$ and $k \\in [ N \\dot { / } 4 ^ { l } ]$ , define $I _ { l , k }$ and $J _ { l , k }$ as in eq. 6. Then, the maximal rank that $\\mathbb { I } \\boldsymbol { \\mathcal { A } } ^ { y } \\mathbb { I } _ { I , J }$ can take (when network weights vary) is: ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "• No greater than $\\begin{array} { r } { \\operatorname* { m i n } \\{ M ^ { \\mathrm { m i n } } \\{ | I | , | J | \\} , r _ { L - 1 } \\prod _ { t = 1 } ^ { 4 } c ^ { L - 1 , t } \\} } \\end{array}$ , where $c ^ { 0 , k } : = 1$ for $k \\in [ N ]$ , and $\\begin{array} { r } { c ^ { l , k } : = \\operatorname* { m i n } \\{ M ^ { \\operatorname* { m i n } \\{ | I _ { l , k } | , | J _ { l , k } | \\} } , r _ { l - 1 } \\prod _ { t = 1 } ^ { 4 } c ^ { l - 1 , 4 ( k - 1 ) + t } \\} f o r l \\in [ L - 1 ] , k \\in [ 0 , T ] \\times [ 0 , 1 ] \\} , } \\end{array}$ . ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Proof. See app. A.3. ",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "The lower bound in theorem 1 is exponential in $S$ , the latter defined to be the number of size-4 patch groups that are split by the partition $( I , J )$ , i.e. whose indexes are divided between $I$ and $J$ . Partitions that split many of the size-4 patch groups will thus lead to a large lower bound. For example, consider the partition $( I ^ { o d d } , J ^ { e v e n } )$ defined as follows: ",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "equation",
+        "img_path": "images/94c9ba7b16af9d0f9786da26068d442072278619caa72b6948d6664afe0eee24.jpg",
+        "text": "$$\nI ^ { o d d } = \\{ 1 , 3 , . . . , N - 1 \\} \\qquad J ^ { e v e n } = \\{ 2 , 4 , . . . , N \\}\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "This partition splits all size-4 patch groups $\\mathit { S } = { N } / { 4 } $ ), leading to a lower bound that is exponential in the number of patches $( N )$ . ",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "The upper bound in theorem 1 is expressed via constants $c ^ { l , k }$ , defined recursively over levels $l = 0 . . . L - 1$ , with $k$ ranging over $\\dot { 1 } . . . N / 4 ^ { l }$ for each level $l$ . What prevents $c ^ { l , \\tilde { k } }$ from growing double-exponentially fast (w.r.t. $l ,$ ) is the minimization with $M ^ { \\operatorname* { m i n } \\{ | I _ { l , k } | , | J _ { l , k } | \\} }$ . Specifically, if $\\mathrm { m i n } \\{ | I _ { l , k } | , | \\bar { J _ { l , k } } | \\}$ is small, i.e. if the partition induced by $( I , J )$ on the $k$ ’th size- $4 ^ { l }$ group of patches is unbalanced (most of the patches belong to one side of the partition, and only a few belong to the other), $c ^ { l , k }$ will be of reasonable size. The higher this takes place in the hierarchy (i.e. the larger $l$ is), the lower our eventual upper bound will be. In other words, if partitions induced by $( I , J )$ on size- $. 4 ^ { l }$ patch groups are unbalanced for large values of $l$ , the upper bound in theorem 1 will be small. For example, consider the partition $( I ^ { l o w } , \\mathsf { \\bar { J } } ^ { h i g h } )$ defined by: ",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "equation",
+        "img_path": "images/4349c7a68265d3311fec2f2d36a4c0b63cc7b335b7e8287e0cdda5724876196a.jpg",
+        "text": "$$\nI ^ { l o w } = \\{ 1 , \\ldots , N / 2 \\} \\qquad J ^ { h i g h } = \\{ N / 2 + 1 , \\ldots , N \\}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            316,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Under $( I ^ { l o w } , J ^ { h i g h } )$ , all partitions induced on size- $\\cdot 4 ^ { L - 1 }$ patch groups (quadrants of $[ N ] )$ are completely one-sided $( \\operatorname* { m i n } \\{ | I _ { L - 1 , k } | , | J _ { L - 1 , k } | \\} = 0$ for all $k \\in [ 4 ] \\cdot$ ), resulting in the upper bound being no greater than $r _ { L - 1 }$ – linear in network size. ",
+        "bbox": [
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+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "To summarize this discussion, theorem 1 states that with the deep network, the maximal rank of a coefficient tensor matricization w.r.t. $( I , J )$ , highly depends on the nature of the partition $( I , J ) - \\mathrm { i t }$ will be exponentially high for partitions such as $( \\bar { I } ^ { o d \\bar { d } } , J ^ { e v e n } )$ , that split many size-4 patch groups, while being only polynomial (or linear) for partitions like $( I ^ { \\mathit { l o w } } , J ^ { h i \\mathit { \\hat { g } } h } )$ , under which size- $\\breve { 4 ^ { l } }$ patch groups are unevenly divided for large values of $l$ . Since the rank of a coefficient tensor matricization w.r.t. $( I , J )$ corresponds to the strength of correlation modeled between input patches indexed by $I$ and those indexed by $J$ (sec. 5.1), we conclude that the ability of a polynomially sized deep network to model correlation between sets of input patches highly depends on the nature of these sets. ",
+        "bbox": [
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+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "5.3 SHALLOW NETWORK ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            287,
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+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "We now turn to study correlations modeled by the shallow network presented in sec. 3 (fig. 1(b)). In line with sec. 5.1, this is achieved by characterizing the maximal ranks of coefficient tensor matricizations under different partitions. ",
+        "bbox": [
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+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Recall from eq. 4 the CP decomposition expressing a coefficient tensor $\\mathcal { A } ^ { y }$ realized by the shallow network. For an arbitrary partition $( I , J )$ of $[ N ]$ , i.e. $I { \\uplus } J = [ N ]$ , matricizing this decomposition with repeated application of the relation in eq. 1, gives the following expression for $[ \\mathcal { A } ^ { y } ] _ { I , J }$ – the matricization w.r.t. $( I , J )$ of a coefficient tensor realized by the shallow network: ",
+        "bbox": [
+            174,
+            362,
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+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "equation",
+        "img_path": "images/daf63bf1f6a114579e361f59469aad9627202a920cb3f7b4d547479cafede620.jpg",
+        "text": "$$\n\\mathbb { L } \\boldsymbol { A } ^ { y } \\mathbb { I } _ { I , J } = \\sum _ { \\gamma = 1 } ^ { r _ { 0 } } a _ { \\gamma } ^ { 1 , y } \\cdot \\left( \\odot ^ { | I | } \\mathbf { a } ^ { 0 , \\gamma } \\right) \\left( \\odot ^ { | J | } \\mathbf { a } ^ { 0 , \\gamma } \\right) ^ { \\top }\n$$",
+        "text_format": "latex",
+        "bbox": [
+            331,
+            422,
+            665,
+            455
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "$\\mathbf { \\Theta } ^ { \\mathrm { ( 0 } \\mathrm { I } I \\vert } \\mathbf { a } ^ { 0 , \\gamma }$ and $\\odot ^ { | J | } \\mathbf { a } ^ { 0 , \\gamma }$ here are column vectors of dimensions $M ^ { | I | }$ and $M ^ { | J | }$ respectively, standing for the Kronecker products of $\\mathbf { a } ^ { 0 , \\gamma } \\in \\mathbb { R } ^ { M }$ with itself $| I |$ and $| J |$ times (respectively). Eq. 10 immediately leads to two observations regarding the ranks that may be taken by $\\mathbb { I } ^ { \\boldsymbol { A } ^ { y } } \\mathbb { I } _ { \\boldsymbol { I } , \\boldsymbol { J } }$ . First, they depend on the partition $( I , J )$ only through its division size, i.e. through $| I |$ J and $| J |$ . Second, they are no greater than $\\operatorname* { m i n } \\{ M ^ { \\mathrm { m i n } \\{ | I | , | J | \\} } , r _ { 0 } \\}$ , meaning that the maximal rank is linear (or less) in network size. In light of sec. 5.1 and 5.2, these findings imply that in contrast to the deep network, which with polynomial size supports exponential separation ranks under favored partitions, the shallow network treats all partitions (of a given division size) equally, and can only give rise to an exponential separation rank if its size is exponential. ",
+        "bbox": [
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+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Suppose now that we would like to use the shallow network to replicate a function realized by a polynomially sized deep network. So long as the deep network’s function admits an exponential separation rank under at least one of the favored partitions (e.g. $( I ^ { o d d } , J ^ { e v e n } ) - { \\bf e q . \\ 8 } )$ , the shallow network would have to be exponentially large in order to replicate it, i.e. depth efficiency takes place. 7 Since all but a negligible set of the functions realizable by the deep network give rise to maximal separation ranks (sec 5.1), we obtain the complete depth efficiency result of Cohen et al. (2016b). However, unlike Cohen et al. (2016b), which did not provide any explanation for the usefulness of functions brought forth by depth, we obtain an insight into their utility – they are able to efficiently model strong correlation under favored partitions of the input. ",
+        "bbox": [
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+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "6 INDUCTIVE BIAS THROUGH POOLING GEOMETRY ",
+        "text_level": 1,
+        "bbox": [
+            174,
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+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "The deep network presented in sec. 3, whose correlations we analyzed in sec. 5.2, was defined as having size-4 pooling windows, i.e. pooling windows covering four entries each. We have yet to specify the shapes of these windows, or equivalently, the spatial (two-dimensional) locations of nodes grouped together in the process of pooling. In compliance with standard convolutional network design, we now assume that the network’s (size-4) pooling windows are contiguous square blocks, i.e. have shape $2 \\times 2$ . Under this configuration, the network’s functional description (eq. 2 with $\\mathcal { A } ^ { y }$ given by eq. 3) induces a spatial ordering of input patches 8 , which may be described by the following recursive process: ",
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+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "• Set the index of the top-left patch to 1.   \n• For $l = 1 , . . . , L = l o g _ { 4 } N$ : Replicate the already-assigned top-left $2 ^ { l - 1 }$ -by- $2 ^ { l - 1 }$ block of indexes, and place copies on its right, bottom-right and bottom. Then, add a $4 ^ { l - 1 }$ offset to all indexes in the right copy, a $2 \\cdot 4 ^ { l - 1 }$ offset to all indexes in the bottom-right copy, and a $3 \\cdot 4 ^ { l - 1 }$ offset to all indexes in the bottom copy. ",
+        "bbox": [
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+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "With this spatial ordering (illustrated in fig. 1(c)), partitions $( I , J )$ of $[ N ]$ convey a spatial pattern. For example, the partition $( I _ { \\cdot } ^ { o d d } , J ^ { e v e n } )$ (eq. 8) corresponds to the pattern illustrated on the left of fig. 1(c), whereas $( I ^ { l o w } , J ^ { h i g h } )$ (eq. 9) corresponds to the pattern illustrated on the right. Our analysis (sec. 5.2) shows that the deep network is able to model strong correlation under $\\mathsf { \\bar { ( } } I ^ { o d d } , J ^ { e v e n } )$ , while being inefficient for modeling correlation under $( I ^ { l o w } , J ^ { h i \\breve { g h } } )$ . More generally, partitions for which $S$ , defined in theorem 1, is high, convey patterns that split many $2 \\times 2$ patch blocks, i.e. are highly entangled. These partitions enjoy the possibility of strong correlation. On the other hand, partitions for which $\\operatorname* { m i n } \\{ \\left| I _ { l , k } \\right| , \\left| J _ { l , k } \\right| \\}$ is small for large values of $l$ (see eq. 6 for definition of $I _ { l , k }$ and ${ { J } _ { l , k } } .$ ) convey patterns that divide large $2 ^ { l } \\times 2 ^ { l }$ patch blocks unevenly, i.e. separate the input to distinct contiguous regions. These partitions, as we have seen, suffer from limited low correlations. ",
+        "bbox": [
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+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "We conclude that with $2 \\times 2$ pooling, the deep network is able to model strong correlation between input regions that are highly entangled, at the expense of being inefficient for modeling correlation between input regions that are far apart. Had we selected a different pooling regime, the preference of input partition patterns in terms of modeled correlation would change. For example, if pooling windows were set to group nodes with their spatial reflections (horizontal, vertical and horizontalvertical), coarse patterns that divide the input symmetrically, such as the one illustrated on the right of fig. 1(c), would enjoy the possibility of strong correlation, whereas many entangled patterns would now suffer from limited low correlation. The choice of pooling shapes thus serves as a means for controlling the inductive bias in terms of correlations modeled between input regions. Square contiguous windows, as commonly employed in practice, lead to a preference that complies with our intuition regarding the statistics of natural images (nearby pixels more correlated than distant ones). Other pooling schemes lead to different preferences, and this allows tailoring a network to data that departs from the usual domain of natural imagery. We demonstrate this experimentally in the next section, where it is shown how different pooling geometries lead to superior performance in different tasks. ",
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+    {
+        "type": "text",
+        "text": "7 EXPERIMENTS ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The main conclusion from our analyses (sec. 5 and 6) is that the pooling geometry of a deep convolutional network controls its inductive bias by determining which correlations between input regions can be modeled efficiently. We have also seen that shallow networks cannot model correlations efficiently, regardless of the considered input regions. In this section we validate these assertions empirically, not only with convolutional arithmetic circuits (subject of our analyses), but also with convolutional rectifier networks – convolutional networks with ReLU activation and max or average pooling. For conciseness, we defer to app. C some details regarding our implementation. The latter is fully available online at https://github.com/HUJI-Deep/inductive-pooling. ",
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+    {
+        "type": "image",
+        "img_path": "images/ec1691f27312d623cb5e3c98cef35c7d72c68d58943ab148f85e159f956ea567.jpg",
+        "image_caption": [
+            "Figure 2: Sample of images from our synthetic classification benchmark. Each image displays a random blob with holes, whose morphological closure and left-right symmetry about its center are measured. Two classification tasks are defined – one for closedness and one for symmetry. In each task, the objective is to distinguish between blobs whose respective property (closedness/symmetry) is high, and ones for which it is low. The tasks differ in nature – closedness requires modeling correlations between neighboring pixels, whereas symmetry requires modeling correlations between pixels and their reflections. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Our experiments are based on a synthetic classification benchmark inspired by medical imaging tasks. Instances to be classified are 32-by-32 binary images, each displaying a random distorted oval shape $( b l o b )$ with missing pixels in its interior (holes). For each image, two continuous scores in range $[ 0 , 1 ]$ are computed. The first, referred to as closedness, reflects how morphologically closed a blob is, and is defined to be the ratio between the number of pixels in the blob, and the number of pixels in its closure (see app. D for exact definition of the latter). The second score, named symmetry, reflects the degree to which a blob is left-right symmetric about its center. It is measured by cropping the bounding box around a blob, applying a left-right flip to the latter, and computing the ratio between the number of pixels in the intersection of the blob and its reflection, and the number of pixels in the blob. To generate labeled sets for classification (train and test), we render multiple images, sort them according to their closedness and symmetry, and for each of the two scores, assign the label “high” to the top $40 \\%$ and the label “low” to the bottom $40 \\%$ (the mid $20 \\%$ are considered ill-defined). This creates two binary (two-class) classification tasks – one for closedness and one for symmetry (see fig. 2 for a sample of images participating in both tasks). Given that closedness is a property of a local nature, we expect its classification task to require a predictor to be able to model strong correlations between neighboring pixels. Symmetry on the other hand is a property that relates pixels to their reflections, thus we expect its classification task to demand that a predictor be able to model correlations across distances. ",
+        "bbox": [
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+        "page_idx": 11
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+    {
+        "type": "text",
+        "text": "We evaluated the deep convolutional arithmetic circuit considered throughout the paper (fig. 1(a) with size-4 pooling windows) under two different pooling geometries. The first, referred to as square, comprises standard $2 \\times 2$ pooling windows. The second, dubbed mirror, pools together nodes with their horizontal, vertical and horizontal-vertical reflections. In both cases, input patches $\\left( \\mathbf { x } _ { i } \\right)$ were set as individual pixels, resulting in $N = 1 0 2 4$ patches and $L = \\log _ { 4 } N = 5$ hidden layers. $M = 2$ representation functions $( f _ { \\theta _ { d } } )$ were fixed, the first realizing the identity on binary inputs $( f _ { \\boldsymbol { \\theta } _ { 1 } } ( b ) = b$ for $b \\in \\{ 0 , 1 \\} ,$ ), and the second realizing negation $( f _ { \\theta _ { 2 } } ( b ) = 1 - b$ for $\\dot { b } \\in \\{ 0 , 1 \\}$ ). Classification was realized through $Y = 2$ network outputs, with prediction following the stronger activation. The number of channels across all hidden layers was uniform, and varied between 8 and 128. Fig. 3 shows the results of applying the deep network with both square and mirror pooling, to both closedness and symmetry tasks, where each of the latter has 20000 images for training and 4000 images for testing. As can be seen in the figure, square pooling significantly outperforms mirror pooling in closedness classification, whereas the opposite occurs in symmetry classification. This complies with our discussion in sec. 6, according to which square pooling supports modeling correlations between entangled (neighboring) regions of the input, whereas mirror pooling puts focus on correlations between input regions that are symmetric w.r.t. one another. We thus obtain a demonstration of how prior knowledge regarding a task at hand may be used to tailor the inductive bias of a deep convolutional network by designing an appropriate pooling geometry. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "In addition to the deep network, we also evaluated the shallow convolutional arithmetic circuit analyzed in the paper (fig. 1(b)). The architectural choices for this network were the same as those described above for the deep network besides the number of hidden channels, which in this case applied to the network’s single hidden layer, and varied between 64 and 4096. The highest train and test accuracies delivered by this network (with 4096 hidden channels) were roughly $6 \\hat { 2 } \\%$ on closedness task, and $7 7 \\%$ on symmetry task. The fact that these accuracies are inferior to those of the deep network, even when the latter’s pooling geometry is not optimal for the task at hand, complies with our analysis in sec. 5. Namely, it complies with the observation that separation ranks (correlations) are sometimes exponential and sometimes polynomial with the deep network, whereas with the shallow one they are never more than linear in network size. ",
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+    {
+        "type": "image",
+        "img_path": "images/2dce20371cae06c31ed9d495bc3afd7a52a1dbcf10a3544fc77e664d88aed1bf.jpg",
+        "image_caption": [
+            "Figure 3: Results of applying a deep convolutional arithmetic circuit to closedness and symmetry classification tasks. Two pooling geometries were evaluated – square, which supports modeling correlations between neighboring input regions, and mirror, which puts focus on correlations between regions that are symmetric w.r.t. one another. Each pooling geometry outperforms the other on the task for which its correlations are important, demonstrating how prior knowledge regarding a task at hand may be used to tailor the inductive bias through proper pooling design. "
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Finally, to assess the validity of our findings for convolutional networks in general, not just convolutional arithmetic circuits, we repeated the above experiments with convolutional rectifier networks. Namely, we placed ReLU activations after every conv operator, switched the pooling operation from product to average, and re-evaluated the deep (square and mirror pooling geometries) and shallow networks. We then reiterated this process once more, with pooling operation set to max instead of average. The results obtained by the deep networks are presented in fig. 4. The shallow network with average pooling reached train/test accuracies of roughly $5 8 \\%$ on closedness task, and $5 5 \\%$ on symmetry task. With max pooling, performance of the shallow network did not exceed chance. Altogether, convolutional rectifier networks exhibit the same phenomena observed with convolutional arithmetic circuits, indicating that the conclusions from our analyses likely apply to such networks as well. Formal adaptation of the analyses to convolutional rectifier networks, similarly to the adaptation of Cohen et al. (2016b) carried out in Cohen and Shashua (2016), is left for future work. ",
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+    },
+    {
+        "type": "text",
+        "text": "8 DISCUSSION ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Through the notion of separation rank, we studied the relation between the architecture of a convolutional network, and its ability to model correlations among input regions. For a given input partition, the separation rank quantifies how far a function is from separability, which in a probabilistic setting, corresponds to statistical independence between sides of the partition. ",
+        "bbox": [
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+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Our analysis shows that a polynomially sized deep convolutional arithmetic circuit supports exponentially high separation ranks for certain input partitions, while being limited to polynomial or linear (in network size) separation ranks for others. The network’s pooling window shapes effectively determine which input partitions are favored in terms of separation rank, i.e. which partitions enjoy the possibility of exponentially high separation ranks with polynomial network size, and which require network to be exponentially large. Pooling geometry thus serves as a means for controlling the inductive bias. The particular pooling scheme commonly employed in practice – square contiguous windows, favors interleaved partitions over ones that divide the input to distinct areas, thus orients the inductive bias towards the statistics of natural images (nearby pixels more correlated than distant ones). Other pooling schemes lead to different preferences, and this allows tailoring the network to data that departs from the usual domain of natural imagery. ",
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+    },
+    {
+        "type": "image",
+        "img_path": "images/41abe156433db432f05f8e96ebf71df175bef2102d5a6fceaf879f92285c0d8f.jpg",
+        "image_caption": [
+            "Figure 4: Results of applying deep convolutional rectifier networks to closedness and symmetry classification tasks. The same trends observed with the deep convolutional arithmetic circuit (fig. 3) are apparent here. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "As opposed to deep convolutional arithmetic circuits, shallow ones support only linear (in network size) separation ranks. Therefore, in order to replicate a function realized by a deep network (exponential separation rank), a shallow network must be exponentially large. By this we derive the depth efficiency result of Cohen et al. (2016b), but in addition, provide an insight into the benefit of functions brought forth by depth – they are able to efficiently model strong correlation under favored partitions of the input. ",
+        "bbox": [
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+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "We validated our conclusions empirically, with convolutional arithmetic circuits as well as convolutional rectifier networks – convolutional networks with ReLU activation and max or average pooling. Our experiments demonstrate how different pooling geometries lead to superior performance in different tasks. Specifically, we evaluate deep networks in the measurement of shape continuity, a task of a local nature, and show that standard square pooling windows outperform ones that join together nodes with their spatial reflections. In contrast, when measuring shape symmetry, modeling correlations across distances is of vital importance, and the latter pooling geometry is superior to the conventional one. Shallow networks are inefficient at modeling correlations of any kind, and indeed lead to poor performance on both tasks. ",
+        "bbox": [
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+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "Finally, our analyses and results bring forth the possibility of expanding the coverage of correlations efficiently modeled by a deep convolutional network. Specifically, by blending together multiple pooling geometries in the hidden layers of a network, it is possible to facilitate simultaneous support for a wide variety of correlations suiting data of different types. Investigation of this direction, from both theoretical and empirical perspectives, is viewed as a promising avenue for future research. ",
+        "bbox": [
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+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "ACKNOWLEDGMENTS ",
+        "text_level": 1,
+        "bbox": [
+            176,
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+            867
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "This work is supported by Intel grant ICRI-CI #9-2012-6133, by ISF Center grant 1790/12 and by the European Research Council (TheoryDL project). Nadav Cohen is supported by a Google Doctoral Fellowship in Machine Learning. ",
+        "bbox": [
+            176,
+            882,
+            823,
+            924
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "REFERENCES ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            103,
+            287,
+            117
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "Richard Bellman. Introduction to matrix analysis, volume 960. SIAM, 1970. ",
+        "bbox": [
+            174,
+            125,
+            629,
+            138
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "Gregory Beylkin and Martin J Mohlenkamp. Numerical operator calculus in higher dimensions. Proceedings of the National Academy of Sciences, 99(16):10246–10251, 2002. ",
+        "bbox": [
+            173,
+            146,
+            818,
+            174
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "Gregory Beylkin, Jochen Garcke, and Martin J Mohlenkamp. Multivariate regression and machine learning with sums of separable functions. SIAM Journal on Scientific Computing, 31(3):1840–1857, 2009. ",
+        "bbox": [
+            174,
+            181,
+            823,
+            208
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "Richard Caron and Tim Traynor. The zero set of a polynomial. WSMR Report 05-02, 2005. ",
+        "bbox": [
+            173,
+            215,
+            717,
+            231
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "Nadav Cohen and Amnon Shashua. Simnets: A generalization of convolutional networks. Advances in Neural Information Processing Systems (NIPS), Deep Learning Workshop, 2014. ",
+        "bbox": [
+            173,
+            239,
+            823,
+            265
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "Nadav Cohen and Amnon Shashua. Convolutional rectifier networks as generalized tensor decompositions. International Conference on Machine Learning (ICML), 2016. ",
+        "bbox": [
+            173,
+            273,
+            823,
+            300
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "Nadav Cohen, Or Sharir, and Amnon Shashua. Deep simnets. IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2016a. ",
+        "bbox": [
+            173,
+            308,
+            825,
+            335
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "Nadav Cohen, Or Sharir, and Amnon Shashua. On the expressive power of deep learning: A tensor analysis. Conference On Learning Theory (COLT), 2016b. ",
+        "bbox": [
+            173,
+            342,
+            823,
+            369
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "Thomas M Cover and Joy A Thomas. Elements of information theory. John Wiley & Sons, 2012. ",
+        "bbox": [
+            171,
+            377,
+            750,
+            392
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "Olivier Delalleau and Yoshua Bengio. Shallow vs. deep sum-product networks. In Advances in Neural Information Processing Systems, pages 666–674, 2011. ",
+        "bbox": [
+            176,
+            398,
+            825,
+            426
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "Carl Eckart and Gale Young. The approximation of one matrix by another of lower rank. Psychometrika, 1(3): 211–218, 1936. ",
+        "bbox": [
+            174,
+            434,
+            821,
+            460
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "Ronen Eldan and Ohad Shamir. The power of depth for feedforward neural networks. arXiv preprint arXiv:1512.03965, 2015. ",
+        "bbox": [
+            173,
+            468,
+            823,
+            496
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "G.H. Golub and C.F. Van Loan. Matrix Computations. Johns Hopkins Studies in the Mathematical Sciences. Johns Hopkins University Press, 2013. ISBN 9781421407944. URL https://books.google.co. il/books?id $_ { \\cdot } =$ X5YfsuCWpxMC. ",
+        "bbox": [
+            176,
+            503,
+            823,
+            542
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "Wolfgang Hackbusch. On the efficient evaluation of coalescence integrals in population balance models. Computing, 78(2):145–159, 2006. ",
+        "bbox": [
+            174,
+            550,
+            823,
+            578
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "Wolfgang Hackbusch. Tensor Spaces and Numerical Tensor Calculus, volume 42 of Springer Series in Computational Mathematics. Springer Science & Business Media, Berlin, Heidelberg, February 2012. ",
+        "bbox": [
+            176,
+            584,
+            821,
+            612
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "Robert M Haralick, Stanley R Sternberg, and Xinhua Zhuang. Image analysis using mathematical morphology. IEEE transactions on pattern analysis and machine intelligence, (4):532–550, 1987. ",
+        "bbox": [
+            171,
+            619,
+            821,
+            647
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "Robert J Harrison, George I Fann, Takeshi Yanai, and Gregory Beylkin. Multiresolution quantum chemistry in multiwavelet bases. In Computational Science-ICCS 2003, pages 103–110. Springer, 2003. ",
+        "bbox": [
+            173,
+            654,
+            823,
+            683
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recognition. arXiv preprint arXiv:1512.03385, 2015. ",
+        "bbox": [
+            174,
+            689,
+            823,
+            717
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "Yangqing Jia, Evan Shelhamer, Jeff Donahue, Sergey Karayev, Jonathan Long, Ross Girshick, Sergio Guadarrama, and Trevor Darrell. Caffe: Convolutional architecture for fast feature embedding. In Proceedings of the 22nd ACM international conference on Multimedia, pages 675–678. ACM, 2014. ",
+        "bbox": [
+            173,
+            723,
+            826,
+            763
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "Frank Jones. Lebesgue integration on Euclidean space. Jones & Bartlett Learning, 2001. ",
+        "bbox": [
+            173,
+            771,
+            699,
+            785
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "Diederik Kingma and Jimmy Ba. Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980, 2014. ",
+        "bbox": [
+            174,
+            792,
+            823,
+            820
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "Tamara G Kolda and Brett W Bader. Tensor Decompositions and Applications. SIAM Review (), 51(3):455–500, 2009. ",
+        "bbox": [
+            173,
+            828,
+            823,
+            854
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "Alex Krizhevsky, Ilya Sutskever, and Geoffrey E Hinton. ImageNet Classification with Deep Convolutional Neural Networks. Advances in Neural Information Processing Systems, pages 1106–1114, 2012. ",
+        "bbox": [
+            174,
+            862,
+            823,
+            890
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "Yann LeCun and Yoshua Bengio. Convolutional networks for images, speech, and time series. The handbook of brain theory and neural networks, 3361(10), 1995. ",
+        "bbox": [
+            173,
+            897,
+            826,
+            924
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "Yann LeCun, Yoshua Bengio, and Geoffrey Hinton. Deep learning. Nature, 521(7553):436–444, May 2015. ",
+        "bbox": [
+            169,
+            103,
+            812,
+            119
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "Hrushikesh Mhaskar, Qianli Liao, and Tomaso Poggio. Learning real and boolean functions: When is deep better than shallow. arXiv preprint arXiv:1603.00988, 2016. ",
+        "bbox": [
+            174,
+            127,
+            821,
+            154
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "Guido F Montufar, Razvan Pascanu, Kyunghyun Cho, and Yoshua Bengio. On the number of linear regions of deep neural networks. In Advances in Neural Information Processing Systems, pages 2924–2932, 2014. ",
+        "bbox": [
+            176,
+            161,
+            823,
+            189
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "Vinod Nair and Geoffrey E Hinton. Rectified linear units improve restricted boltzmann machines. In Proceedings of the 27th International Conference on Machine Learning (ICML-10), pages 807–814, 2010. ",
+        "bbox": [
+            176,
+            196,
+            821,
+            224
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "Razvan Pascanu, Guido Montufar, and Yoshua Bengio. On the number of inference regions of deep feed forward networks with piece-wise linear activations. arXiv preprint arXiv, 1312, 2013. ",
+        "bbox": [
+            174,
+            232,
+            821,
+            260
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "Tomaso Poggio, Fabio Anselmi, and Lorenzo Rosasco. I-theory on depth vs width: hierarchical function composition. Technical report, Center for Brains, Minds and Machines (CBMM), 2015. ",
+        "bbox": [
+            176,
+            267,
+            823,
+            295
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "Walter Rudin. Functional analysis. international series in pure and applied mathematics, 1991. ",
+        "bbox": [
+            173,
+            303,
+            732,
+            318
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "Or Sharir, Ronen Tamari, Nadav Cohen, and Amnon Shashua. Tensorial mixture models. arXiv preprint arXiv:1610.04167, 2016. ",
+        "bbox": [
+            173,
+            325,
+            825,
+            352
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "Karen Simonyan and Andrew Zisserman. Very deep convolutional networks for large-scale image recognition. arXiv preprint arXiv:1409.1556, 2014. ",
+        "bbox": [
+            171,
+            361,
+            821,
+            387
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "Nitish Srivastava, Geoffrey E Hinton, Alex Krizhevsky, Ilya Sutskever, and Ruslan Salakhutdinov. Dropout: a simple way to prevent neural networks from overfitting. Journal of Machine Learning Research, 15(1): 1929–1958, 2014. ",
+        "bbox": [
+            173,
+            395,
+            821,
+            435
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "Christian Szegedy, Wei Liu, Yangqing Jia, Pierre Sermanet, Scott Reed, Dragomir Anguelov, Dumitru Erhan, Vincent Vanhoucke, and Andrew Rabinovich. Going Deeper with Convolutions. CVPR, 2015. ",
+        "bbox": [
+            171,
+            444,
+            823,
+            470
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "Matus Telgarsky. Representation benefits of deep feedforward networks. arXiv preprint arXiv:1509.08101, 2015. ",
+        "bbox": [
+            173,
+            479,
+            823,
+            506
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "A DEFERRED PROOFS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            102,
+            370,
+            118
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "text",
+        "text": "A.1 PROOF OF CLAIM 1 ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            132,
+            349,
+            147
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "text",
+        "text": "We prove the equality in two steps, first showing that $s e p ( h _ { y } ; I , J ) { \\le } r a n k  { \\mathbb { [ } } A ^ { y }  { ] } | I , J$ , and then establishing the J Kconverse. The first step is elementary, and does not make use of the representation functions’ $( f _ { \\theta _ { d } } )$ linear independence, or of measurability/square-integrability. The second step does rely on these assumptions, and employs slightly more advanced mathematical machinery. Throughout the proof, we assume without loss of generality that the partition $( I , J )$ of $[ N ]$ is such that $I$ takes on lower values, while $J$ takes on higher ones. That is to say, we assume that $I = \\{ 1 , \\ldots , | I | \\}$ and $J = \\{ | I | + 1 , \\ldots , N \\}$ . 9 ",
+        "bbox": [
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+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "text",
+        "text": "To prove that $s e p ( h _ { y } ; I , J ) { \\le } r a n k  { \\mathbb { [ } } A ^ { y }  { ] } | I , J$ , denote by $R$ the rank of $\\mathbb { I } A ^ { y } \\mathbb { I } _ { I , J }$ . The latter is an $M ^ { | I | }$ -by- $M ^ { | J | }$ J Kmatrix, thus there exist vectors u1. . .uR ∈ RM|I| and $\\mathbf { v } _ { 1 \\cdot \\cdot \\cdot \\mathbf { v } _ { R } } \\in \\mathbb { R } ^ { M ^ { | J | } }$ Ksuch that $\\begin{array} { r } { \\mathbb { I } \\boldsymbol { \\mathcal { A } } ^ { y } \\mathbb { I } _ { I , J } = \\sum _ { \\nu = 1 } ^ { R } \\mathbf { u } _ { \\nu } \\mathbf { v } _ { \\nu } ^ { \\top } } \\end{array}$ For every $\\nu \\in [ R ]$ , let $B ^ { \\nu }$ be the tensor of order $| I |$ and dimension $M$ J K in each mode whose arrangement as a column vector gives $\\mathbf { u } _ { \\nu }$ , i.e. whose matricization w.r.t. the partition $( [ | I | ] , \\emptyset )$ is equal to $\\mathbf { u } _ { \\nu }$ . Similarly, let $\\mathcal { C } ^ { \\nu }$ , $\\nu \\in [ R ]$ , be the tensor of order $\\vert J \\vert = N - \\vert I \\vert$ and dimension $M$ in each mode whose matricization w.r.t. the partition $( \\emptyset , [ | J | ] )$ (arrangement as a row vector) is equal to $\\mathbf { v } _ { \\nu } ^ { \\top }$ . It holds that: ",
+        "bbox": [
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+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "equation",
+        "img_path": "images/eecfbcbb02fca1848203542b1a451edcb4fcaee888457e73cd78cad0899a9940.jpg",
+        "text": "$$\n\\begin{array} { l l l } { [ A ^ { y } ] _ { I , J } } & { = } & { \\sum _ { \\nu = 1 } ^ { R } \\mathbf { u } _ { \\nu } \\mathbf { v } _ { \\nu } ^ { \\top } } \\\\ & { = } & { \\sum _ { \\nu = 1 } ^ { R } [ \\mathcal { B } ^ { \\nu } ] _ { [ [ I ] ] , \\theta } \\odot [ \\mathcal { C } ^ { \\nu } ] _ { \\emptyset , [ [ J ] ] } } \\\\ & { = } & { \\sum _ { \\nu = 1 } ^ { R } [ \\mathcal { B } ^ { \\nu } ] _ { I \\cap [ [ I ] ] , J \\cap [ [ I ] ] } \\odot [ \\mathcal { C } ^ { \\nu } ] _ { ( I - | I ] ) \\cap [ [ J ] ] , ( J - | I ] ) \\cap [ [ J ] ] } } \\\\ & { = } & { \\sum _ { \\nu = 1 } ^ { R } [ \\mathcal { B } ^ { \\nu } \\otimes \\mathcal { C } ^ { \\nu } ] _ { I , J } } \\\\ & { = } & { \\left[ \\sum _ { \\nu = 1 } ^ { R } \\mathcal { B } ^ { \\nu } \\otimes \\mathcal { C } ^ { \\nu } \\right] _ { I , J } } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "where the third equality relies on the assumption $I = \\{ 1 , \\dots , | I | \\} , J = \\{ | I | + 1 , \\dots , N \\}$ , the fourth equality makes use of the relation in eq. 1, and the last equality is based on the linearity of the matricization operator. Since matricizations are merely rearrangements of tensors, the fact that $\\begin{array} { r } { \\mathcal { A } ^ { y } = \\sum _ { \\nu = 1 } ^ { R } \\mathcal { B } ^ { \\nu } \\otimes \\mathcal { C } ^ { \\nu } } \\end{array}$ , or equivalently, $\\begin{array} { r } { \\mathcal { A } _ { d _ { 1 } . . . d _ { N } } ^ { y } = \\sum _ { \\nu = 1 } ^ { R } \\mathcal { B } _ { d _ { 1 } . . . d _ { | I | } } ^ { \\nu } \\cdot \\mathcal { C } _ { d _ { | I | + 1 } . . . d _ { N } } ^ { \\nu } } \\end{array}$ $\\begin{array} { r } { \\mathbb { [ } \\mathcal { A } ^ { y } ] _ { I , J } = \\mathbb { [ } \\sum _ { \\nu = 1 } ^ { R } \\mathcal { B } ^ { \\nu } \\otimes \\mathcal { C } ^ { \\nu } \\mathbb { ] } _ { I , J } } \\end{array}$ ν=1 for every $d _ { 1 } . . . d _ { N } \\in [ M ]$ implies Plugging this into eq. 2 gives: ",
+        "bbox": [
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+            478,
+            825,
+            550
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "equation",
+        "img_path": "images/b39fd31d10d5b3ee37e15210686a6c183d1914be8d516cd33f093598afef09eb.jpg",
+        "text": "$$\n\\begin{array} { l l l } { { { h } _ { y } } \\left( { { \\bf { x } } _ { 1 } } , \\ldots , { { \\bf { x } } _ { N } } \\right) } & { { = } } & { { \\displaystyle \\sum _ { { d } _ { 1 } \\ldots { d } _ { N } = 1 } ^ { M } { \\cal A } _ { { d } _ { 1 } \\ldots { d } _ { N } } ^ { y } \\prod _ { i = 1 } ^ { N } { f } _ { { \\theta } _ { { d } _ { i } } } \\left( { { \\bf { x } } _ { i } } \\right) } } \\\\ { { } } & { { = } } & { { \\displaystyle \\sum _ { { d } _ { 1 } \\ldots { d } _ { N } = 1 } ^ { M } \\sum _ { { \\nu = 1 } } ^ { R } { \\cal B } _ { { d } _ { 1 } \\ldots { d } _ { | I | } } ^ { \\nu } \\cdot { \\cal C } _ { { d } _ { | I | + 1 } \\ldots { d } _ { N } } ^ { \\nu } \\prod _ { i = 1 } ^ { N } { f } _ { { \\theta } _ { { d } _ { i } } } \\left( { { \\bf { x } } _ { i } } \\right) } } \\\\ { { } } & { { = } } & { { \\displaystyle \\sum _ { { \\nu = 1 } } ^ { R } \\left( { \\displaystyle \\sum _ { { d } _ { 1 } \\ldots { d } _ { | I | } = 1 } ^ { M } { \\cal B } _ { { d } _ { 1 } \\ldots { d } _ { | I | } } ^ { \\nu } \\prod _ { i = 1 } ^ { | I | } { f } _ { { \\theta } _ { { d } _ { i } } } \\left( { { \\bf { x } } _ { i } } \\right) } \\right) } } \\\\ { { } } & { { } } & { { \\displaystyle \\cdot \\left( \\sum _ { { d } _ { | I | + 1 } \\ldots { d } _ { N } = 1 } ^ { M } { \\cal C } _ { { d } _ { | I | + 1 } \\ldots { d } _ { N } } ^ { \\nu } \\prod _ { i = | I | + 1 } ^ { N } { f } _ { { \\theta } _ { { d } _ { i } } } \\left( { { \\bf { x } } _ { i } } \\right) \\right) } } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            232,
+            555,
+            764,
+            678
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "text",
+        "text": "For every $\\nu \\in [ R ]$ , define the functions $g _ { \\nu } : ( \\mathbb { R } ^ { s } ) ^ { | I | } \\to \\mathbb { R }$ and $g _ { \\nu } ^ { \\prime } : ( \\mathbb { R } ^ { s } ) ^ { | J | } \\to \\mathbb { R }$ as follows: ",
+        "bbox": [
+            173,
+            681,
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+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "equation",
+        "img_path": "images/6326c3b40078552a2c97faedf01c3ba3e62e9cd10a778f725aa855bb2f9ba1e7.jpg",
+        "text": "$$\n\\begin{array} { l c l } { { g _ { \\nu } ( { \\bf x } _ { 1 } , \\ldots , { \\bf x } _ { | I | } ) } } & { { : = } } & { { \\sum _ { d _ { 1 } \\ldots d _ { | I | } = 1 } ^ { M } { \\cal B } _ { d _ { 1 } \\ldots d _ { | I | } } ^ { \\nu } \\prod _ { i = 1 } ^ { | I | } f _ { { \\theta } _ { d _ { i } } } ( { \\bf x } _ { i } ) } } \\\\ { { g _ { \\nu } ^ { \\prime } ( { \\bf x } _ { 1 } , \\ldots , { \\bf x } _ { | J | } ) } } & { { : = } } & { { \\sum _ { d _ { 1 } \\ldots d _ { | J | } = 1 } ^ { M } { \\cal C } _ { d _ { 1 } \\ldots d _ { | J | } } ^ { \\nu } \\prod _ { i = 1 } ^ { | J | } f _ { { \\theta } _ { d _ { i } } } ( { \\bf x } _ { i } ) } } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            303,
+            704,
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+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "text",
+        "text": "Substituting these into eq. 11 leads to: ",
+        "bbox": [
+            174,
+            104,
+            400,
+            118
+        ],
+        "page_idx": 17
+    },
+    {
+        "type": "equation",
+        "img_path": "images/5ae0094a4ac7224f1e807bd4f088285c91ad63153de72e7e8bf1594cdbc8c744.jpg",
+        "text": "$$\nh _ { y } \\left( \\mathbf { x } _ { 1 } , \\ldots , \\mathbf { x } _ { N } \\right) = \\sum _ { \\nu = 1 } ^ { R } g _ { \\nu } ( \\mathbf { x } _ { 1 } , \\ldots , \\mathbf { x } _ { | I | } ) g _ { \\nu } ^ { \\prime } ( \\mathbf { x } _ { | I | + 1 } , \\ldots , \\mathbf { x } _ { N } )\n$$",
+        "text_format": "latex",
+        "bbox": [
+            303,
+            130,
+            692,
+            155
+        ],
+        "page_idx": 17
+    },
+    {
+        "type": "text",
+        "text": "which by definition of the separation rank (eq. 5), implies $s e p ( h _ { y } ; I , J ) { \\le } R$ . By this we have shown that $s e p ( h _ { y } ; I , J ) { \\le } r a n k [ [ \\boldsymbol { A } ^ { y } ] ] _ { I , J }$ , as required. ",
+        "bbox": [
+            173,
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+        ],
+        "page_idx": 17
+    },
+    {
+        "type": "text",
+        "text": "For proving the converse inequality, i.e. $s e p ( h _ { y } ; I , J ) \\ge r a n k \\perp ^ { y } \\perp _ { I , J } ^ { }$ , we rely on basic concepts and results Jfrom functional analysis, or more specifically, from the topic of $L ^ { 2 }$ spaces. While a full introduction to this topic is beyond our scope (the interested reader is referred to Rudin (1991)), we briefly lay out here the minimal background required in order to follow our proof. For any $n \\in \\mathbb N$ , $L ^ { 2 } ( \\mathbb { R } ^ { n } )$ is formally defined as the Hilbert space of Lebesgue measurable square-integrable real functions over $\\mathbb { R } ^ { n }$ 10 , equipped with standard (pointwise) addition and scalar multiplication, as well as the inner product defined by integration over point-wise multiplication. For our purposes, $L ^ { 2 } ( \\mathbb { R } ^ { n } )$ may simply be thought of as the (infinite-dimensional) vector space of functions $g : \\mathbb { R } ^ { n }  \\mathbb { R }$ satisfying $\\textstyle \\int g ^ { 2 } < \\infty$ , with inner product defined by $\\textstyle \\left. g _ { 1 } , g _ { 2 } \\right. : = \\int g _ { 1 } \\cdot g _ { 2 }$ . Our proof will make use of the following basic facts related to $L ^ { 2 }$ spaces: ",
+        "bbox": [
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+        ],
+        "page_idx": 17
+    },
+    {
+        "type": "text",
+        "text": "Fact 1. If $V$ is a finite-dimensional subspace of $L ^ { 2 } ( \\mathbb { R } ^ { n } )$ , then any $g \\in L ^ { 2 } ( \\mathbb { R } ^ { n } )$ may be expressed as $g = p + \\delta$ , with $p { \\in } V$ and $\\delta \\in V ^ { \\perp }$ (i.e. $\\delta$ is orthogonal to all elements in $V$ ). Moreover, such a representation is unique, so in the case where $g \\in V$ , we necessarily have $p = g$ and $\\delta \\equiv 0$ . ",
+        "bbox": [
+            174,
+            334,
+            825,
+            377
+        ],
+        "page_idx": 17
+    },
+    {
+        "type": "text",
+        "text": "Fact 2. I $\\{ \\mathbf { \\psi } _ { g \\in L ^ { 2 } ( \\mathbb { R } ^ { n } ) , g ^ { \\prime } \\in L ^ { 2 } ( \\mathbb { R } ^ { n \\prime } ) }$ , then the function $( \\mathbf { x } _ { 1 } , \\mathbf { x } _ { 2 } ) { \\mapsto } g ( \\mathbf { x } _ { 1 } ) { \\cdot } g ^ { \\prime } ( \\mathbf { x } _ { 2 } )$ belongs to $L ^ { 2 } ( \\mathbb { R } ^ { n } \\times \\mathbb { R } ^ { n \\prime } )$ . ",
+        "bbox": [
+            169,
+            381,
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+        ],
+        "page_idx": 17
+    },
+    {
+        "type": "text",
+        "text": "Fact 3. Let $V$ and $V ^ { \\prime }$ be finite-dimensional subspaces of $L ^ { 2 } ( \\mathbb { R } ^ { n } )$ and $L ^ { 2 } ( \\mathbb { R } ^ { n \\prime } )$ respectively, and define $U { \\subset } L ^ { 2 } ( \\mathbb { R } ^ { n } \\times \\mathbb { R } ^ { n \\prime } )$ to be the subspace spanned by $\\{ ( \\mathbf { x } _ { 1 } , \\mathbf { x } _ { 2 } ) {  } p ( \\mathbf { x } _ { 1 } ) { \\cdot } p ^ { \\prime } ( \\mathbf { x } _ { 2 } ) : p { \\in } V , p ^ { \\prime } { \\in } V ^ { \\prime } \\}$ . Given $g { \\in } L ^ { 2 } ( \\mathbb { R } ^ { n } ) , \\mathsf { \\Gamma } _ { g } ^ { \\prime } { \\in } L ^ { 2 } ( \\mathbb { R } ^ { n ^ { \\prime } } )$ , consider the function $( \\mathbf { x } _ { 1 } , \\mathbf { x } _ { 2 } ) { \\mapsto } g ( \\mathbf { x } _ { 1 } ) { \\cdot } g ^ { \\prime } ( \\mathbf { x } _ { 2 } )$ in $L ^ { 2 } ( \\mathbb { R } ^ { n } \\times \\mathbb { R } ^ { n \\prime } )$ . This function belongs to $U ^ { \\perp }$ if $g { \\in } V ^ { \\bot }$ or $g ^ { \\prime } { \\in } V ^ { \\prime \\bot }$ . ",
+        "bbox": [
+            173,
+            401,
+            825,
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+        ],
+        "page_idx": 17
+    },
+    {
+        "type": "text",
+        "text": "Fact 4. If $g _ { 1 } . . . g _ { m } { \\in } L ^ { 2 } ( \\mathbb { R } ^ { n } )$ are linearly independent, then for any $k \\in \\mathbb { N } ,$ , the set of functions $\\begin{array} { r } { \\{ ( \\mathbf { x } _ { 1 } , \\ldots , \\mathbf { x } _ { k } ) \\mapsto \\prod _ { i = 1 } ^ { k } g _ { d _ { i } } ( \\mathbf { x } _ { i } ) \\} _ { d _ { 1 } \\ldots d _ { k } \\in [ m ] } } \\end{array}$ is linearly independent in $L ^ { 2 } ( ( \\mathbb { R } ^ { n } ) ^ { k } )$ . ",
+        "bbox": [
+            173,
+            462,
+            823,
+            492
+        ],
+        "page_idx": 17
+    },
+    {
+        "type": "text",
+        "text": "To facilitate application of the theory of $L ^ { 2 }$ spaces, we now make use of the assumption that the network’s representation functions $f _ { \\theta _ { d } }$ , as well as the functions $g _ { \\nu } , g _ { \\nu } ^ { \\prime }$ in the definition of separation rank (eq. 5), are measurable and square-integrable. Taking into account the expression given in eq. 2 for $h _ { y }$ , as well as fact 2 above, one readily sees that $f _ { \\theta _ { 1 } } . . . f _ { \\theta _ { M } } \\in L ^ { 2 } ( \\mathbb { R } ^ { s } )$ implies $h _ { y } { \\in } L ^ { 2 } ( ( \\mathbb { R } ^ { s } ) ^ { N } )$ . The separation rank $s e p ( h _ { y } ; I , J )$ will be the minimal non-negative integer $R$ such that there exist $g _ { 1 } . . . g _ { R } { \\in } L ^ { 2 } ( ( \\mathbb { R } ^ { s } ) ^ { | I | } )$ and $g _ { 1 } ^ { \\prime } . . . g _ { R } ^ { \\prime } { \\in } L ^ { 2 } ( ( \\mathbb { R } ^ { s } ) ^ { | J | } )$ for which: ",
+        "bbox": [
+            173,
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+        ],
+        "page_idx": 17
+    },
+    {
+        "type": "equation",
+        "img_path": "images/cea5ad848ea2f0d87e9679217e0a67df6d5986f04b72b4a21a19f781cb035bf8.jpg",
+        "text": "$$\nh _ { \\mathcal { Y } } \\big ( \\mathbf { x } _ { 1 } , \\ldots , \\mathbf { x } _ { N } \\big ) = \\sum _ { \\nu = 1 } ^ { R } g _ { \\nu } \\big ( \\mathbf { x } _ { 1 } , \\ldots , \\mathbf { x } _ { | I | } \\big ) g _ { \\nu } ^ { \\prime } \\big ( \\mathbf { x } _ { | I | + 1 } , \\ldots , \\mathbf { x } _ { N } \\big )\n$$",
+        "text_format": "latex",
+        "bbox": [
+            303,
+            590,
+            692,
+            616
+        ],
+        "page_idx": 17
+    },
+    {
+        "type": "text",
+        "text": "We would like to show that $s e p ( h _ { y } ; I , J ) \\ge r a n k \\perp ^ { y } \\perp ^ { } I , J$ . Our strategy for achieving this will be to start from eq. 12, and derive an expression for $\\mathbb { I } A ^ { y } \\mathbb { I } _ { I , J }$ J Kcomprising a sum of $R$ rank-1 matrices. As an initial step along J Kthis path, define the following finite-dimensional subspaces: ",
+        "bbox": [
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+            632,
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+        ],
+        "page_idx": 17
+    },
+    {
+        "type": "equation",
+        "img_path": "images/5f059092eee86ed1d7bcf7f438298e82f5dc2165d696de45954f66b5cd0345db.jpg",
+        "text": "$$\n\\begin{array} { l l l l } { V } & { : = } & { s p a n \\left\\{ ( \\mathbf { x } _ { 1 } , \\dots , \\mathbf { x } _ { | I | } ) \\mapsto \\prod _ { i = 1 } ^ { | I | } f _ { \\theta _ { d _ { i } } } ( \\mathbf { x } _ { i } ) \\right\\} _ { d _ { 1 } \\dots d _ { | I | } \\in [ M ] } \\subset L ^ { 2 } \\left( ( \\mathbb { R } ^ { s } ) ^ { | I | } \\right) } \\\\ { V ^ { \\prime } } & { : = } & { s p a n \\left\\{ ( \\mathbf { x } _ { 1 } , \\dots , \\mathbf { x } _ { | J | } ) \\mapsto \\prod _ { i = 1 } ^ { | J | } f _ { \\theta _ { d _ { i } } } ( \\mathbf { x } _ { i } ) \\right\\} _ { d _ { 1 } \\dots d _ { | J | } \\in [ M ] } \\subset L ^ { 2 } \\left( ( \\mathbb { R } ^ { s } ) ^ { | J | } \\right) } \\\\ { U } & { : = } & { s p a n \\left\\{ ( \\mathbf { x } _ { 1 } , \\dots , \\mathbf { x } _ { N } ) \\mapsto \\prod _ { i = 1 } ^ { N } f _ { \\theta _ { d _ { i } } } ( \\mathbf { x } _ { i } ) \\right\\} _ { d _ { 1 } \\dots d _ { N } \\in [ M ] } \\subset L ^ { 2 } \\left( ( \\mathbb { R } ^ { s } ) ^ { N } \\right) } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            238,
+            683,
+            754,
+            786
+        ],
+        "page_idx": 17
+    },
+    {
+        "type": "text",
+        "text": "Notice that $h _ { y } { \\in } U$ (eq. 2), and that $U$ is the span of products from $V$ and $V ^ { \\prime }$ , i.e.: ",
+        "bbox": [
+            174,
+            796,
+            651,
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+        ],
+        "page_idx": 17
+    },
+    {
+        "type": "equation",
+        "img_path": "images/9809ba6147964ad7ea97a5aa957b54c95d80154ce136f6b4daa1f04cf68bbab8.jpg",
+        "text": "$$\nU = s p a n \\{ ( \\mathbf { x } _ { 1 } , \\ldots , \\mathbf { x } _ { N } ) { \\overset {  } { \\to } } p ( \\mathbf { x } _ { 1 } , \\ldots , \\mathbf { x } _ { | I | } ) \\cdot p ^ { \\prime } ( \\mathbf { x } _ { | I | + 1 } , \\ldots , \\mathbf { x } _ { N } ) : p { \\in } V , p ^ { \\prime } { \\in } V ^ { \\prime } \\}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            256,
+            820,
+            740,
+            839
+        ],
+        "page_idx": 17
+    },
+    {
+        "type": "text",
+        "text": "Returning to eq. 12, we apply fact 1 to obtain orthogonal decompositions of $g 1 . . . g _ { R }$ w.r.t. $V$ , and of $g _ { 1 } ^ { \\prime } . . . g _ { R } ^ { \\prime }$ w.r.t. $V ^ { \\prime }$ . This gives $p _ { 1 } . . . p _ { R } { \\in } V$ , $\\delta _ { 1 } . . . \\delta _ { R } \\in V ^ { \\perp }$ , ${ p _ { 1 } ^ { \\prime } . . . p _ { R } ^ { \\prime } } { \\in } V ^ { \\prime }$ and $\\delta _ { 1 } ^ { \\prime } . . . \\delta _ { R } ^ { \\prime } \\in V ^ { \\prime \\perp }$ , such that $g _ { \\nu } = p _ { \\nu } + \\delta _ { \\nu }$ an d ",
+        "bbox": [
+            173,
+            851,
+            826,
+            878
+        ],
+        "page_idx": 17
+    },
+    {
+        "type": "text",
+        "text": "$g _ { \\nu } ^ { \\prime } = p _ { \\nu } ^ { \\prime } + \\delta _ { \\nu } ^ { \\prime }$ for every $\\nu \\in [ R ]$ . Plug this into eq. 12: ",
+        "bbox": [
+            173,
+            103,
+            495,
+            119
+        ],
+        "page_idx": 18
+    },
+    {
+        "type": "equation",
+        "img_path": "images/fcea37cb31726ba8ca340818e77cdf6baf2c407e4fb2dbebf5312d18d5b6d41a.jpg",
+        "text": "$$\n\\begin{array} { r c l } { { h _ { y } ( { \\bf x } { \\bf x } _ { 1 } , \\ldots , { \\bf x } { \\bf x } ) } } & { { = } } & { { \\sum _ { \\nu = 1 } ^ { R } g _ { \\nu } ( { \\bf x } { \\bf _ { 1 } } , \\ldots , { \\bf x } _ { | I | } ) \\cdot g _ { \\nu } ^ { \\prime } ( { \\bf x } | _ { I | + 1 } , \\ldots , { \\bf x } , { \\bf x } ) } } \\\\ { { } } & { { = } } & { { \\displaystyle \\sum _ { \\nu = 1 } ^ { R } \\left( p _ { \\nu } ( { \\bf x } _ { 1 } , \\ldots , { \\bf x } _ { | I | } ) + \\delta _ { \\nu } ( { \\bf x } _ { 1 } , \\ldots , { \\bf x } _ { | I | } ) \\right) } } \\\\ { { } } & { { } } & { { \\displaystyle \\cdot \\left( p _ { \\nu } ^ { \\prime } ( { \\bf x } _ { | I | + 1 } , \\ldots , { \\bf x } _ { N } ) + \\delta _ { \\nu } ^ { \\prime } ( { \\bf x } _ { | I | + 1 } , \\ldots , { \\bf x } _ { N } ) \\right) } } \\\\ { { } } & { { = } } & { { \\displaystyle \\sum _ { \\nu = 1 } ^ { R } p _ { \\nu } ( { \\bf x } _ { 1 } , \\ldots , { \\bf x } _ { | I | } ) \\cdot p _ { \\nu } ^ { \\prime } ( { \\bf x } _ { | I | + 1 } , \\ldots , { \\bf x } _ { N } ) } } \\\\ { { } } & { { } } & { { \\displaystyle + \\sum _ { \\nu = 1 } ^ { R } p _ { \\nu } ( { \\bf x } _ { 1 } , \\ldots , { \\bf x } _ { | I | } ) \\cdot \\delta _ { \\nu } ^ { \\prime } ( { \\bf x } _ { | I | + 1 } , \\ldots , { \\bf x } _ { N } ) } } \\\\ { { } } & { { } } & { { \\displaystyle + \\sum _ { \\nu = 1 } ^ { R } \\delta _ { \\nu } ( { \\bf x } _ { 1 } , \\ldots , { \\bf x } _ { | I | } ) \\cdot p _ { \\nu } ^ { \\prime } ( { \\bf x } _ { | I | + 1 } , \\ldots , { \\bf x } _ { N } ) } } \\\\ { { } } & { { } } &   \\displaystyle + \\sum _ { \\nu = 1 } ^ { R } \\delta _ { \\nu } ( { \\bf x } _ { 1 } , \\ldots , { \\bf x } _ { | I | } ) \\cdot p _ { \\nu } ^ { \\prime } ( { \\bf x } _  | I | + 1 \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            254,
+            125,
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+            299
+        ],
+        "page_idx": 18
+    },
+    {
+        "type": "text",
+        "text": "Given that $U$ is the span of products from $V$ and $V ^ { \\prime }$ (eq. 16), and that $p _ { \\nu } { \\in } V , { \\delta } _ { \\nu } { \\in } V ^ { \\perp } , p _ { \\nu } ^ { \\prime } { \\in } V ^ { \\prime } , { \\delta } _ { \\nu } ^ { \\prime } { \\in } V ^ { \\prime \\perp }$ , one readily sees that the first term in the latter expression belongs to $U$ , while, according to fact 3, the second, third and fourth terms are orthogonal to $U$ . We thus obtained an orthogonal decomposition of $h _ { y }$ w.r.t. $U$ . Since $h _ { y }$ is contained in $U$ , the orthogonal component must vanish (fact 1), and we amount at: ",
+        "bbox": [
+            173,
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+        ],
+        "page_idx": 18
+    },
+    {
+        "type": "equation",
+        "img_path": "images/ec04f5f1b615fd258bb63012fdc05067624d38378401c6a99d342756e0d7c0b2.jpg",
+        "text": "$$\nh _ { y } ( \\mathbf { x } _ { 1 } , \\ldots , \\mathbf { x } _ { N } ) = \\sum _ { \\nu = 1 } ^ { R } p _ { \\nu } ( \\mathbf { x } _ { 1 } , \\ldots , \\mathbf { x } _ { | I | } ) { \\cdot } p _ { \\nu } ^ { \\prime } ( \\mathbf { x } _ { | I | + 1 } , \\ldots , \\mathbf { x } _ { N } )\n$$",
+        "text_format": "latex",
+        "bbox": [
+            302,
+            359,
+            694,
+            385
+        ],
+        "page_idx": 18
+    },
+    {
+        "type": "text",
+        "text": "For every $\\nu \\in [ R ]$ , let $B ^ { \\nu }$ and $\\mathcal { C } ^ { \\nu }$ be coefficient tensors of $p _ { \\nu }$ and $p _ { \\nu } ^ { \\prime }$ w.r.t. the functions that span $V$ and $V ^ { \\prime }$ (eq. 13 and 14), respectively. Put formally, $B ^ { \\nu }$ and $\\mathcal { C } ^ { \\nu }$ are tensors of orders $| I |$ and $| J |$ (respectively), with dimension $M$ in each mode, meeting: ",
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+        "page_idx": 18
+    },
+    {
+        "type": "equation",
+        "img_path": "images/2d619e3f73241ab453d72905801bef3bf8dc5084028fc540aab4ff5fcbecfc04.jpg",
+        "text": "$$\n\\begin{array} { r c l } { { p _ { \\nu } ( { \\bf x } _ { 1 } , \\ldots , { \\bf x } _ { | I | } ) } } & { { = } } & { { \\sum _ { d _ { 1 } \\ldots d _ { | I | } = 1 } ^ { M } { \\mathcal B } _ { d _ { 1 } \\ldots d _ { | I | } } ^ { \\nu } \\prod _ { i = 1 } ^ { | I | } f _ { \\theta _ { d _ { i } } } ( { \\bf x } _ { i } ) } } \\\\ { { p _ { \\nu } ^ { \\prime } ( { \\bf x } _ { 1 } , \\ldots , { \\bf x } _ { | J | } ) } } & { { = } } & { { \\sum _ { d _ { 1 } \\ldots d _ { | J | } = 1 } ^ { M } { \\mathcal C } _ { d _ { 1 } \\ldots d _ { | J | } } ^ { \\nu } \\prod _ { i = 1 } ^ { | J | } f _ { \\theta _ { d _ { i } } } ( { \\bf x } _ { i } ) } } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            303,
+            433,
+            692,
+            494
+        ],
+        "page_idx": 18
+    },
+    {
+        "type": "text",
+        "text": "Substitute into eq. 17: ",
+        "bbox": [
+            173,
+            497,
+            305,
+            511
+        ],
+        "page_idx": 18
+    },
+    {
+        "type": "equation",
+        "img_path": "images/00acac0ccd7b074894a1888030daff76753d113ab2e74c17954dc5392ea6a106.jpg",
+        "text": "$$\n\\begin{array} { r c l } { { h _ { y } \\left( { \\bf x } _ { 1 } , \\ldots , { \\bf x } _ { N } \\right) } } & { { = } } & { { \\displaystyle \\sum _ { \\nu = 1 } ^ { R } \\left( \\sum _ { d _ { 1 } \\ldots d _ { | I | } = 1 } ^ { M } \\mathcal { B } _ { d _ { 1 } \\ldots d _ { | I | } } ^ { \\nu } \\prod _ { i = 1 } ^ { | I | } f _ { \\theta _ { d _ { i } } \\left( { \\bf x } _ { i } \\right) } \\right) } } \\\\ { { } } & { { } } & { { \\displaystyle \\cdot \\left( \\sum _ { d _ { | I | + 1 } \\ldots d _ { N } = 1 } ^ { M } \\mathcal { C } _ { d _ { | I | + 1 } \\ldots d _ { N } } ^ { \\nu } \\prod _ { i = | I | + 1 } ^ { N } f _ { \\theta _ { d _ { i } } \\left( { \\bf x } _ { i } \\right) } \\right) } } \\\\ { { } } & { { = } } & { { \\displaystyle \\sum _ { \\nu = 1 } ^ { R } \\sum _ { d _ { 1 } \\ldots d _ { N } = 1 } ^ { M } \\mathcal { B } _ { d _ { 1 } \\ldots d _ { | I | } } ^ { \\nu } \\cdot \\mathcal { C } _ { d _ { | I | + 1 } \\ldots d _ { N } } ^ { \\nu } \\prod _ { i = 1 } ^ { N } f _ { \\theta _ { d _ { i } } \\left( { \\bf x } _ { i } \\right) } } } \\\\ { { } } & { { = } } & { { \\displaystyle \\sum _ { d _ { 1 } \\ldots d _ { N } = 1 } ^ { M } \\left( \\sum _ { \\nu = 1 } ^ { R } \\mathcal { B } _ { d _ { 1 } \\ldots d _ { | I | } } ^ { \\nu } \\cdot \\mathcal { C } _ { d _ { | I | + 1 } \\ldots d _ { N } } ^ { \\nu } \\right) \\prod _ { i = 1 } ^ { N } f _ { \\theta _ { d _ { i } } \\left( { \\bf x } _ { i } \\right) } } } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            232,
+            516,
+            761,
+            637
+        ],
+        "page_idx": 18
+    },
+    {
+        "type": "text",
+        "text": "Compare this expression for $h _ { y }$ to that given in eq. 2: ",
+        "bbox": [
+            173,
+            638,
+            488,
+            654
+        ],
+        "page_idx": 18
+    },
+    {
+        "type": "equation",
+        "img_path": "images/544cc44a54746b523809993ab655ea33857dce48806364f1ba13ead1c7c72681.jpg",
+        "text": "$$\n\\sum _ { d _ { 1 } . . . d _ { N } = 1 } ^ { M } \\left( \\sum _ { \\nu = 1 } ^ { R } \\mathcal { B } _ { d _ { 1 } . . . d _ { | I | } } ^ { \\nu } \\cdot \\mathcal { C } _ { d _ { | I | + 1 } . . . d _ { N } } ^ { \\nu } \\right) \\prod _ { i = 1 } ^ { N } f _ { \\theta _ { d _ { i } } } ( \\mathbf { x } _ { i } ) = \\sum _ { d _ { 1 } . . . d _ { N } = 1 } ^ { M } \\mathcal { A } _ { d _ { 1 } . . . d _ { N } } ^ { y } \\prod _ { i = 1 } ^ { N } f _ { \\theta _ { d _ { i } } } ( \\mathbf { x } _ { i } )\n$$",
+        "text_format": "latex",
+        "bbox": [
+            181,
+            657,
+            816,
+            685
+        ],
+        "page_idx": 18
+    },
+    {
+        "type": "text",
+        "text": "At this point we utilize the given linear independence of $f _ { \\theta _ { 1 } } . . . f _ { \\theta _ { M } } \\in L ^ { 2 } ( \\mathbb { R } ^ { s } )$ , from which it follows (fact 4) that the functions spanning $U$ (eq. 15) are linearly independent in $L ^ { 2 } ( ( \\mathbb { R } ^ { s } ) ^ { N } )$ . Both sides of eq. 18 are linear combinations of these functions, thus their coefficients must coincide: ",
+        "bbox": [
+            174,
+            694,
+            826,
+            734
+        ],
+        "page_idx": 18
+    },
+    {
+        "type": "equation",
+        "img_path": "images/aa4efd24e98a8858dea42a7ae11a74b435c53317bbbeaf09b7e6f659bc204665.jpg",
+        "text": "$$\n\\mathcal { A } _ { d _ { 1 } . . . d _ { N } } ^ { y } = \\sum _ { \\nu = 1 } ^ { R } \\mathcal { B } _ { d _ { 1 } . . . d _ { | I | } } ^ { \\nu } \\cdot \\mathcal { C } _ { d _ { | I | + 1 } . . . d _ { N } } ^ { \\nu } , \\forall d _ { 1 } . . . d _ { N } \\in [ M ] \\iff \\mathcal { A } ^ { y } = \\sum _ { \\nu = 1 } ^ { R } \\mathcal { B } ^ { \\nu } \\otimes \\mathcal { C } ^ { \\nu }\n$$",
+        "text_format": "latex",
+        "bbox": [
+            218,
+            738,
+            779,
+            765
+        ],
+        "page_idx": 18
+    },
+    {
+        "type": "text",
+        "text": "Matricizing the tensor equation on the right w.r.t. $( I , J )$ gives: ",
+        "bbox": [
+            174,
+            768,
+            542,
+            784
+        ],
+        "page_idx": 18
+    },
+    {
+        "type": "equation",
+        "img_path": "images/e0f9944d6cfd5f5b816fc302d47d6308be52bf61e511db2e9507fdfa1b7a9ff7.jpg",
+        "text": "$$\n\\begin{array} { l l l } { [ A ^ { y } ] _ { I , J } } & { = } & { \\left[ \\sum _ { \\nu = 1 } ^ { R } B ^ { \\nu } \\otimes { \\mathcal C } ^ { \\nu } \\right] _ { I , J } } \\\\ & { = } & { \\sum _ { \\nu = 1 } ^ { R } [ | B ^ { \\nu } \\otimes { \\mathcal C } ^ { \\nu } ] _ { I , J } } \\\\ & { = } & { \\sum _ { \\nu = 1 } ^ { R } [ | B ^ { \\nu } | ] _ { I \\cap [ | I | ] , J \\cap [ | I | ] } \\odot [ { \\mathcal C } ^ { \\nu } ] _ { ( I - | I | ) \\cap [ | J | ] , ( J - | I | ) \\cap [ | J | ] } } \\\\ & { = } & { \\sum _ { \\nu = 1 } ^ { R } [ | B ^ { \\nu } ] _ { [ | I | ] , \\emptyset } \\odot [ | { \\mathcal C } ^ { \\nu } ] _ { \\mathcal { \\theta } , [ | J | ] } } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            277,
+            787,
+            717,
+            896
+        ],
+        "page_idx": 18
+    },
+    {
+        "type": "text",
+        "text": "where the second equality is based on the linearity of the matricization operator, the third equality relies on the relation in eq. 1, and the last equality makes use of the assumption $I = \\stackrel { \\cdot } { \\{ 1 , \\dotsc , | I | \\} } , J = \\stackrel { \\cdot } { \\{ | I | \\stackrel { \\cdot } { + } 1 , \\dotsc , N \\} }$ . ",
+        "bbox": [
+            171,
+            897,
+            826,
+            924
+        ],
+        "page_idx": 18
+    },
+    {
+        "type": "text",
+        "text": "For every $\\nu \\in [ R ]$ , $\\mathbb { [ } B ^ { \\nu } \\mathbb { ] } _ { [ | I | ] , \\emptyset }$ is a column vector of dimension $M ^ { | I | }$ and $\\mathbb { [ } \\mathcal { C } ^ { \\nu } ] _ { \\| , [ | J | ] }$ is a row vector of dimension $M ^ { | J | }$ J K. Denoting these by $\\mathbf { u } _ { \\nu }$ and $\\mathbf { v } _ { \\nu } ^ { \\top }$ respectively, we may write: ",
+        "bbox": [
+            171,
+            102,
+            823,
+            133
+        ],
+        "page_idx": 19
+    },
+    {
+        "type": "equation",
+        "img_path": "images/11d21a19803ea253e646737f391efbe6dd66c497374bf3a3e93e3341d423f75d.jpg",
+        "text": "$$\n\\mathbb { I } \\boldsymbol { \\mathcal { A } } ^ { y } \\mathbb { I } _ { I , J } = \\sum _ { \\nu = 1 } ^ { R } \\mathbf { u } _ { \\nu } \\mathbf { v } _ { \\nu } ^ { \\top }\n$$",
+        "text_format": "latex",
+        "bbox": [
+            419,
+            141,
+            576,
+            167
+        ],
+        "page_idx": 19
+    },
+    {
+        "type": "text",
+        "text": "This shows that $r a n k \\mathbb { [ } \\mathbf { \\mathcal { A } } ^ { y } \\mathbb { ] } _ { I , J \\leq R }$ . Since $R$ is a general non-negative integer that admits eq. 12, we may take J Kit to be minimal, i.e. to be equal to $s e p ( h _ { y } ; I , J )$ – the separation rank of $h _ { y }$ w.r.t. $( I , J )$ . By this we obtain $r a n k \\ [ \\mathcal { A } ^ { y } \\ ] _ { I , J } \\leq s e p ( h _ { y } ; I , J )$ , which is what we set out to prove. ",
+        "bbox": [
+            173,
+            175,
+            825,
+            214
+        ],
+        "page_idx": 19
+    },
+    {
+        "type": "text",
+        "text": "A.2 PROOF OF CLAIM 2 ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            252,
+            351,
+            265
+        ],
+        "page_idx": 19
+    },
+    {
+        "type": "text",
+        "text": "The claim is framed in measure theoretical terms, and in accordance, so will its proof be. While a complete introduction to measure theory is beyond our scope (the interested reader is referred to Jones (2001)), we briefly convey here the intuition behind the concepts we will be using, as well as facts we rely upon. The Lebesgue measure is defined over sets in a Euclidean space, and may be interpreted as quantifying their “volume”. For example, the Lebesgue measure of a unit hypercube is one, of the entire space is infinity, and of a finite set of points is zero. In this context, when a phenomenon is said to occur almost everywhere, it means that the set of points in which it does not occur has Lebesgue measure zero, i.e. is negligible. An important result we will make use of (proven in Caron and Traynor (2005) for example) is the following. Given a polynomial defined over $_ n$ real variables, the set of points in $\\mathbb { R } ^ { n }$ on which it vanishes is either the entire space (when the polynomial in question is the zero polynomial), or it must have Lebesgue measure zero. In other words, if a polynomial is not identically zero, it must be different from zero almost everywhere. ",
+        "bbox": [
+            173,
+            276,
+            825,
+            417
+        ],
+        "page_idx": 19
+    },
+    {
+        "type": "text",
+        "text": "Heading on to the proof, we recall from sec. 3 that the entries of the coefficient tensor $\\mathcal { A } ^ { y }$ (eq. 2) are given by polynomials in the network’s conv weights $\\{ \\mathbf { a } ^ { l , \\gamma } \\} _ { l , \\gamma }$ and output weights $\\mathbf { a } ^ { L , y }$ . Since $\\mathbb { I } A ^ { y } \\mathbb { I } _ { I , J }$ – the matricization of $\\mathcal { A } ^ { y }$ w.r.t. the partition $( I , J )$ J K, is merely a rearrangement of the tensor as a matrix, this matrix too has entries given by polynomials in the network’s linear weights. Now, denote by $r$ the maximal rank taken by $\\mathbb { I } A ^ { y } \\mathbb { I } _ { I , J }$ as network weights vary, and consider a specific setting of weights for which this rank is J Kattained. We may assume without loss of generality that under this setting, the top-left $r$ -by- $\\mathbfit { \\nabla } \\cdot \\mathbfit { r }$ block of $\\mathbb { I } A ^ { y } \\mathbb { I } _ { I , J }$ is non-singular. The corresponding minor, i.e. the determinant of the sub-matrix $( \\mathbb { I } \\boldsymbol { \\mathcal { A } } ^ { y } \\mathbb { \\bar { I } } _ { I , J } ) _ { 1 : r , 1 : r }$ J K, is thus a polynomial defined over $\\{ \\mathbf { a } ^ { l , \\gamma } \\} _ { l , \\gamma }$ and $\\mathbf { a } ^ { L , y }$ which is not identically zero. In light of the above, this polynomial is different from zero almost everywhere, implying that $r a n k ( \\mathbb { [ } \\mathcal { A ^ { y } ] ] } _ { I , J } ) _ { 1 : r , 1 : r } = r$ almost everywhere. Since $r a n k \\mathbb { [ } \\mathcal { A } ^ { y } ] \\rvert _ { I , J } \\ge r a n k ( \\mathbb { [ } \\mathcal { A } ^ { y } \\mathbb { ] } \\rvert _ { I , J } ) _ { 1 : r , 1 : r }$ , and since by definition $r$ J K is the maximal rank that $\\mathbb { I } \\boldsymbol { \\mathcal { A } } ^ { y } \\mathbb { I } _ { I , J }$ can take, we Jhave that $r a n k \\ [ \\boldsymbol { \\mathcal { A } } ^ { y } ] ] _ { I , J }$ Kis maximal almost everywhere. ",
+        "bbox": [
+            173,
+            422,
+            825,
+            565
+        ],
+        "page_idx": 19
+    },
+    {
+        "type": "text",
+        "text": "A.3 PROOF OF THEOREM 1 ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            603,
+            372,
+            616
+        ],
+        "page_idx": 19
+    },
+    {
+        "type": "text",
+        "text": "The matrix decomposition in eq. 7 expresses $\\mathbb { I } \\mathbb { A } \\mathbb { I } _ { I , J }$ in terms of the network’s linear weights – $\\{ \\mathbf { a } ^ { 0 , \\gamma } ~ \\in$ $\\mathbb { R } ^ { M } \\} _ { \\gamma \\in [ r _ { 0 } ] }$ Jfor conv operator in hidden layer 0, $\\{ \\mathbf { a } ^ { l , \\gamma } \\ \\in \\ \\mathbb { R } ^ { r _ { l - 1 } } \\} _ { \\gamma \\in [ r _ { l } ] }$ for conv operator in hidden layer $l = 1 . . . L - 1$ , and $\\mathbf { a } ^ { L , y } \\in \\mathbb { R } ^ { r _ { L - 1 } }$ for node $y$ of dense output operator. We prove lower and upper bounds on the maximal rank that $\\mathbb { I } A \\mathbb { I } _ { I , J }$ can take as these weights vary. Our proof relies on the rank-multiplicative property J Kof the Kronecker product $( r a n k ( A @ B ) = r a n k ( A ) { \\cdot } r a n k ( B )$ for any real matrices $A$ and $B -$ see Bellman (1970) for proof), but is otherwise elementary. ",
+        "bbox": [
+            173,
+            627,
+            825,
+            709
+        ],
+        "page_idx": 19
+    },
+    {
+        "type": "text",
+        "text": "Beginning with the lower bound, consider the following weight setting $\\scriptstyle ( \\mathbf { e } _ { \\gamma }$ here stands for a vector holding 1 in entry $\\gamma$ and 0 at all other entries, 0 stands for a vector holding 0 at all entries, and 1 stands for a vector holding 1 at all entries, with the dimension of a vector to be understood by context): ",
+        "bbox": [
+            173,
+            715,
+            823,
+            753
+        ],
+        "page_idx": 19
+    },
+    {
+        "type": "equation",
+        "img_path": "images/9f3854a63c947c03c21655bf21296d524b1141a4815860fa03120f531fb8b009.jpg",
+        "text": "$$\n\\begin{array} { r c l } { { \\mathbf a ^ { 0 , \\gamma } } } & { { = } } & { { \\left\\{ \\begin{array} { l l } { { \\mathbf e _ { \\gamma } } } & { { , \\gamma \\leq \\operatorname* { m i n } \\{ r _ { 0 } , M \\} } } \\\\ { { \\mathbf 0 } } & { { , \\mathrm { o t h e r w i s e } } } \\end{array} \\right. } } \\\\ { { \\mathbf a ^ { 1 , \\gamma } } } & { { = } } & { { \\left\\{ \\begin{array} { l l } { { \\mathbf 1 } } & { { , \\gamma = 1 } } \\\\ { { \\mathbf 0 } } & { { , \\mathrm { o t h e r w i s e } } } \\end{array} \\right. } } \\\\ { { \\mathbf a ^ { l , \\gamma } } } & { { = } } & { { \\left\\{ \\begin{array} { l l } { { \\mathbf e _ { 1 } } } & { { , \\gamma = 1 } } \\\\ { { \\mathbf 0 } } & { { , \\mathrm { o t h e r w i s e } } } \\end{array} \\right. \\mathrm { f o r } \\ l = 2 . . . L - 1 } } \\\\ { { \\mathbf a ^ { L , y } } } & { { = } } & { { \\mathbf e _ { 1 } } } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            343,
+            762,
+            655,
+            877
+        ],
+        "page_idx": 19
+    },
+    {
+        "type": "text",
+        "text": "Let $n \\in [ N / 4 ]$ . Recalling the definition of $I _ { l , k }$ and $J _ { l , k }$ from eq. 6, consider the sets $I _ { 1 , n }$ and $J _ { 1 , n }$ , as well as $I _ { 0 , 4 ( n - 1 ) + t }$ and $J _ { 0 , 4 ( n - 1 ) + t }$ for $t \\in [ 4 ]$ . $\\left( I _ { 1 , n } , J _ { 1 , n } \\right)$ is a partition of [4], i.e. $I _ { 1 , n } \\cup J _ { 1 , n } = [ 4 ]$ , and for every $t \\in$ [4] we have $I _ { 0 , 4 ( n - 1 ) + t } = \\{ 1 \\}$ and $J _ { 0 , 4 ( n - 1 ) + t } = \\emptyset$ if $t$ belongs to $I _ { 1 , n }$ , and otherwise $\\mathbf { \\tilde { \\Gamma } } _ { I _ { 0 , 4 ( n - 1 ) + t } } = \\tilde { \\varnothing }$ ",
+        "bbox": [
+            174,
+            885,
+            823,
+            926
+        ],
+        "page_idx": 19
+    },
+    {
+        "type": "text",
+        "text": "and $J _ { 0 , 4 ( n - 1 ) + t } = \\{ 1 \\}$ if $t$ belongs to $J _ { 1 , n }$ . This implies that for an arbitrary vector $\\mathbf { v }$ , the matricization $\\left[ \\left[ \\mathbf { v } \\right] \\right] I _ { 0 , 4 ( n - 1 ) + t } , J _ { 0 , 4 ( n - 1 ) + t }$ is equal to $\\mathbf { v }$ if $t \\in { \\cal I } _ { 1 , n }$ , and to $\\mathbf { v } ^ { \\top }$ if $t \\in J _ { 1 , n }$ . Accordingly, for any $\\gamma \\in [ r _ { 0 } ]$ : ",
+        "bbox": [
+            168,
+            103,
+            825,
+            135
+        ],
+        "page_idx": 20
+    },
+    {
+        "type": "equation",
+        "img_path": "images/4b8ecc71483cf5dfa86c4eda54183b94018dbfc527499a780a7d1707377bea95.jpg",
+        "text": "$$\n\\underset { t = 1 } { \\overset { ( \\ b { \\Omega } ) } { \\subset } } \\Vert \\mathbf { a } ^ { 0 , \\gamma } \\Vert _ { I _ { 0 , 4 ( n - 1 ) + t } , J _ { 0 , 4 ( n - 1 ) + t } } = \\left\\{ \\begin{array} { l l } { \\left( \\mathbf { a } ^ { 0 , \\gamma } \\odot \\mathbf { a } ^ { 0 , \\gamma } \\odot \\mathbf { a } ^ { 0 , \\gamma } \\odot \\mathbf { a } ^ { 0 , \\gamma } \\odot \\mathbf { a } ^ { 0 , \\gamma } \\right) } & { , | I _ { 1 , n } | = 4 \\mid J _ { 1 , n } | = 0 } \\\\ { \\left( \\mathbf { a } ^ { 0 , \\gamma } \\odot \\mathbf { a } ^ { 0 , \\gamma } \\odot \\mathbf { a } ^ { 0 , \\gamma } \\right) ( \\mathbf { a } ^ { 0 , \\gamma } ) ^ { \\top } } & { , | I _ { 1 , n } | = 3 \\mid J _ { 1 , n } | = 1 } \\\\ { \\left( \\mathbf { a } ^ { 0 , \\gamma } \\odot \\mathbf { a } ^ { 0 , \\gamma } \\right) \\left( \\mathbf { a } ^ { 0 , \\gamma } \\odot \\mathbf { a } ^ { 0 , \\gamma } \\right) ^ { \\top } } & { , | I _ { 1 , n } | = 2 \\mid J _ { 1 , n } | = 2 } \\\\ { \\left( \\mathbf { a } ^ { 0 , \\gamma } \\right) \\left( \\mathbf { a } ^ { 0 , \\gamma } \\odot \\mathbf { a } ^ { 0 , \\gamma } \\odot \\mathbf { a } ^ { 0 , \\gamma } \\right) ^ { \\top } } & { , | I _ { 1 , n } | = 1 \\mid J _ { 1 , n } | = 3 } \\\\ { \\left( \\mathbf { a } ^ { 0 , \\gamma } \\odot \\mathbf { a } ^ { 0 , \\gamma } \\odot \\mathbf { a } ^ { 0 , \\gamma } \\odot \\mathbf { a } ^ { 0 , \\gamma } \\right) ^ { \\top } } & { , | I _ { 1 , n } | = 0 \\mid J _ { 1 , n } | = 4 } \\end{array} \\right.\n$$",
+        "text_format": "latex",
+        "bbox": [
+            205,
+            137,
+            782,
+            212
+        ],
+        "page_idx": 20
+    },
+    {
+        "type": "text",
+        "text": "Assume that $\\gamma \\leq \\operatorname* { m i n } \\{ r _ { 0 } , M \\}$ . By our setting $ { \\mathbf { a } } ^ { 0 , \\gamma } =  { \\mathbf { e } } _ { \\gamma }$ , so the above matrix holds 1 in a single entry and 0 in all the rest. Moreover, if the matrix is not a row or column vector, i.e. if both $I _ { 1 , n }$ and $J _ { 1 , n }$ are non-empty, the column index and row index of the entry holding 1 are both unique w.r.t. $\\gamma$ , i.e. they do not repeat as $\\gamma$ ranges over $1 \\ldots \\operatorname* { m i n } \\{ r _ { 0 } , M \\}$ . We thus have: ",
+        "bbox": [
+            176,
+            214,
+            823,
+            267
+        ],
+        "page_idx": 20
+    },
+    {
+        "type": "equation",
+        "img_path": "images/bc5af61495fb2981e55138bb2816107e0f5dd4a41be7c4c4226f448329f83bf2.jpg",
+        "text": "$$\nr a n k \\left( \\sum _ { \\gamma = 1 } ^ { \\operatorname* { m i n } \\{ r _ { 0 } , M \\} } \\underset { t = 1 } { \\overset { 4 } { \\odot } } \\mathbb { I } \\mathbf { a } ^ { 0 , \\gamma } \\mathbb { I } _ { I _ { 0 , 4 ( n - 1 ) + t } , J _ { 0 , 4 ( n - 1 ) + t } } \\right) = \\left\\{ \\begin{array} { l l } { \\operatorname* { m i n } \\{ r _ { 0 } , M \\} } & { , I _ { 1 , n } \\neq \\emptyset \\land J _ { 1 , n } \\neq \\emptyset } \\\\ { 1 } & { , I _ { 1 , n } = \\emptyset \\lor J _ { 1 , n } = \\emptyset } \\end{array} \\right.\n$$",
+        "text_format": "latex",
+        "bbox": [
+            186,
+            270,
+            800,
+            301
+        ],
+        "page_idx": 20
+    },
+    {
+        "type": "text",
+        "text": "Since we set $\\mathbf { a } ^ { 1 , 1 } = \\mathbf { 1 }$ and $\\mathbf { a } ^ { 0 , \\gamma } = \\mathbf { 0 }$ for $\\gamma > \\mathrm { m i n } \\{ r _ { 0 } , M \\}$ , we may write: ",
+        "bbox": [
+            176,
+            304,
+            616,
+            319
+        ],
+        "page_idx": 20
+    },
+    {
+        "type": "equation",
+        "img_path": "images/f365fb25e569803c7364b00010ec0a2d084686141f4bad9c803aabd6373c2dad.jpg",
+        "text": "$$\nr a n k \\left( \\sum _ { \\gamma = 1 } ^ { r _ { 0 } } a _ { \\gamma } ^ { 1 , 1 } \\cdot \\underbrace { \\stackrel { 4 } { \\longleftrightarrow } } _ { t = 1 } [ \\mathbf { a ^ { 0 , \\gamma } } ] I _ { 0 , 4 ( n - 1 ) + t } , J _ { 0 , 4 ( n - 1 ) + t } \\right) = \\left\\{ \\begin{array} { l l } { \\operatorname* { m i n } \\{ r _ { 0 } , M \\} } & { , I _ { 1 , n } \\neq \\emptyset \\wedge J _ { 1 , n } \\neq \\emptyset } \\\\ { 1 } & { , I _ { 1 , n } = \\emptyset \\vee J _ { 1 , n } = \\emptyset } \\end{array} \\right.\n$$",
+        "text_format": "latex",
+        "bbox": [
+            191,
+            321,
+            802,
+            354
+        ],
+        "page_idx": 20
+    },
+    {
+        "type": "text",
+        "text": "The latter matrix is by definition equal to $\\mathbb { [ } \\boldsymbol { \\phi } ^ { 1 , 1 } ] _ { I _ { 1 , n } , J _ { 1 , n } }$ (see top row of eq. 7), and so for every $n \\in [ N / 4 ]$ : ",
+        "bbox": [
+            171,
+            357,
+            810,
+            373
+        ],
+        "page_idx": 20
+    },
+    {
+        "type": "equation",
+        "img_path": "images/527f36642e552becb1402582f2da413624012e2cedd1befc3d08aa633aec7294.jpg",
+        "text": "$$\nr a n k \\left[ \\phi ^ { 1 , 1 } \\right] _ { I _ { 1 , n } , J _ { 1 , n } } = \\left\\{ \\begin{array} { l l } { \\operatorname* { m i n } \\{ r _ { 0 } , M \\} } & { , I _ { 1 , n } \\neq \\emptyset \\land J _ { 1 , n } \\neq \\emptyset } \\\\ { 1 } & { , I _ { 1 , n } = \\emptyset \\lor J _ { 1 , n } = \\emptyset } \\end{array} \\right.\n$$",
+        "text_format": "latex",
+        "bbox": [
+            292,
+            376,
+            697,
+            406
+        ],
+        "page_idx": 20
+    },
+    {
+        "type": "text",
+        "text": "Now, the fact that we set $\\mathbf { a } ^ { L , y } = \\mathbf { e } _ { 1 }$ and $\\mathbf { a } ^ { l , 1 } = \\mathbf { e } _ { 1 }$ for $l = 2 . . . L - 1$ , implies that the second to last levels of the decomposition in eq. 7 collapse to: ",
+        "bbox": [
+            171,
+            410,
+            826,
+            438
+        ],
+        "page_idx": 20
+    },
+    {
+        "type": "equation",
+        "img_path": "images/ddcd3032cabb9ab1e2293545e72f1fe2dd1fe8ad01085d23888b3e1d03f4cec3.jpg",
+        "text": "$$\n[ \\mathcal { A } ^ { y } ] ] _ { I , J } = \\underset { t = 1 } { \\overset { N / 4 } { \\odot } } [ \\left[ \\phi ^ { 1 , 1 } \\right] ] _ { I _ { 1 , t } , J _ { 1 , t } }\n$$",
+        "text_format": "latex",
+        "bbox": [
+            410,
+            441,
+            586,
+            469
+        ],
+        "page_idx": 20
+    },
+    {
+        "type": "text",
+        "text": "Applying the rank-multiplicative property of the Kronecker product, and plugging in eq. 20, we obtain: ",
+        "bbox": [
+            171,
+            473,
+            781,
+            487
+        ],
+        "page_idx": 20
+    },
+    {
+        "type": "equation",
+        "img_path": "images/d158093c0de645136752944fce7cb3ae6cf10e517dec496bd4ec595cf3da5959.jpg",
+        "text": "$$\nr a n k \\ [ \\boldsymbol { A } ^ { y } \\ ] _ { I , J } = \\prod _ { t = 1 } ^ { N / 4 } r a n k \\bigl [ \\boldsymbol { \\phi } ^ { 1 , 1 } \\bigr ] \\bigr | _ { I _ { 1 , t } , J _ { 1 , t } } = \\operatorname* { m i n } \\bigl \\{ r _ { 0 } , M \\bigr \\} ^ { S }\n$$",
+        "text_format": "latex",
+        "bbox": [
+            312,
+            489,
+            684,
+            515
+        ],
+        "page_idx": 20
+    },
+    {
+        "type": "text",
+        "text": "where $S : = | \\{ t \\in [ N / 4 ] : I _ { 1 , t } \\neq \\emptyset \\land J _ { 1 , t } \\neq \\emptyset \\} |$ . This equality holds for the specific weight setting we defined in eq. 19. Maximizing over all weight settings gives the sought after lower bound: ",
+        "bbox": [
+            173,
+            517,
+            821,
+            545
+        ],
+        "page_idx": 20
+    },
+    {
+        "type": "equation",
+        "img_path": "images/9eee5622517f899b0f9d088b219f7b25c1251af381fc94bd4726a82f32d0cdaa.jpg",
+        "text": "$$\n\\operatorname* { m a x } _ { \\{ \\mathbf { a } ^ { l , \\gamma } \\} _ { l , \\gamma } , \\mathbf { a } ^ { L , y } } r a n k \\ [ \\mathcal { A } ^ { y } ] _ { I , J } \\ge \\operatorname* { m i n } \\{ r _ { 0 } , M \\} ^ { S }\n$$",
+        "text_format": "latex",
+        "bbox": [
+            362,
+            547,
+            633,
+            573
+        ],
+        "page_idx": 20
+    },
+    {
+        "type": "text",
+        "text": "Moving on to the upper bound, we show by induction over $l = 1 . . . L - 1$ that for any $k \\in [ N / 4 ^ { l } ]$ and $\\gamma \\in [ r _ { l } ]$ , the rank of $\\mathbb { [ } \\phi ^ { l , \\gamma } \\ ] _ { I _ { l , k } , J _ { l , k } }$ is no greater than $c ^ { l , k }$ , regardless of the chosen weight setting. For the base case $l = 1$ Jwe have: ",
+        "bbox": [
+            173,
+            592,
+            825,
+            632
+        ],
+        "page_idx": 20
+    },
+    {
+        "type": "equation",
+        "img_path": "images/b6b8fb740131eb48233d497fd3b83e4e3d934193b80639f464ec450ca65c60d8.jpg",
+        "text": "$$\n\\begin{array} { r } { \\big [ \\phi ^ { { 1 } , \\gamma } \\big ] _ { I _ { 1 , k } , J _ { 1 , k } } = \\sum _ { \\alpha = 1 } ^ { r _ { 0 } } a _ { \\alpha } ^ { 1 , \\gamma } \\cdot \\underset { t = 1 } { \\overset { 4 } { \\odot } } \\big [ \\big [ \\mathbf { a } ^ { 0 , \\alpha } \\big ] \\big ] _ { I _ { 0 , 4 ( k - 1 ) + t } , J _ { 0 , 4 ( k - 1 ) + t } } } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            305,
+            628,
+            691,
+            656
+        ],
+        "page_idx": 20
+    },
+    {
+        "type": "text",
+        "text": "The $M ^ { | I _ { 1 , k } | }$ -by- $M ^ { | J _ { 1 , k } | }$ matrix $\\mathbb { [ } \\phi ^ { 1 , \\gamma } \\ ] _ { I _ { 1 , k } , J _ { 1 , k } }$ is given here as a sum of $r _ { 0 }$ rank-1 terms, thus obviously its rank is no greater than ${ \\operatorname* { m i n } \\{ M ^ { \\operatorname* { m i n } \\{ | I _ { 1 , k } | , | J _ { 1 , k } | \\} } , r _ { 0 } \\} }$ . Since by definition $c ^ { 0 , t } = 1$ for all $t \\in [ N ]$ , we may write: ",
+        "bbox": [
+            173,
+            659,
+            825,
+            700
+        ],
+        "page_idx": 20
+    },
+    {
+        "type": "equation",
+        "img_path": "images/00c925c8d662d892aa9c8b3e99a3113347fb79cd753dbce5f23075dec67646e2.jpg",
+        "text": "$$\nr a n k [ \\phi ^ { 1 , \\gamma } ] _ { I _ { 1 , k } , J _ { 1 , k } } \\leq \\operatorname* { m i n } \\left\\{ M ^ { \\operatorname* { m i n } \\{ | I _ { 1 , k } | , | J _ { 1 , k } | \\} } , r _ { 0 } \\prod _ { t = 1 } ^ { 4 } c ^ { 0 , 4 ( k - 1 ) + t } \\right\\}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            279,
+            696,
+            717,
+            722
+        ],
+        "page_idx": 20
+    },
+    {
+        "type": "text",
+        "text": "$c ^ { 1 , k }$ is defined by the right hand side of this inequality, so our inductive hypotheses holds for $l = 1$ . For $l > 1$ ",
+        "bbox": [
+            174,
+            724,
+            820,
+            738
+        ],
+        "page_idx": 20
+    },
+    {
+        "type": "equation",
+        "img_path": "images/f4da0d62e0b742f13611ccef00211901f647a1bd96752c6278d8f19948a9b1fe.jpg",
+        "text": "$$\n\\begin{array} { r } { \\mathbb { [ } \\phi ^ { l , \\gamma } ] _ { I _ { l , k } , J _ { l , k } } = \\sum _ { \\alpha = 1 } ^ { r _ { l - 1 } } a _ { \\alpha } ^ { l , \\gamma } \\cdot \\underset { t = 1 } { \\overset { 4 } { \\odot } } \\mathbb { [ } \\phi ^ { l - 1 , \\alpha } ] _ { I _ { l - 1 , 4 ( k - 1 ) + t } , J _ { l - 1 , 4 ( k - 1 ) + t } } } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            289,
+            742,
+            709,
+            768
+        ],
+        "page_idx": 20
+    },
+    {
+        "type": "text",
+        "text": "Taking ranks: ",
+        "bbox": [
+            173,
+            772,
+            256,
+            785
+        ],
+        "page_idx": 20
+    },
+    {
+        "type": "equation",
+        "img_path": "images/8e88b431d23adc6bcbdc4eaef6eb3cd171d88ad42880cabe5da52116e6ae67c5.jpg",
+        "text": "$$\n\\begin{array} { l c l } { r a n k [ \\phi ^ { l , \\gamma } ] _ { I _ { l , k } , J _ { l , k } } } & { = } & { r a n k \\left( \\sum _ { \\alpha = 1 } ^ { r _ { l - 1 } } a _ { \\alpha } ^ { l , \\gamma } \\cdot \\underset { t = 1 } { \\overset { \\ll } { \\prod } } [ \\phi ^ { l - 1 , \\alpha } ] _ { I _ { l - 1 , 4 ( k - 1 ) + t } , J _ { l - 1 , 4 ( k - 1 ) + t } } \\right) } \\\\ & { \\leq } & { \\sum _ { \\alpha = 1 } ^ { r _ { l - 1 } } r a n k \\left( \\underset { t = 1 } { \\overset { \\ll } { \\longrightarrow } } [ \\phi ^ { l - 1 , \\alpha } ] _ { I _ { l - 1 , 4 ( k - 1 ) + t } , J _ { l - 1 , 4 ( k - 1 ) + t } } \\right) } \\\\ & { = } & { \\sum _ { \\alpha = 1 } ^ { r _ { l - 1 } } \\prod _ { t = 1 } ^ { 4 } r a n k [ \\phi ^ { l - 1 , \\alpha } ] _ { I _ { l - 1 , 4 ( k - 1 ) + t } , J _ { l - 1 , 4 ( k - 1 ) + t } } } \\\\ & { \\leq } & { \\sum _ { \\alpha = 1 } ^ { r _ { l - 1 } } \\prod _ { t = 1 } ^ { 4 } c ^ { l - 1 , 4 ( k - 1 ) + t } } \\\\ & { = } & { r _ { l - 1 } \\prod _ { t = 1 } ^ { 4 } c ^ { l - 1 , 4 ( k - 1 ) + t } } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            230,
+            789,
+            766,
+            933
+        ],
+        "page_idx": 20
+    },
+    {
+        "type": "text",
+        "text": "where we used rank sub-additivity in the second line, the rank-multiplicative property of the Kronecker product in the third line, and our inductive hypotheses for $l - 1$ in the fourth line. Since the number rows and columns in $\\mathbb { [ } \\boldsymbol { \\phi } ^ { l , \\gamma } \\ ] _ { I _ { l , k } , J _ { l , k } }$ is $M ^ { | I _ { l , k } | }$ and $M ^ { | J _ { l , k } | }$ respectively, we may incorporate these terms into the inequality, obJtaining: ",
+        "bbox": [
+            173,
+            103,
+            825,
+            156
+        ],
+        "page_idx": 21
+    },
+    {
+        "type": "equation",
+        "img_path": "images/ff667c2f797635f3276034338400cd6e42ba7bd6b5fb04c574c0216ba8a0e3f2.jpg",
+        "text": "$$\nr a n k [ \\phi ^ { l , \\gamma } ] _ { I _ { l , k } , J _ { l , k } } \\leq \\operatorname* { m i n } \\left\\{ M ^ { \\operatorname* { m i n } \\{ | I _ { l , k } | , | J _ { l , k } | \\} } , r _ { l - 1 } \\prod _ { t = 1 } ^ { 4 } c ^ { l - 1 , 4 ( k - 1 ) + t } \\right\\}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            271,
+            155,
+            727,
+            180
+        ],
+        "page_idx": 21
+    },
+    {
+        "type": "text",
+        "text": "The right hand side here is equal to $c ^ { l , k }$ by definition, so our inductive hypotheses indeed holds for all $l =$ $1 \\ldots L - 1$ . To establish the sought after upper bound on the rank of $\\mathbb { I } A ^ { y } \\mathbb { I } _ { I , J }$ , we recall that the latter is given by: ",
+        "bbox": [
+            173,
+            181,
+            823,
+            220
+        ],
+        "page_idx": 21
+    },
+    {
+        "type": "equation",
+        "img_path": "images/02e36e7eff0624855bca2dce57aad575b0913fba9fe5f096287d2a6025fed5d0.jpg",
+        "text": "$$\n\\ [ \\mathcal { A } ^ { y } ] _ { I , J } = \\sum _ { \\alpha = 1 } ^ { r _ { L - 1 } } a _ { \\alpha } ^ { L , y } \\cdot \\underset { t = 1 } { \\overset { 4 } { \\odot } } [ [ \\phi ^ { L - 1 , \\alpha } ] ] _ { I _ { L - 1 , t } , J _ { L - 1 , t } }\n$$",
+        "text_format": "latex",
+        "bbox": [
+            338,
+            219,
+            656,
+            247
+        ],
+        "page_idx": 21
+    },
+    {
+        "type": "text",
+        "text": "Carry out a series of steps similar to before, while making use of our inductive hypotheses for $l = L - 1$ ",
+        "bbox": [
+            174,
+            247,
+            789,
+            261
+        ],
+        "page_idx": 21
+    },
+    {
+        "type": "equation",
+        "img_path": "images/6038fa8b15331a793e46e07dc2a32d571372b9402fe19df5414813647632d843.jpg",
+        "text": "$$\n\\begin{array} { l l l } { r a n k \\| A ^ { y } \\| _ { I , J } } & { = } & { r a n k \\left( \\sum _ { \\alpha = 1 } ^ { r _ { L - 1 } } a _ { \\alpha } ^ { L , y } \\cdot \\underset { i = 1 } { \\overset { \\llangle } { \\langle } } \\| \\phi ^ { L - 1 , \\alpha } \\| _ { I _ { L - 1 , t } , J _ { L - 1 , t } } \\right) } \\\\ & { \\leq } & { \\sum _ { \\alpha = 1 } ^ { r _ { L - 1 } } r a n k \\left( \\underset { i = 1 } { \\overset { \\llangle } { \\langle } } \\| \\phi ^ { L - 1 , \\alpha } \\| _ { I _ { L - 1 , t } , J _ { L - 1 , t } } \\right) } \\\\ & { = } & { \\sum _ { \\alpha = 1 } ^ { r _ { L - 1 } } \\prod _ { t = 1 } ^ { 4 } r a n k \\| \\phi ^ { L - 1 , \\alpha } \\| _ { I _ { L - 1 , t } , J _ { L - 1 , t } } } \\\\ & { \\leq } & { \\sum _ { \\alpha = 1 } ^ { r _ { L - 1 } } \\prod _ { t = 1 } ^ { 4 } c ^ { L - 1 , t } } \\\\ & { = } & { r L - 1 \\prod _ { t = 1 } ^ { 4 } c ^ { L - 1 , t } } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            279,
+            263,
+            717,
+            405
+        ],
+        "page_idx": 21
+    },
+    {
+        "type": "text",
+        "text": "Since $\\mathbb { I } A ^ { y } \\mathbb { I } _ { I , J }$ has $M ^ { \\left| I \\right| }$ rows and $M ^ { | J | }$ columns, we may include these terms in the inequality, thus reaching J Kthe upper bound we set out to prove. ",
+        "bbox": [
+            173,
+            407,
+            823,
+            434
+        ],
+        "page_idx": 21
+    },
+    {
+        "type": "text",
+        "text": "B SEPARATION RANK AND THE $L ^ { 2 }$ DISTANCE FROM SEPARABLE FUNCTIONS ",
+        "text_level": 1,
+        "bbox": [
+            173,
+            472,
+            818,
+            489
+        ],
+        "page_idx": 21
+    },
+    {
+        "type": "text",
+        "text": "Our analysis of correlations modeled by convolutional networks is based on the concept of separation rank, conveyed in sec. 4. When the separation rank of a function w.r.t. a partition of its input is equal to 1, the function is separable, meaning it does not model any interaction between sides of the partition. We argued that the higher the separation rank, the farther the function is from this situation, i.e. the stronger the correlation it induces between sides of the partition. In the current appendix we formalize this argument, by relating separation rank to the $L ^ { 2 }$ distance from the set of separable functions. We begin by defining and characterizing a normalized (scale invariant) version of this distance (app. B.1). It is then shown (app. B.2) that separation rank provides an upper bound on the normalized distance. Finally, a lower bound that applies to deep convolutional arithmetic circuits is derived (app. B.3), based on the lower bound for their separation ranks established in sec. 5.2. Together, these steps imply that our entire analysis, facilitated by upper and lower bounds on separation ranks of convolutional arithmetic circuits, can be interpreted as based on upper and lower bounds on (normalized) $L ^ { 2 }$ distances from separable functions. ",
+        "bbox": [
+            173,
+            502,
+            825,
+            655
+        ],
+        "page_idx": 21
+    },
+    {
+        "type": "text",
+        "text": "In the text hereafter, we assume familiarity of the reader with the contents of sec. 2, 3, 4, 5 and the proofs given in app. A. We also rely on basic knowledge in the topic of $L ^ { 2 }$ spaces (see discussion in app. A.1 for minimal background required in order to follow our arguments), as well as several results concerning singular values of matrices. In line with sec. 5, an assumption throughout this appendix is that all functions in question are measurable and square-integrable (i.e. belong to $L ^ { 2 }$ over the respective Euclidean space), and in app. B.3, we also make use of the fact that representation functions $( f _ { \\theta _ { d } } )$ of a convolutional arithmetic circuit can be regarded as linearly independent (see sec. 5.1). Finally, for convenience, we now fix $( I , J ) - \\mathrm { a n }$ arbitrary partition of $[ N ]$ . Specifically, $I$ and $J$ are disjoint subsets of $[ N ]$ whose union gives $[ N ]$ , denoted by $I = \\{ i _ { 1 } , \\ldots , i _ { | I | } \\}$ with $i _ { 1 } < \\cdots < i _ { | I | }$ , and $J = \\{ j _ { 1 } , \\dots , j _ { | J | } \\}$ with $j _ { 1 } < \\cdots < j _ { | J | }$ . ",
+        "bbox": [
+            173,
+            660,
+            825,
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+        ],
+        "page_idx": 21
+    },
+    {
+        "type": "text",
+        "text": "B.1 NORMALIZED $L ^ { 2 }$ DISTANCE FROM SEPARABLE FUNCTIONS ",
+        "text_level": 1,
+        "bbox": [
+            173,
+            790,
+            624,
+            806
+        ],
+        "page_idx": 21
+    },
+    {
+        "type": "text",
+        "text": "For a function $h { \\in } L ^ { 2 } ( ( \\mathbb { R } ^ { s } ) ^ { N } )$ (which is not identically zero), the normalized $L ^ { 2 }$ distance from the set of separable functions w.r.t. $( I , J )$ , is defined as follows: ",
+        "bbox": [
+            171,
+            815,
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+        ],
+        "page_idx": 21
+    },
+    {
+        "type": "equation",
+        "img_path": "images/b87dc8eea0d7a34480d0da97b1dc6a5d9f4d9785f6f6c1af9847f63f8fce19c9.jpg",
+        "text": "$$\nD ( h ; I , J ) : = \\frac { 1 } { | | h | | } \\cdot \\operatorname* { i n f } _ { g \\in L ^ { 2 } ( ( \\mathbb { R } ^ { \\delta } ) ^ { \\lfloor J \\rfloor } ) } \\left| \\left| h ( \\mathbf { x } _ { 1 } , \\dots , \\mathbf { x } _ { N } ) - g ( \\mathbf { x } _ { i _ { 1 } } , \\dots , \\mathbf { x } _ { i _ { | I | } } ) g ^ { \\prime } ( \\mathbf { x } _ { j _ { 1 } } , \\dots , \\mathbf { x } _ { j _ { | J | } } ) \\right| \\right|\n$$",
+        "text_format": "latex",
+        "bbox": [
+            223,
+            845,
+            776,
+            887
+        ],
+        "page_idx": 21
+    },
+    {
+        "type": "text",
+        "text": "where $\\left\\| \\cdot \\right\\|$ refers to the norm of $L ^ { 2 }$ space, e.g. $\\textstyle \\| h \\| : = ( \\int _ { ( \\mathbb { R } ^ { s } ) ^ { N } } h ^ { 2 } ) ^ { 1 / 2 }$ . In words, $D ( h ; I , J )$ is defined as the minimal $L ^ { 2 }$ distance between $h$ and a function that is separable w.r.t. $( I , J )$ , divided by the norm of $h$ . The normalization (division by $\\| h \\| )$ admits scale invariance to $D ( h ; I , J )$ , and is of critical importance – without it, rescaling $h$ would accordingly rescale the distance measure, rendering the latter uninformative in terms of deviation from separability. ",
+        "bbox": [
+            176,
+            891,
+            823,
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+        ],
+        "page_idx": 21
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            174,
+            103,
+            823,
+            143
+        ],
+        "page_idx": 22
+    },
+    {
+        "type": "text",
+        "text": "It is worthwhile noting the resemblance between $D ( h ; I , J )$ and the concept of mutual information (see Cover and Thomas (2012) for a comprehensive introduction). Both measures quantify the interaction that a normalized function 11 induces between input variables, by measuring distance from separable functions. The difference between the measures is threefold. First, mutual information considers probability density functions (non-negative and in $L ^ { 1 }$ ), while $D ( h ; I , J )$ applies to functions in $L ^ { 2 }$ . Second, the notion of distance in mutual information is quantified through the Kullback-Leibler divergence, whereas in $D ( h ; I , J )$ it is simply the $L ^ { 2 }$ metric. Third, while mutual information evaluates the distance from a specific separable function – product of marginal distributions, $D ( h ; I , J )$ evaluates the minimal distance across all separable functions. ",
+        "bbox": [
+            173,
+            148,
+            825,
+            252
+        ],
+        "page_idx": 22
+    },
+    {
+        "type": "text",
+        "text": "We now turn to establish a spectral characterization of $D ( h ; I , J )$ , which will be used in app. B.2 and B.3 for deriving upper and lower bounds (respectively). Assume we have the following expression for $h$ : ",
+        "bbox": [
+            173,
+            265,
+            823,
+            292
+        ],
+        "page_idx": 22
+    },
+    {
+        "type": "equation",
+        "img_path": "images/29e293f83152ec467348acea2e0dedfdcfb5b9e1a93207b9be3993266b51d600.jpg",
+        "text": "$$\nh ( { \\bf x } _ { 1 } , \\ldots , { \\bf x } _ { N } ) = \\sum _ { \\mu = 1 } ^ { m } \\sum _ { \\mu ^ { \\prime } = 1 } ^ { m ^ { \\prime } } A _ { \\mu , \\mu ^ { \\prime } } \\cdot \\phi _ { \\mu } ( { \\bf x } _ { i _ { 1 } } , \\ldots , { \\bf x } _ { i _ { | I | } } ) \\phi _ { \\mu ^ { \\prime } } ^ { \\prime } ( { \\bf x } _ { j _ { 1 } } , \\ldots , { \\bf x } _ { j _ { | J | } } )\n$$",
+        "text_format": "latex",
+        "bbox": [
+            254,
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+            327
+        ],
+        "page_idx": 22
+    },
+    {
+        "type": "text",
+        "text": "where $m$ and $m ^ { \\prime }$ are positive integers, $A$ is an $m$ -by- $m ^ { \\prime }$ real matrix, and $\\{ \\phi _ { \\mu } \\} _ { \\mu = 1 } ^ { m } , \\{ \\phi _ { \\mu ^ { \\prime } } ^ { \\prime } \\} _ { \\mu ^ { \\prime } = 1 } ^ { m ^ { \\prime } }$ are orthonormal sets of functions in $L ^ { 2 } ( ( \\mathbb { R } ^ { s } ) ^ { | I | } ) , L ^ { 2 } ( ( \\mathbb { R } ^ { s } ) ^ { | J | } )$ respectively. We refer to such expression as an orthonormal separable decomposition of $h$ , with $A$ being its coefficient matrix. We will show that for any orthonormal separable decomposition, $D ( h ; I , J )$ is given by the following formula: ",
+        "bbox": [
+            174,
+            335,
+            825,
+            392
+        ],
+        "page_idx": 22
+    },
+    {
+        "type": "equation",
+        "img_path": "images/43bba4be15493ad765da20116eb82f0af456c3a1a4d61dcc1eda7229ba0d52b6.jpg",
+        "text": "$$\nD ( h ; I , J ) = { \\sqrt { 1 - { \\frac { \\sigma _ { 1 } ^ { 2 } ( A ) } { \\sigma _ { 1 } ^ { 2 } ( A ) + \\cdots + \\sigma _ { \\operatorname* { m i n } \\{ m , m ^ { \\prime } \\} } } } ( A ) } }\n$$",
+        "text_format": "latex",
+        "bbox": [
+            338,
+            398,
+            660,
+            438
+        ],
+        "page_idx": 22
+    },
+    {
+        "type": "text",
+        "text": "where $\\sigma _ { 1 } ( A ) \\geq \\cdot \\cdot \\cdot \\geq \\sigma _ { \\operatorname* { m i n } \\{ m , m ^ { \\prime } \\} } ( A ) \\geq 0$ are the singular values of the coefficient matrix $A$ . This implies that if the largest singular value of $A$ accounts for a significant portion of the spectral energy, the normalized $L ^ { 2 }$ distance of $h$ from separable functions is small. On the other hand, if all but a fraction of the spectral energy is attributed to trailing singular values, $h$ is far from being separable $( D ( h ; I , J )$ is close to 1). ",
+        "bbox": [
+            174,
+            444,
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+            497
+        ],
+        "page_idx": 22
+    },
+    {
+        "type": "text",
+        "text": "As a first step in deriving eq. 23, we show that $\\| h \\| ^ { 2 } = \\sigma _ { 1 } ^ { 2 } ( A ) + \\cdot \\cdot \\cdot + \\sigma _ { \\operatorname* { m i n } \\{ m , m ^ { \\prime } \\} } ^ { 2 } ( A ) \\colon$ ",
+        "bbox": [
+            174,
+            511,
+            694,
+            527
+        ],
+        "page_idx": 22
+    },
+    {
+        "type": "equation",
+        "img_path": "images/22b6e8ec3f7f0efe607364152c4b0882eaa040a5c35aa4fc62703c3ede16e7fc.jpg",
+        "text": "$$\n\\begin{array} { r l r } { \\mathrm { d } t ^ { 2 } } & { = } & { \\int \\boldsymbol { \\mu } ^ { \\nu } ( \\mathbf { S } _ { \\mu \\nu } - \\mathbf { S } _ { \\nu \\mu } ) \\mathrm { d } \\mathbf { S } _ { \\nu \\mu } \\mathrm { d } t ^ { 2 } , } \\\\ & { \\in \\int \\left( \\sum _ { s ^ { \\prime } = - 1 } ^ { \\infty } \\sum _ { \\nu ^ { \\prime } = 1 } ^ { \\infty } A _ { \\mu \\nu } - \\boldsymbol { S } _ { \\nu \\mu } \\right) \\mathrm { d } s , } \\\\ & { \\in \\mathbb { R } ^ { 3 } \\sum _ { \\nu \\in \\mathcal { S } _ { \\mu \\nu } } \\sum _ { \\nu ^ { \\prime } = 1 } ^ { \\infty } A _ { \\mu \\nu } - \\boldsymbol { S } _ { \\nu \\mu } \\mathrm { d } s , } \\\\ & { \\in \\mathbb { R } ^ { 3 } \\sum _ { \\nu \\in \\mathcal { S } _ { \\mu \\nu } } \\sum _ { \\nu ^ { \\prime } = 1 } ^ { \\infty } A _ { \\mu \\nu } \\mathrm { d } s , } \\\\ & { \\in \\mathbb { R } ^ { 3 } \\sum _ { \\nu \\in \\mathcal { S } _ { \\mu \\nu } } \\sum _ { \\nu ^ { \\prime } = 1 } ^ { \\infty } A _ { \\mu \\nu } \\mathrm { d } s , } \\\\ & { \\in \\mathbb { R } ^ { 3 } \\sum _ { \\nu \\in \\mathcal { S } _ { \\mu \\nu } } \\sum _ { \\nu ^ { \\prime } = 1 } ^ { \\infty } A _ { \\mu \\nu } \\mathrm { d } s , } \\\\ & { = } & { \\int \\mathrm { e } ^ { \\mathrm { i } ( s ) } , } \\\\ &  \\frac { \\sum _ { s ^ { \\prime } = 1 } ^ { \\infty } \\sum _ { \\nu ^ { \\prime } = 1 } ^ { \\infty } \\sum _ { \\nu ^ { \\prime } = 1 } ^ { \\infty } A _ { \\mu \\nu ^ { \\prime } } \\mathrm { d } s , } \\\\ & { } & { \\mathrm { e } ^ { \\mathrm { i } ( s ) } , } \\\\ &  \\frac  \\sum _ { s ^ { \\prime } = 1 } ^ { \\infty } \\sum _ { \\nu ^ { \\prime } = 1 } ^ { \\infty } \\sum _ { \\nu ^ { \\prime } = 1 } ^ { \\infty } \\sum _ { \\nu ^ { \\prime } = 1 } ^ { \\infty } \\sum _ { \\nu ^ { \\prime } = 1 } ^ { \\infty } \\sum _ { \\nu ^ { \\prime } = 1 } ^ { \\infty } \\sum _ { \\nu ^ { \\prime } = 1 } ^ { \\infty } \\sum _ { \\nu ^ { \\prime } = 1 } ^ { \\infty } A _ { \\mu \\nu ^ { \\prime } } \\mathrm \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
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+            536,
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+        ],
+        "page_idx": 22
+    },
+    {
+        "type": "text",
+        "text": "Equality (1) here originates from the definition of $L ^ { 2 }$ norm. (2) is obtained by plugging in the expression in eq. 22. (3) is merely an arithmetic manipulation. (4) follows from the linearity of integration. (5) makes use of Fubini’s theorem (see Jones (2001)). (6) results from the orthonormality of $\\{ \\phi _ { \\mu } \\} _ { \\mu = 1 } ^ { m }$ and $\\{ \\phi _ { \\mu ^ { \\prime } } ^ { \\prime } \\} _ { \\mu ^ { \\prime } = 1 } ^ { m ^ { \\prime } }$ . (7) is a trivial computation. Finally, (8) is an outcome of the fact that the squared Frobenius norm of a matrix, i.e. the sum of squares over its entries, is equal to the sum of squares over its singular values (see Golub and Van Loan (2013) for proof). ",
+        "bbox": [
+            171,
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+            825,
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+        ],
+        "page_idx": 22
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            173,
+            103,
+            825,
+            157
+        ],
+        "page_idx": 23
+    },
+    {
+        "type": "text",
+        "text": "Let $g { \\in } L ^ { 2 } ( ( \\mathbb { R } ^ { s } ) ^ { | I | } )$ . By fact 1 in app. A.1, there exist scalars $\\alpha _ { 1 } \\ldots \\alpha _ { m } \\in \\mathbb { R }$ , and a function $\\delta { \\in } L ^ { 2 } ( ( \\mathbb { R } ^ { s } ) ^ { | I | } )$ orthogonal to sp $i n \\{ \\phi _ { 1 } \\ldots \\phi _ { m } \\}$ , such that $\\begin{array} { r } { g = \\sum _ { \\mu = 1 } ^ { m } \\alpha _ { \\mu } \\cdot \\phi _ { \\mu } + \\delta . } \\end{array}$ . Similarly, for any $g ^ { \\prime } { \\in } L ^ { 2 } ( ( \\mathbb { R } ^ { s } ) ^ { | J | } )$ there exist $\\alpha _ { 1 } ^ { \\prime } \\ldots \\alpha _ { m ^ { \\prime } } ^ { \\prime } \\in \\mathbb { R }$ and $\\delta ^ { \\prime } \\in s p a n \\{ \\phi _ { 1 } ^ { \\prime } \\ldots \\phi _ { m ^ { \\prime } } ^ { \\prime } \\} ^ { \\perp }$ such that $\\begin{array} { r } { g ^ { \\prime } = \\sum _ { \\mu ^ { \\prime } = 1 } ^ { m ^ { \\prime } } \\alpha _ { \\mu ^ { \\prime } } ^ { \\prime } \\cdot \\phi _ { \\mu ^ { \\prime } } ^ { \\prime } + \\delta ^ { \\prime } } \\end{array}$ . Fact 2 in app. A.1 indicates that the function given by $( \\mathbf { x } _ { 1 } , \\ldots , \\mathbf { x } _ { N } ) { \\mapsto } g ( \\mathbf { x } _ { i _ { 1 } } , \\ldots , \\mathbf { x } _ { i _ { | I | } } ) g ^ { \\prime } ( \\mathbf { x } _ { j _ { 1 } } , \\ldots , \\mathbf { x } _ { j _ { | J | } } )$ belongs to $L ^ { 2 } ( ( \\mathbb { R } ^ { s } ) ^ { N } )$ . We may express it as follows: ",
+        "bbox": [
+            173,
+            164,
+            825,
+            242
+        ],
+        "page_idx": 23
+    },
+    {
+        "type": "equation",
+        "img_path": "images/972ccdea83ccc1ccd87aebf245abe590ae7a3c66849d1557f13480c76887d26b.jpg",
+        "text": "$$\n\\begin{array} { r l r } { g ( { \\bf x } _ { i _ { 1 } } , \\ldots , { \\bf x } _ { i _ { | I | } } ) g ^ { \\prime } ( { \\bf x } _ { j _ { 1 } } , \\ldots , { \\bf x } _ { j _ { | J | } } ) } & { = } & { \\sum _ { \\mu = 1 } ^ { m } \\sum _ { \\mu ^ { \\prime } = 1 } ^ { m ^ { \\prime } } \\alpha _ { \\mu } \\alpha _ { \\mu ^ { \\prime } } ^ { \\prime } \\cdot \\phi _ { \\mu } ( { \\bf x } _ { i _ { 1 } } , \\ldots , { \\bf x } _ { i _ { | I | } } ) \\phi _ { \\mu ^ { \\prime } } ^ { \\prime } ( { \\bf x } _ { j _ { 1 } } , \\ldots , { \\bf x } _ { j _ { | J | } } ) } \\\\ & { } & { + \\left( \\sum _ { \\mu = 1 } ^ { m } \\alpha _ { \\mu } \\cdot \\phi _ { \\mu } ( { \\bf x } _ { i _ { 1 } } , \\ldots , { \\bf x } _ { i _ { | I | } } ) \\right) \\cdot \\delta ^ { \\prime } ( { \\bf x } _ { j _ { 1 } } , \\ldots , { \\bf x } _ { j _ { | J | } } ) } \\\\ & { } & { + \\delta ( { \\bf x } _ { i _ { 1 } } , \\ldots , { \\bf x } _ { i _ { | I | } } ) \\cdot \\left( \\sum _ { \\mu ^ { \\prime } = 1 } ^ { m ^ { \\prime } } \\alpha _ { \\mu ^ { \\prime } } ^ { \\prime } \\cdot \\phi _ { \\mu ^ { \\prime } } ^ { \\prime } ( { \\bf x } _ { j _ { 1 } } , \\ldots , { \\bf x } _ { j _ { | J | } } ) \\right) } \\\\ & { } & { + \\delta ( { \\bf x } _ { i _ { 1 } } , \\ldots , { \\bf x } _ { i _ { | I | } } ) \\delta ^ { \\prime } ( { \\bf x } _ { j _ { 1 } } , \\ldots , { \\bf x } _ { j _ { | J | } } ) } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            181,
+            242,
+            818,
+            352
+        ],
+        "page_idx": 23
+    },
+    {
+        "type": "text",
+        "text": "According to fact 3 in app. A.1, the second, third and fourth terms on the right hand side of the above are orthogonal to $s \\bar { p } a n \\{ ( { \\bf x } _ { 1 } , \\ldots , \\hat { \\bf x } _ { N } ) { \\mapsto } { \\phi } _ { \\mu } ( { \\bf x } _ { i _ { 1 } } , \\ldots , { \\bf x } _ { i _ { | I | } } ) { \\phi } _ { \\mu ^ { \\prime } } ^ { \\prime } ( { \\bf x } _ { j _ { 1 } } , \\ldots , { \\bf x } _ { j _ { | J | } } ) \\} _ { \\mu \\in [ m ] , \\mu ^ { \\prime } \\in [ m ^ { \\prime } ] } ,$ . Denote their summation by $\\mathcal { E } ( \\mathbf { x } _ { 1 } , \\ldots , \\mathbf { x } _ { N } )$ , and subtract the overall function from $h$ (given by eq. 22): ",
+        "bbox": [
+            174,
+            352,
+            820,
+            393
+        ],
+        "page_idx": 23
+    },
+    {
+        "type": "equation",
+        "img_path": "images/2a93730259be61a1af17a786609ffddd9d11f8a62459ef2344bd6c21da194138.jpg",
+        "text": "$$\n\\begin{array} { r l } & { h ( { \\mathbf x } _ { 1 } , \\ldots , { \\mathbf x } _ { N } ) - g ( { \\mathbf x } _ { i _ { 1 } } , \\ldots , { \\mathbf x } _ { i _ { | I | } } ) g ^ { \\prime } ( { \\mathbf x } _ { j _ { 1 } } , \\ldots , { \\mathbf x } _ { j _ { | J | } } ) } \\\\ & { \\qquad = \\sum _ { \\mu = 1 } ^ { m } \\sum _ { \\mu ^ { \\prime } = 1 } ^ { m ^ { \\prime } } A _ { \\mu , \\mu ^ { \\prime } } \\cdot \\phi _ { \\mu } ( { \\mathbf x } _ { i _ { 1 } } , \\ldots , { \\mathbf x } _ { i _ { | I | } } ) \\phi _ { \\mu ^ { \\prime } } ^ { \\prime } ( { \\mathbf x } _ { j _ { 1 } } , \\ldots , { \\mathbf x } _ { j _ { | J | } } ) } \\\\ & { \\qquad - \\sum _ { \\mu = 1 } ^ { m } \\sum _ { \\mu ^ { \\prime } = 1 } ^ { m ^ { \\prime } } \\alpha _ { \\mu } \\alpha _ { \\mu ^ { \\prime } } ^ { \\prime } \\cdot \\phi _ { \\mu } ( { \\mathbf x } _ { i _ { 1 } } , \\ldots , { \\mathbf x } _ { i _ { | I | } } ) \\phi _ { \\mu ^ { \\prime } } ^ { \\prime } ( { \\mathbf x } _ { j _ { 1 } } , \\ldots , { \\mathbf x } _ { j _ { | J | } } ) - \\mathcal { E } ( { \\mathbf x } _ { 1 } , \\ldots , { \\mathbf x } _ { N } ) } \\\\ & { \\qquad = \\sum _ { \\mu = 1 } ^ { m } \\sum _ { \\mu ^ { \\prime } = 1 } ^ { m ^ { \\prime } } ( A _ { \\mu , \\mu ^ { \\prime } } - \\alpha _ { \\mu } \\alpha _ { \\mu ^ { \\prime } } ^ { \\prime } ) \\cdot \\phi _ { \\mu } ( { \\mathbf x } _ { i _ { 1 } } , \\ldots , { \\mathbf x } _ { i _ { | I | } } ) \\phi _ { \\mu ^ { \\prime } } ^ { \\prime } ( { \\mathbf x } _ { j _ { 1 } } , \\ldots , { \\mathbf x } _ { j _ { | J | } } ) - \\mathcal { E } ( { \\mathbf x } _ { 1 } , \\ldots , { \\mathbf x } _ { N } ) } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            204,
+            393,
+            830,
+            502
+        ],
+        "page_idx": 23
+    },
+    {
+        "type": "text",
+        "text": "Since the two terms in the latter expression are orthogonal to one another, we have: ",
+        "bbox": [
+            173,
+            501,
+            665,
+            515
+        ],
+        "page_idx": 23
+    },
+    {
+        "type": "equation",
+        "img_path": "images/7c78b57fd3cb5232861db7dc5d54b23ca163e7c02869e163910f917118d46943.jpg",
+        "text": "$$\n\\begin{array} { r l } & { \\left\\| h ( \\mathbf x _ { 1 } , \\dots , \\mathbf x _ { N } ) - g ( \\mathbf x _ { i _ { 1 } } , \\dots , \\mathbf x _ { i _ { | I | } } ) g ^ { \\prime } ( \\mathbf x _ { j _ { 1 } } , \\dots , \\mathbf x _ { j _ { | J | } } ) \\right\\| ^ { 2 } } \\\\ & { \\quad = \\left\\| \\sum _ { \\mu = 1 } ^ { m } \\sum _ { \\mu ^ { \\prime } = 1 } ^ { m ^ { \\prime } } ( A _ { \\mu , \\mu ^ { \\prime } } - \\alpha _ { \\mu } \\alpha _ { \\mu ^ { \\prime } } ^ { \\prime } ) \\cdot \\phi _ { \\mu } ( \\mathbf x _ { i _ { 1 } } , \\dots , \\mathbf x _ { i _ { | I | } } ) \\phi _ { \\mu ^ { \\prime } } ^ { \\prime } ( \\mathbf x _ { j _ { 1 } } , \\dots , \\mathbf x _ { j _ { | J | } } ) \\right\\| ^ { 2 } + \\| \\mathcal E ( \\mathbf x _ { 1 } , \\dots , \\mathbf x _ { N } ) \\| ^ { 2 } } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            181,
+            517,
+            821,
+            579
+        ],
+        "page_idx": 23
+    },
+    {
+        "type": "text",
+        "text": "Applying a sequence of steps as in eq. 24 to the first term in the second line of the above, we obtain: ",
+        "bbox": [
+            171,
+            579,
+            766,
+            593
+        ],
+        "page_idx": 23
+    },
+    {
+        "type": "equation",
+        "img_path": "images/822c91ee9dc1b05a89f49c6dd8b17db3f02aa30792013d27f0511da8789c97b3.jpg",
+        "text": "$$\n\\left| h ( { \\bf x } _ { 1 } , \\ldots , { \\bf x } _ { N } ) - g ( { \\bf x } _ { i _ { 1 } } , \\ldots , { \\bf x } _ { i _ { | I | } } ) g ^ { \\prime } ( { \\bf x } _ { j _ { 1 } } , \\ldots , { \\bf x } _ { j _ { | I | } } ) \\right| ^ { 2 } = \\sum _ { \\mu = 1 } ^ { m } \\sum _ { \\mu ^ { \\prime } = 1 } ^ { m ^ { \\prime } } ( A _ { \\mu , \\mu ^ { \\prime } } - \\alpha _ { \\mu } \\alpha _ { \\mu ^ { \\prime } } ^ { \\prime } ) ^ { 2 } + \\| \\mathcal E ( { \\bf x } _ { 1 } , \\ldots , { \\bf x } _ { N } ) \\| ^ { 2 }\n$$",
+        "text_format": "latex",
+        "bbox": [
+            181,
+            594,
+            826,
+            638
+        ],
+        "page_idx": 23
+    },
+    {
+        "type": "text",
+        "text": "$\\mathcal { E } ( { \\bf x } _ { 1 } , . . . , { \\bf x } _ { N } ) = 0$ if $\\delta$ and $\\delta ^ { \\prime }$ are the zero functions, implying that: ",
+        "bbox": [
+            171,
+            640,
+            580,
+            655
+        ],
+        "page_idx": 23
+    },
+    {
+        "type": "equation",
+        "img_path": "images/d9feebaf1d53a53b551f48cc62100e04a01b9e1cf77f01ff6329eb0f310030d8.jpg",
+        "text": "$$\n\\left\\| h ( { \\bf x } _ { 1 } , \\ldots , { \\bf x } _ { N } ) - g ( { \\bf x } _ { i _ { 1 } } , \\ldots , { \\bf x } _ { i _ { | I | } } ) g ^ { \\prime } ( { \\bf x } _ { j _ { 1 } } , \\ldots , { \\bf x } _ { j _ { | J | } } ) \\right\\| ^ { 2 } \\geq \\sum _ { \\mu = 1 } ^ { m } \\sum _ { \\mu ^ { \\prime } = 1 } ^ { m ^ { \\prime } } ( A _ { \\mu , \\mu ^ { \\prime } } - \\alpha _ { \\mu } \\alpha _ { \\mu ^ { \\prime } } ^ { \\prime } ) ^ { 2 }\n$$",
+        "text_format": "latex",
+        "bbox": [
+            210,
+            657,
+            785,
+            685
+        ],
+        "page_idx": 23
+    },
+    {
+        "type": "text",
+        "text": "with equality holding if $\\begin{array} { r } { g = \\sum _ { \\mu = 1 } ^ { m } \\alpha _ { \\mu } \\cdot \\phi _ { \\mu } } \\end{array}$ and $\\begin{array} { r } { g ^ { \\prime } = \\sum _ { \\mu ^ { \\prime } = 1 } ^ { m ^ { \\prime } } \\alpha _ { \\mu ^ { \\prime } } ^ { \\prime } \\cdot \\phi _ { \\mu ^ { \\prime } } ^ { \\prime } } \\end{array}$ . Now, $\\begin{array} { r } { \\sum _ { \\mu = 1 } ^ { m } \\sum _ { \\mu ^ { \\prime } = 1 } ^ { m ^ { \\prime } } ( A _ { \\mu , \\mu ^ { \\prime } } - \\alpha _ { \\mu } \\alpha _ { \\mu ^ { \\prime } } ^ { \\prime } ) ^ { 2 } } \\end{array}$ is the squared Frobenius distance between the matrix $A$ and the rank-1 matrix $\\pmb { \\alpha } \\pmb { \\alpha } ^ { \\prime \\top }$ , where $_ { \\pmb { \\alpha } }$ and $\\mathbf { \\Delta } _ { \\mathbf { { \\alpha } } \\mathbf { { \\alpha } } } ^ { \\prime }$ are column vectors holding $\\alpha _ { 1 } \\ldots \\alpha _ { m }$ and $\\alpha _ { 1 } ^ { \\prime } \\ldots \\alpha _ { m ^ { \\prime } } ^ { \\prime }$ respectively. This squared distance is greater than or equal to the sum of squares over the second to last singular values of $A$ , and moreover, the inequality holds with equality for proper choices of $_ { \\pmb { \\alpha } }$ and $\\mathbf { \\Delta } _ { \\mathbf { { \\alpha } } \\mathbf { { \\alpha } } } ^ { \\prime }$ (Eckart and Young (1936)). From this we conclude that: ",
+        "bbox": [
+            173,
+            689,
+            825,
+            760
+        ],
+        "page_idx": 23
+    },
+    {
+        "type": "equation",
+        "img_path": "images/b9ad47b9166ec6f9fa2cc4850d4b2abac78485286b1de4fffe9415df5de02e1b.jpg",
+        "text": "$$\n\\begin{array} { r } { \\left| \\left| h ( \\mathbf { x } _ { 1 } , \\ldots , \\mathbf { x } _ { N } ) - g ( \\mathbf { x } _ { i _ { 1 } } , \\ldots , \\mathbf { x } _ { i _ { | I | } } ) g ^ { \\prime } ( \\mathbf { x } _ { j _ { 1 } } , \\ldots , \\mathbf { x } _ { j _ { | J | } } ) \\right| \\right| ^ { 2 } \\geq \\sigma _ { 2 } ^ { 2 } ( A ) + \\cdot \\cdot \\cdot + \\sigma _ { \\operatorname* { m i n } \\{ m , m ^ { \\prime } \\} } ^ { 2 } ( A ) } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            220,
+            762,
+            776,
+            787
+        ],
+        "page_idx": 23
+    },
+    {
+        "type": "text",
+        "text": "with equality holding if $g$ and $g ^ { \\prime }$ are set to $\\scriptstyle \\sum _ { \\mu = 1 } ^ { m } \\alpha _ { \\mu } \\cdot \\phi _ { \\mu }$ and $\\scriptstyle \\sum _ { \\mu ^ { \\prime } = 1 } ^ { m ^ { \\prime } } \\alpha _ { \\mu ^ { \\prime } } ^ { \\prime } \\cdot \\phi _ { \\mu ^ { \\prime } } ^ { \\prime }$ (respectively) for proper choices of $\\alpha _ { 1 } \\ldots \\alpha _ { m }$ and $\\alpha _ { 1 } ^ { \\prime } \\ldots \\alpha _ { m ^ { \\prime } } ^ { \\prime }$ . We thus have the infimum over all possible $g , g ^ { \\prime }$ : ",
+        "bbox": [
+            173,
+            791,
+            823,
+            823
+        ],
+        "page_idx": 23
+    },
+    {
+        "type": "equation",
+        "img_path": "images/50609ae38b6dc980893592e633fb3ac8039ee6a4670c04bf2001d3a7989995ff.jpg",
+        "text": "$$\n \\underset { g \\in L ^ { 2 } ( \\mathbb { R } ^ { 3 } ) ^ { | \\mathcal { I } | } } { \\operatorname* { i n f } } | | h ( \\mathbf { x } _ { 1 } , \\ldots , \\mathbf { x } _ { N } ) - g ( \\mathbf { x } _ { i _ { 1 } } , \\ldots , \\mathbf { x } _ { i _ { | I | } } ) g ^ { \\prime } ( \\mathbf { x } _ { j _ { 1 } } , \\ldots , \\mathbf { x } _ { j _ { | J | } } ) | | ^ { 2 } = \\sigma _ { 2 } ^ { 2 } ( A ) + \\cdot \\cdot \\cdot + \\sigma _ { \\operatorname* { m i n } \\{ m , m ^ { \\prime } \\} } ^ { 2 } ( A )\n$$",
+        "text_format": "latex",
+        "bbox": [
+            178,
+            824,
+            815,
+            867
+        ],
+        "page_idx": 23
+    },
+    {
+        "type": "text",
+        "text": "Recall that we would like to derive the formula in eq. 23 for $D ( h ; I , J )$ , assuming $h$ is given by the orthonormal separable decomposition in eq. 22. Taking square root of the equalities established in eq. 24 and 25, and plugging them into the definition of $D ( h ; I , J )$ (eq. 21), we obtain the sought after result. ",
+        "bbox": [
+            174,
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+            825,
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+        ],
+        "page_idx": 23
+    },
+    {
+        "type": "text",
+        "text": "B.2 UPPER BOUND THROUGH SEPARATION RANK ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            103,
+            526,
+            118
+        ],
+        "page_idx": 24
+    },
+    {
+        "type": "text",
+        "text": "We now relate $D ( h ; I , J )$ – the normalized $L ^ { 2 }$ distance of $h { \\in } L ^ { 2 } ( ( \\mathbb { R } ^ { s } ) ^ { N } )$ from the set of separable functions w.r.t. $( I , J )$ (eq. 21), to $s e p  ( h ; I , J )$ – the separation rank of $h$ w.r.t. $( I , J )$ (eq. 5). Specifically, we make use of the formula in eq. 23 to derive an upper bound on $D ( h ; I , J )$ in terms of $s e p  ( h ; I , J )$ . ",
+        "bbox": [
+            173,
+            127,
+            825,
+            169
+        ],
+        "page_idx": 24
+    },
+    {
+        "type": "text",
+        "text": "Assuming $h$ has finite separation rank (otherwise the bound we derive is trivial), we may express it as: ",
+        "bbox": [
+            169,
+            172,
+            776,
+            188
+        ],
+        "page_idx": 24
+    },
+    {
+        "type": "equation",
+        "img_path": "images/084d7317fd9c83994a5f68eccf0748ef6101a00ba8f30a24d1687115b3c212be.jpg",
+        "text": "$$\nh ( { \\bf x } _ { 1 } , \\ldots , { \\bf x } _ { N } ) = \\sum _ { \\nu = 1 } ^ { R } g _ { \\nu } ( { \\bf x } _ { i _ { 1 } } , \\ldots , { \\bf x } _ { i _ { | I | } } ) g _ { \\nu } ^ { \\prime } ( { \\bf x } _ { j _ { 1 } } , \\ldots , { \\bf x } _ { j _ { | J | } } )\n$$",
+        "text_format": "latex",
+        "bbox": [
+            307,
+            194,
+            691,
+            220
+        ],
+        "page_idx": 24
+    },
+    {
+        "type": "text",
+        "text": "where $R$ is some positive integer (necessarily greater than or equal to $s e p ( h ; I , J ) )$ , and $g _ { 1 } . . . g _ { R } { \\in } L ^ { 2 } ( ( \\mathbb { R } ^ { s } ) ^ { | I | } )$ , $g _ { 1 } ^ { \\prime } . . . g _ { R } ^ { \\prime } { \\in } L ^ { 2 } ( ( \\mathbb { R } ^ { s } ) ^ { | J | } )$ . Let $\\{ \\phi _ { 1 } , . . . , \\phi _ { m } \\} { \\subset } L ^ { 2 } ( ( \\mathbb { R } ^ { s } ) ^ { | I | } )$ and $\\{ \\phi _ { 1 } ^ { \\prime } , . . . , \\phi _ { m ^ { \\prime } } ^ { \\prime } \\} { \\subset } L ^ { 2 } ( ( \\mathbb { R } ^ { s } ) ^ { | J | } )$ be two sets of orthery mal functionthere exist $s p a n \\{ g _ { 1 } . . . g _ { R } \\}$ $s p a n \\{ g _ { 1 } ^ { \\prime } . . . g _ { R } ^ { \\prime } \\}$ respectch that r ev-and $\\nu { \\in } R$ $\\alpha _ { \\nu , 1 } \\ldots \\alpha _ { \\nu , m } \\ \\in \\mathbb { R }$ $\\alpha _ { \\nu , 1 } ^ { \\prime } \\ldots \\alpha _ { \\nu , m ^ { \\prime } } ^ { \\prime } \\ \\in \\mathbb { R }$ $\\begin{array} { r } { g _ { \\nu } = \\sum _ { \\mu = 1 } ^ { m } \\alpha _ { \\nu , \\mu } \\cdot \\phi _ { \\mu } } \\end{array}$ $\\begin{array} { r } { g _ { \\nu } ^ { \\prime } = \\sum _ { \\mu ^ { \\prime } = 1 } ^ { m ^ { \\prime } } \\alpha _ { \\nu , \\mu ^ { \\prime } } ^ { \\prime } \\cdot \\phi _ { \\mu ^ { \\prime } } ^ { \\prime } } \\end{array}$ . Plugging this into eq. 26, we obtain: ",
+        "bbox": [
+            173,
+            228,
+            825,
+            303
+        ],
+        "page_idx": 24
+    },
+    {
+        "type": "equation",
+        "img_path": "images/beadf34b2407927707b4bed021c1f40ae53fd437bfe3e0694d07605efa66010d.jpg",
+        "text": "$$\nh ( { \\bf x } _ { 1 } , . . . , { \\bf x } _ { N } ) = \\sum _ { \\mu = 1 } ^ { m } \\sum _ { \\mu ^ { \\prime } = 1 } ^ { m ^ { \\prime } } \\left( \\sum _ { \\nu = 1 } ^ { R } \\alpha _ { \\nu , \\mu } \\alpha _ { \\nu , \\mu ^ { \\prime } } ^ { \\prime } \\right) \\cdot \\phi _ { \\mu } ( { \\bf x } _ { i _ { 1 } } , . . . , { \\bf x } _ { i _ { | I | } } ) \\phi _ { \\mu ^ { \\prime } } ^ { \\prime } ( { \\bf x } _ { j _ { 1 } } , . . . , { \\bf x } _ { j _ { | J | } } )\n$$",
+        "text_format": "latex",
+        "bbox": [
+            209,
+            310,
+            787,
+            339
+        ],
+        "page_idx": 24
+    },
+    {
+        "type": "text",
+        "text": "This is an orthonormal separable decomposition of $h$ (eq. 22), with coefficient matrix $\\begin{array} { r } { A = \\sum _ { \\nu = 1 } ^ { R } \\pmb { \\alpha } _ { \\nu } ( \\pmb { \\alpha } _ { \\nu } ^ { \\prime } ) ^ { \\top } } \\end{array}$ , where $\\pmb { \\alpha } _ { \\nu } : = [ \\alpha _ { \\nu , 1 } \\ldots \\alpha _ { \\nu , m } ] ^ { \\top }$ and $\\pmb { \\alpha } _ { \\nu } ^ { \\prime } : = [ \\alpha _ { \\nu , 1 } ^ { \\prime } \\ldots \\alpha _ { \\nu , m ^ { \\prime } } ^ { \\prime } ] ^ { \\top }$ for every $\\nu { \\in } R$ . Obviously the rank of $A$ is no greater than $R$ , implying: ",
+        "bbox": [
+            173,
+            347,
+            826,
+            388
+        ],
+        "page_idx": 24
+    },
+    {
+        "type": "equation",
+        "img_path": "images/0a2e529a3967b6bfc371cc58127a3d1b590aa77a7e56e23126d5fbdaa9b538b4.jpg",
+        "text": "$$\n\\frac { \\sigma _ { 1 } ^ { 2 } ( A ) } { \\sigma _ { 1 } ^ { 2 } ( A ) + \\cdots + \\sigma _ { \\operatorname* { m i n } \\{ m , m ^ { \\prime } \\} } ^ { 2 } ( A ) } \\geq \\frac { 1 } { R }\n$$",
+        "text_format": "latex",
+        "bbox": [
+            385,
+            386,
+            614,
+            421
+        ],
+        "page_idx": 24
+    },
+    {
+        "type": "text",
+        "text": "where as in app. B.1, $\\sigma _ { 1 } ( A ) \\geq \\cdot \\cdot \\cdot \\geq \\sigma _ { \\operatorname* { m i n } \\{ m , m ^ { \\prime } \\} } ( A ) \\geq 0$ stand for the singular values of $A$ . Introducing this inequality into eq. 23 gives: ",
+        "bbox": [
+            174,
+            424,
+            825,
+            452
+        ],
+        "page_idx": 24
+    },
+    {
+        "type": "equation",
+        "img_path": "images/29279ed8afb4d0f53ca41c102b1a18edbd673eaf0d7d7d894e623133f381fd0e.jpg",
+        "text": "$$\nD ( h ; I , J ) = { \\sqrt { 1 - { \\frac { \\sigma _ { 1 } ^ { 2 } ( A ) } { \\sigma _ { 1 } ^ { 2 } ( A ) + \\cdots + \\sigma _ { \\operatorname* { m i n } \\{ m , m ^ { \\prime } \\} } } ^ { ( A ) } } } } \\leq { \\sqrt { 1 - { \\frac { 1 } { R } } } }\n$$",
+        "text_format": "latex",
+        "bbox": [
+            299,
+            458,
+            699,
+            497
+        ],
+        "page_idx": 24
+    },
+    {
+        "type": "text",
+        "text": "The latter holds for any $R \\in \\mathbb N$ that admits eq. 26, so in particular we may take it to be minimal, i.e. to be equal to $s e p ( h ; I , J ) ~ ^ { 1 2 }$ , bringing forth the sought after upper bound: ",
+        "bbox": [
+            171,
+            503,
+            823,
+            530
+        ],
+        "page_idx": 24
+    },
+    {
+        "type": "equation",
+        "img_path": "images/6c2461b4b78f03105a662f1ee59ba578fc4f9fc63fcd30976389c1262ae04285.jpg",
+        "text": "$$\nD ( h ; I , J ) \\leq \\sqrt { 1 - \\frac { 1 } { s e p ( h ; I , J ) } }\n$$",
+        "text_format": "latex",
+        "bbox": [
+            397,
+            537,
+            602,
+            577
+        ],
+        "page_idx": 24
+    },
+    {
+        "type": "text",
+        "text": "By eq. 27, low separation rank implies proximity (in normalized $L ^ { 2 }$ sense) to a separable function. We may use the inequality to translate the upper bounds on separation ranks established for deep and shallow convolutional arithmetic circuits (sec. 5.2 and 5.3 respectively), into upper bounds on normalized $\\cdot ^ { 2 }$ distances from separable functions. To completely frame our analysis in terms of the latter measure, a translation of the lower bound on separation ranks of deep convolutional arithmetic circuits (sec. 5.2) is also required. Eq. 27 does not facilitate such translation, and in fact, it is easy to construct functions $h$ whose separation ranks are high yet are very close (in normalized $L ^ { 2 }$ sense) to separable functions. 13 However, as we show in app. B.3 below, the specific lower bound of interest can indeed be translated, and our analysis may entirely be framed in terms of normalized $L ^ { 2 }$ distance from separable functions. ",
+        "bbox": [
+            173,
+            590,
+            826,
+            707
+        ],
+        "page_idx": 24
+    },
+    {
+        "type": "text",
+        "text": "B.3 LOWER BOUND FOR DEEP CONVOLUTIONAL ARITHMETIC CIRCUITS ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            723,
+            684,
+            737
+        ],
+        "page_idx": 24
+    },
+    {
+        "type": "text",
+        "text": "Let $h _ { y } { \\in } L ^ { 2 } ( ( \\mathbb { R } ^ { s } ) ^ { N } )$ be a function realized by a deep convolutional arithmetic circuit (fig. 1(a) with size-4 pooling windows and $L = \\log _ { 4 } N$ hidden layers), i.e. $h _ { y }$ is given by eq. 2, where $f _ { \\theta _ { 1 } } . . . f _ { \\theta _ { M } } \\in L ^ { 2 } ( \\mathbb { R } ^ { s } )$ are linearly independent representation functions, and $\\mathcal { A } ^ { y }$ is a coefficient tensor of order $N$ and dimension $M$ in each mode, determined by the linear weights of the network $( \\{ \\mathbf { a } ^ { l , \\gamma } \\} _ { l , \\gamma } , \\mathbf { a } ^ { L , y } )$ through the hierarchical decomposition in eq. 3. Rearrange eq. 2 by grouping indexes $d _ { 1 } . . . d _ { N }$ in accordance with the partition $( I , J )$ : ",
+        "bbox": [
+            173,
+            747,
+            825,
+            813
+        ],
+        "page_idx": 24
+    },
+    {
+        "type": "equation",
+        "img_path": "images/4f2415e87ab1e160e114b32399c2e91eaeab6568433e0d1142ec992b92ac982c.jpg",
+        "text": "$$\nh _ { y } \\left( \\mathbf { x } _ { 1 } , . . . , \\mathbf { x } _ { N } \\right) = \\sum _ { d _ { i _ { 1 } } , . . . d _ { i _ { | I | } } = 1 } ^ { M } \\sum _ { d _ { j _ { 1 } } . . . d _ { j _ { | J | } } = 1 } ^ { M } \\mathcal { A } _ { d _ { 1 } . . . d _ { N } } ^ { y } \\cdot \\left( \\prod _ { t = 1 } ^ { | I | } f _ { \\theta _ { d _ { i _ { t } } } } ( \\mathbf { x } _ { i _ { t } } ) \\right) \\left( \\prod _ { t = 1 } ^ { | J | } f _ { \\theta _ { d _ { j _ { t } } } } ( \\mathbf { x } _ { j _ { t } } ) \\right)\n$$",
+        "text_format": "latex",
+        "bbox": [
+            181,
+            829,
+            818,
+            863
+        ],
+        "page_idx": 24
+    },
+    {
+        "type": "text",
+        "text": "Let $m = M ^ { \\lvert I \\rvert }$ , and define the following mapping: ",
+        "bbox": [
+            174,
+            103,
+            472,
+            118
+        ],
+        "page_idx": 25
+    },
+    {
+        "type": "equation",
+        "img_path": "images/4d0386f9c8419cdc53ef594644d9f15a14df9c3fd339d54799a2a5dc2f4056f2.jpg",
+        "text": "$$\n\\mu : [ M ] ^ { | I | }  [ m ] \\quad , \\quad \\mu ( d _ { i _ { 1 } } , \\ldots , d _ { i _ { | I | } } ) = 1 + \\sum _ { t = 1 } ^ { | I | } ( d _ { i _ { t } } - 1 ) \\cdot M ^ { | I | - t }\n$$",
+        "text_format": "latex",
+        "bbox": [
+            279,
+            122,
+            718,
+            148
+        ],
+        "page_idx": 25
+    },
+    {
+        "type": "text",
+        "text": "$\\mu$ is a one-to-one correspondence between the index sets $[ M ] ^ { | I | }$ and $[ m ]$ . We slightly abuse notation, and denote by $( d _ { i _ { 1 } } ( \\mu ) , \\ldots , d _ { i _ { | I | } } ( \\mu ) )$ the tuple in $[ M ] ^ { | I | }$ that maps to $\\mu \\in [ m ]$ . Additionally, we denote the function $\\prod _ { t = 1 } ^ { \\left| I \\right| } f _ { \\theta _ { d _ { t } ( \\mu ) } } \\left( \\mathbf { x } _ { i _ { t } } \\right)$ , which according to fact 2 in app. A.1 belongs to $L ^ { 2 } ( ( R ^ { s } ) ^ { \\left| I \\right| } )$ , by $\\phi _ { \\mu } ( \\mathbf { x } _ { i _ { 1 } } , \\ldots , \\mathbf { x } _ { i _ { | I | } } )$ . In the exact same manner, we let $m ^ { \\prime } = M ^ { \\vert J \\vert }$ , and define the bijective mapping: ",
+        "bbox": [
+            173,
+            151,
+            826,
+            218
+        ],
+        "page_idx": 25
+    },
+    {
+        "type": "equation",
+        "img_path": "images/cb72731811080a5b8c2c8e3de2ffd8f741e2e0da49b3eb0d17014ad4e30af2d2.jpg",
+        "text": "$$\n\\mu ^ { \\prime } : [ M ] ^ { | J | }  [ m ^ { \\prime } ] \\quad , \\quad \\mu ^ { \\prime } ( d _ { j _ { 1 } } , \\ldots , d _ { j _ { | J | } } ) = 1 + \\sum _ { t = 1 } ^ { | J | } ( d _ { j _ { t } } - 1 ) \\cdot M ^ { | J | - t }\n$$",
+        "text_format": "latex",
+        "bbox": [
+            269,
+            222,
+            727,
+            247
+        ],
+        "page_idx": 25
+    },
+    {
+        "type": "text",
+        "text": "As before, $( d _ { j 1 } ( \\mu ^ { \\prime } ) , \\dots , d _ { j _ { | J | } } ( \\mu ^ { \\prime } ) )$ stands for the tuple in $[ M ] ^ { | J | }$ that maps to $\\mu ^ { \\prime } \\in [ m ^ { \\prime } ]$ , and the function $\\begin{array} { r } { \\prod _ { t = 1 } ^ { | J | } f _ { \\theta _ { d _ { j _ { t } } ( \\mu ^ { \\prime } ) } } ( \\mathbf { x } _ { j _ { t } } ) { \\in } L ^ { 2 } ( ( R ^ { s } ) ^ { | J | } ) } \\end{array}$ is denoted by $\\phi _ { \\mu ^ { \\prime } } ^ { \\prime } ( \\mathbf { x } _ { j _ { 1 } } , \\ldots , \\mathbf { x } _ { j _ { | J | } } )$ . Now, recall the definition of matricization given in sec. 2, and consider $\\mathbb { I } A ^ { y } \\mathbb { I } _ { I , J }$ – the matricization of the coefficient tensor $A ^ { y }$ w.r.t. $( I , J )$ . This is a matrix of size $m$ -by- $m ^ { \\prime }$ , holding $\\mathcal { A } _ { d _ { 1 } . . . d _ { N } }$ in row index $\\mu ( d _ { i _ { 1 } } , \\ldots , d _ { i _ { | I | } } )$ and column index $\\mu ^ { \\prime } ( d _ { j _ { 1 } } , \\dots , d _ { j _ { | J | } } )$ . Rewriting eq. 28 with the indexes $\\mu$ and $\\mu ^ { \\prime }$ instead of $( d _ { i _ { 1 } } , \\ldots , d _ { i _ { | I | } } )$ and $( d _ { j _ { 1 } } , \\dotsc , d _ { j _ { | J | } } )$ , we obtain: ",
+        "bbox": [
+            173,
+            251,
+            825,
+            332
+        ],
+        "page_idx": 25
+    },
+    {
+        "type": "equation",
+        "img_path": "images/352c1febe27750ca4ce873240f52d84d31618387fefc7a2f9dae4d00d085f160.jpg",
+        "text": "$$\nh _ { y } \\left( { \\bf x } _ { 1 } , \\ldots , { \\bf x } _ { N } \\right) = \\sum _ { \\mu = 1 } ^ { m } \\sum _ { \\mu ^ { \\prime } = 1 } ^ { m ^ { \\prime } } \\left( \\mathbb { I } A ^ { y } \\mathbb { I } _ { I , J } \\right) _ { \\mu , \\mu ^ { \\prime } } \\cdot \\phi _ { \\mu } ( { \\bf x } _ { i 1 } , \\ldots , { \\bf x } _ { i _ { | I | } } ) \\phi _ { \\mu ^ { \\prime } } ^ { \\prime } ( { \\bf x } _ { j 1 } , \\ldots , { \\bf x } _ { j _ { | J | } } ) \\mathrm { I } .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            223,
+            337,
+            772,
+            364
+        ],
+        "page_idx": 25
+    },
+    {
+        "type": "text",
+        "text": "This equation has the form of eq. 22. However, for it to qualify as an orthonormal separable decomposition, the sets of functions $\\{ \\phi _ { 1 } , . . . , \\phi _ { m } \\} { \\subset } L ^ { 2 } ( ( \\mathbb { R } ^ { s } ) ^ { | I | } )$ and $\\{ \\phi _ { 1 } ^ { \\prime } , . . . , \\phi _ { m ^ { \\prime } } ^ { \\prime } \\} { \\subset } L ^ { 2 } ( ( \\mathbb { R } ^ { s } ) ^ { | J | } )$ must be orthonormal. If the latter holds eq. 23 may be applied, giving an expression for $D ( h _ { y } ; I , J ) .$ – the normalized $L ^ { 2 }$ distance of $h _ { y }$ from the set of separable functions w.r.t. $( I , J )$ , in terms of the singular values of $\\mathbb { I } ^ { \\boldsymbol { A } ^ { y } } \\mathbb { I } , \\boldsymbol { J }$ . ",
+        "bbox": [
+            173,
+            367,
+            825,
+            421
+        ],
+        "page_idx": 25
+    },
+    {
+        "type": "text",
+        "text": "We now direct our attention to the special case where $f _ { \\theta _ { 1 } \\cdot \\cdot \\cdot \\cdot f _ { \\theta _ { M } } \\in L ^ { 2 } ( \\mathbb { R } ^ { s } ) - }$ the network’s representation functions, are known to be orthonormal. The general setting, in which only linear independence is known, will be treated thereafter. Orthonormality of representation functions implies that $\\phi _ { 1 } \\hdots \\phi _ { m } { \\in } L ^ { 2 } ( ( \\mathbb { R } ^ { s } ) ^ { | I | } )$ are orthonormal as well: ",
+        "bbox": [
+            174,
+            431,
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+        ],
+        "page_idx": 25
+    },
+    {
+        "type": "equation",
+        "img_path": "images/00fe12267cb9b32f29be3eedc08ecd94f557c99c6cf6302402a8578586d1f206.jpg",
+        "text": "$$\n\\begin{array} { r l } { \\langle \\phi _ { n } , \\phi _ { n } \\rangle } & { \\frac { 1 } { ( n ) } ( \\begin{array} { l } { \\phi _ { n } ( \\mathbf { x } _ { i _ { 1 } } , . . . , \\mathbf { x } _ { i _ { 1 } / i } ) \\phi _ { \\theta _ { n } } ( \\mathbf { x } _ { i _ { 1 } } , . . . , \\mathbf { x } _ { i _ { 1 } / i } ) d \\mathbf { x } _ { i _ { 1 } } \\cdots d \\mathbf { x } _ { i _ { 1 / i } } } \\\\ { \\frac { 1 } { ( n ) } } \\end{array} ) } \\\\ & { \\frac { 1 } { ( n ) } ( \\begin{array} { l } { \\prod _ { i = 1 } ^ { [ n ] } f \\phi _ { \\varepsilon _ { i _ { 1 } } ( \\omega ) } ( \\mathbf { x } _ { i _ { 1 } } ) \\prod _ { i = 1 } ^ { [ n ] } \\beta _ { \\phi _ { \\varepsilon _ { i _ { 1 } } ( \\omega ) } } ( \\mathbf { x } _ { i _ { 1 } } ) d \\mathbf { x } _ { i _ { 1 } } \\cdots d \\mathbf { x } _ { i _ { 1 / i } } } \\\\ { \\frac { 1 } { ( n ) } } \\end{array}  } \\\\ & { \\frac { 1 } { ( n ) } \\prod _ { i = 1 } ^ { [ n ] } \\int \\beta _ { \\phi _ { \\varepsilon _ { i _ { 1 } } ( \\omega ) } } ( \\mathbf { x } _ { i _ { 1 } } ) d \\rho _ { \\phi _ { \\varepsilon _ { i _ { 1 } } ( \\omega ) } } ( \\mathbf { x } _ { i _ { 1 } } ) d \\mathbf { x } _ { i _ { 1 } } } \\\\ & { \\frac { 1 } { ( n ) } \\prod _ { i = 1 } ^ { [ n ] }  f \\phi _ { \\varepsilon _ { i _ { 1 } } ( \\omega ) } , f \\phi _ { \\varepsilon _ { i _ { 1 } } ( \\omega ) }  } \\\\ & { \\frac { 1 } { ( n ) } \\prod _ { i = 1 } ^ { [ n ] } \\{ \\begin{array} { l l } { 1 } & { \\alpha _ { i } , \\beta _ { \\phi _ { \\varepsilon _ { i } } ( \\omega ) } - d _ { i _ { 1 } } ( \\mu ) } \\\\ { 0 } & { \\alpha _ { i } \\ln \\cosh \\sinh \\sinh \\sinh } \\end{array} \\} } \\\\ &  \\frac { 1 } { ( n ) } \\{ \\begin{array} { l l } { 1 } & { \\alpha _ { j } \\leq d _ { i _ { 1 } } ( \\mu ) - d _ { i _ { 1 } } ( \\mu ) } \\\\ { 0 } &  \\beta _  \\phi _ { \\varepsilon } \\end{array} \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            276,
+            489,
+            720,
+            708
+        ],
+        "page_idx": 25
+    },
+    {
+        "type": "text",
+        "text": "(1) and (4) here follow from the definition of inner product in $L ^ { 2 }$ space, (2) replaces $\\phi _ { \\mu }$ and $\\phi _ { \\bar { \\mu } }$ by their definitions, (3) makes use of Fubini’s theorem (see Jones (2001)), (5) relies on the (temporary) assumption that representation functions are orthonormal, (6) is a trivial step, and (7) owes to the fact that $\\mu \\mapsto ( d _ { i _ { 1 } } ( \\mu ) , \\ldots , d _ { i _ { | I | } } ( \\mu ) )$ is an injective mapping. A similar sequence of steps (applied to $\\langle \\phi _ { \\mu ^ { \\prime } } ^ { \\prime } , \\phi _ { \\bar { \\mu } ^ { \\prime } } ^ { \\prime } \\rangle $ ) shows that in addition to $\\phi _ { 1 } \\ldots \\phi _ { m }$ , the functions $\\phi _ { 1 } ^ { \\prime } \\ldots \\phi _ { m ^ { \\prime } } ^ { \\prime } \\in L ^ { 2 } ( ( \\mathbb { R } ^ { s } ) ^ { | J | } )$ will also be orthonormal if $f _ { \\boldsymbol { \\theta } _ { 1 } } . . . f _ { \\boldsymbol { \\theta } _ { M } }$ are. We conclude that if representation functions are orthonormal, eq. 29 indeed provides an orthonormal separable decomposition of $h _ { y }$ , and the formula in eq. 23 may be applied: ",
+        "bbox": [
+            173,
+            712,
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+        ],
+        "page_idx": 25
+    },
+    {
+        "type": "equation",
+        "img_path": "images/ae786c25764bdb02f668e48b92029ab5d9ac23f5102d3d0a55a1a55fa9a1aaba.jpg",
+        "text": "$$\nD ( h _ { y } ; I , J ) = \\sqrt { 1 - \\frac { \\sigma _ { 1 } ^ { 2 } ( [ \\mathscr { A } ^ { y } ] _ { I , J } ) } { \\sigma _ { 1 } ^ { 2 } ( [ \\mathscr { A } ^ { y } ] _ { I , J } ) + \\cdots + \\sigma _ { \\operatorname* { m i n } \\{ m , m ^ { \\prime } \\} } ^ { 2 } ( [ \\mathscr { A } ^ { y } ] _ { I , J } ) } }\n$$",
+        "text_format": "latex",
+        "bbox": [
+            297,
+            809,
+            702,
+            848
+        ],
+        "page_idx": 25
+    },
+    {
+        "type": "text",
+        "text": "where $\\sigma _ { 1 } ( [ \\bar { \\jmath } { \\cal A } _ { - } ^ { y } ] [ . , . ] ) \\geq \\dots \\geq \\sigma _ { \\operatorname* { m i n } \\{ m , m ^ { \\prime } \\} } ( [ \\bar { \\jmath } { \\cal A } ^ { y } ] _ { I , J } ) \\geq 0$ are the singular values of the coefficient tensor Jmatricization $\\mathbb { I } A ^ { y } \\mathbb { I } _ { I , J }$ . ",
+        "bbox": [
+            171,
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+            880
+        ],
+        "page_idx": 25
+    },
+    {
+        "type": "text",
+        "text": "In sec. 5.2 we showed that the maximal separation rank realizable by a deep network is greater than or equal to $\\operatorname* { m i n } \\{ r _ { 0 } , M \\} ^ { S }$ , where $M , r _ { 0 }$ are the number of channels in the representation and first hidden layers (respectively), and $S$ stands for the number of index quadruplets (sets of the form $\\{ 4 k { - } 3 , 4 k { - } 2 , 4 k { - } 1 , 4 k \\}$ for some $k \\in$ $[ N / 4 ] )$ that are split by the partition $( I , J )$ . To prove this lower bound, we presented in app. A.3 a specific setting for the linear weights of the network $( \\{ \\mathbf { a } ^ { l , \\gamma } \\} _ { l , \\gamma } , \\mathbf { a } ^ { L , y } )$ under which $r a n k \\mathbb { [ } \\mathcal { A } ^ { y } ] _ { I , J } = \\operatorname* { m i n } \\{ r _ { 0 } , M \\} ^ { S }$ . J KCareful examination of the proof shows that with this particular weight setting, not only is the rank of $\\mathbb { I } A ^ { y } \\mathbb { I } _ { I , J }$ equal to $\\operatorname* { m i n } \\{ r _ { 0 } , M \\} ^ { S }$ J K, but also, all of its non-zero singular values are equal to one another. 14 This implies that $\\sigma _ { 1 } ^ { 2 } ( [ \\mathcal { A } ^ { y } ] _ { I , J } ) / ( \\sigma _ { 1 } ^ { 2 } ( [ \\mathcal { A } ^ { y } ] _ { I , J } ) + \\cdot \\cdot \\cdot + \\sigma _ { \\operatorname* { m i n } \\{ m , m ^ { \\prime } \\} } ^ { 2 } ( [ \\mathcal { A } ^ { y } ] _ { I , J } ) ) = \\operatorname* { m i n } \\{ r _ { 0 } , M \\} ^ { - S }$ , and since we currently assume that $f _ { \\boldsymbol { \\theta } _ { 1 } } . . . f _ { \\boldsymbol { \\theta } _ { M } }$ are orthonormal, eq. 30 applies and we obtain $D ( h _ { y } ; I , J ) = \\sqrt { 1 - \\operatorname* { m i n } \\{ r _ { 0 } , M \\} ^ { - S } }$ . Maximizing over all possible weight settings, we arrive at the following lower bound for the normalized $L ^ { 2 }$ distance from separable functions brought forth by a deep convolutional arithmetic circuit: ",
+        "bbox": [
+            174,
+            885,
+            825,
+            924
+        ],
+        "page_idx": 25
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            173,
+            103,
+            825,
+            217
+        ],
+        "page_idx": 26
+    },
+    {
+        "type": "equation",
+        "img_path": "images/c551458a664dd5782761e6b6ecf37f10239af918bd76a75e59f31c501f759e8b.jpg",
+        "text": "$$\n\\operatorname* { s u p } _ { \\{ \\mathbf { a } ^ { l , \\gamma } \\} _ { l , \\gamma } , \\ \\mathbf { a } ^ { L , y } } D \\left( h _ { y } | _ { \\{ \\mathbf { a } ^ { l , \\gamma } \\} _ { l , \\gamma } , \\mathbf { a } ^ { L , y } } ; I , J \\right) \\geq \\sqrt { 1 - \\frac { 1 } { \\operatorname* { m i n } \\{ r _ { 0 } , M \\} ^ { S } } }\n$$",
+        "text_format": "latex",
+        "bbox": [
+            294,
+            218,
+            704,
+            257
+        ],
+        "page_idx": 26
+    },
+    {
+        "type": "text",
+        "text": "Turning to the general case, we omit the assumption that representation functions $f _ { \\theta _ { 1 } } . . . f _ { \\theta _ { M } } \\in L ^ { 2 } ( \\mathbb { R } ^ { s } )$ are orthonormal, and merely rely on their linear independence. The latter implies that the dimension of $s p a n \\{ f _ { \\theta _ { 1 } } . . . f _ { \\theta _ { M } } \\}$ is ionepl $M$ , thus there exist orthonormal functiatrix between the bases – the matrix de the original representation functions $\\varphi _ { 1 } . . . \\varphi _ { M } \\in L ^ { 2 } ( \\mathbf { \\hat { \\mathbb { R } } } ^ { s } )$ p, l $F \\in$ $\\mathbb { R } ^ { M \\times M }$ $\\begin{array} { r } { \\varphi _ { c } = \\sum _ { d = 1 } ^ { M } F _ { c , d } \\cdot f _ { \\theta _ { d } } } \\end{array}$ $\\forall c \\in [ M ]$ $f _ { \\boldsymbol { \\theta } _ { 1 } \\cdot \\cdot \\cdot \\cdot } f _ { \\boldsymbol { \\theta } _ { M } }$ $\\varphi _ { 1 } . . . \\varphi _ { M }$ Using the latter, the lower bound in eq. 31 applies, and there exists a setting for the linear weights of the network – $\\{ \\mathbf { a } ^ { l , \\gamma } \\} _ { l , \\gamma } , \\mathbf { a } ^ { L , y }$ , such that $D ( \\bar { h } _ { y } ; I , \\bar { J } ) \\ge \\sqrt { 1 - \\operatorname* { m i n } \\{ r _ { 0 } , M \\} ^ { - S } }$ . Recalling the structure of convolutional arithmetic circuits (fig. 1(a)), one readily sees that if we return to the original representation functions $f _ { \\boldsymbol { \\theta } _ { 1 } } . . . f _ { \\boldsymbol { \\theta } _ { M } }$ , while multiplying conv weights in hidden layer 0 by $F ^ { \\top }$ (i.e. mapping $\\mathbf { a } ^ { 0 , \\gamma } { \\mapsto } F ^ { \\top } \\mathbf { a } ^ { 0 , \\gamma } ,$ ), the overall function $h _ { y }$ remains unchanged, and in particular $D ( h _ { y } ; I , J ) \\ge \\sqrt { 1 - \\operatorname* { m i n } \\{ r _ { 0 } , M \\} ^ { - S } }$ still holds. We conclude that the lower bound in eq. 31 applies, even if representation functions are not orthonormal. ",
+        "bbox": [
+            173,
+            272,
+            825,
+            419
+        ],
+        "page_idx": 26
+    },
+    {
+        "type": "text",
+        "text": "To summarize, we translated the lower bound from sec. 5.2 on the maximal separation rank realized by a deep convolutional arithmetic circuit, into a lower bound on the maximal normalized $L ^ { 2 }$ distance from separable functions (eq. 31). This, along with the translation of upper bounds facilitated in app. B.2, implies that the analysis carried out in the paper, which studies correlations modeled by convolutional networks through the notion of separation rank, may equivalently be framed in terms of normalized $L ^ { 2 }$ distance from separable functions. We note however that there is one particular aspect in our original analysis that does not carry through the translation. Namely, in sec. 5.1 it was shown that separation ranks realized by convolutional arithmetic circuits are maximal almost always, i.e. for all linear weight settings but a set of (Lebesgue) measure zero. Put differently, for a given partition $( I , J )$ , the maximal separation rank brought forth by a network characterizes almost all functions realized by it. An equivalent statement does not hold with the continuous measure of normalized $L ^ { 2 }$ distance from separable functions. The behavior of this measure across the hypotheses space of a network is non-trivial, and forms a subject for future research. ",
+        "bbox": [
+            173,
+            430,
+            825,
+            582
+        ],
+        "page_idx": 26
+    },
+    {
+        "type": "text",
+        "text": "C IMPLEMENTATION DETAILS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            602,
+            434,
+            617
+        ],
+        "page_idx": 26
+    },
+    {
+        "type": "text",
+        "text": "In this appendix we provide implementation details omitted from the description of our experiments in sec. 7. Our implementation, available online at https://github.com/HUJI-Deep/inductive-pooling, is based on the SimNets branch (Cohen et al. (2016a)) of Caffe toolbox (Jia et al. (2014)). The latter realizes convolutional arithmetic circuits in log-space for numerical stability. ",
+        "bbox": [
+            174,
+            631,
+            825,
+            681
+        ],
+        "page_idx": 26
+    },
+    {
+        "type": "text",
+        "text": "When training convolutional arithmetic circuits, we followed the hyper-parameter choices made by Sharir et al. (2016). In particular, our objective function was the cross-entropy loss with no $L ^ { 2 }$ regularization (i.e. with weight decay set to 0), optimized using Adam (Kingma and Ba (2014)) with step-size $\\alpha = 0 . 0 0 3$ and moment decay rates $\\beta _ { 1 } = \\beta _ { 2 } = 0 . 9$ . 15000 iterations with batch size 64 (48 epochs) were run, with the step-size $\\alpha$ decreasing by a factor of 10 after 12000 iterations (38.4 epochs). We did not use dropout (Srivastava et al. (2014)), as the limiting factor in terms of accuracies was the difficulty of fitting training data (as opposed to overfitting) – see fig. 3. ",
+        "bbox": [
+            173,
+            688,
+            825,
+            777
+        ],
+        "page_idx": 26
+    },
+    {
+        "type": "text",
+        "text": "For training the conventional convolutional rectifier networks, we merely switched the hyper-parameters of Adam to the recommended settings specified in Kingma and Ba (2014) $( \\alpha = 0 . 0 0 1 , \\beta _ { 1 } = \\bar { 0 } . 9 , \\bar { \\beta } _ { 2 } = 0 . 9 9 9 )$ , and set weight decay to the standard value of 0.0001. ",
+        "bbox": [
+            176,
+            784,
+            823,
+            821
+        ],
+        "page_idx": 26
+    },
+    {
+        "type": "text",
+        "text": "D MORPHOLOGICAL CLOSURE ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            102,
+            444,
+            118
+        ],
+        "page_idx": 27
+    },
+    {
+        "type": "text",
+        "text": "The synthetic dataset used in our experiments (sec. 7) consists of binary images displaying different shapes (blobs). One of the tasks facilitated by this dataset is the detection of morphologically closed blobs, i.e. of images that are relatively similar to their morphological closure. The procedure we followed for computing the morphological closure of a binary image is: ",
+        "bbox": [
+            176,
+            132,
+            825,
+            184
+        ],
+        "page_idx": 27
+    },
+    {
+        "type": "text",
+        "text": "1. Pad the given image with background (0 value) pixels   \n2. Morphological dilation: simultaneously turn on (set to 1) all pixels that have a (left, right, top or bottom) neighbor originally active (holding 1)   \n3. Morphological erosion: simultaneously turn off (set to 0) all pixels that have a (left, right, top or bottom) neighbor currently inactive (holding 0)   \n4. Remove pixels introduced in padding ",
+        "bbox": [
+            210,
+            195,
+            825,
+            287
+        ],
+        "page_idx": 27
+    },
+    {
+        "type": "text",
+        "text": "It is not difficult to see that any pixel active in the original image is necessarily active in its closure. Moreover, pixels that are originally inactive yet are surrounded by active ones will also be turned on in the closure, hence the effect of “gap filling”. Finally, we note that the particular sequence of steps described above represents the most basic form of morphological closure. The interested reader is referred to Haralick et al. (1987) for a much more comprehensive introduction. ",
+        "bbox": [
+            174,
+            297,
+            825,
+            362
+        ],
+        "page_idx": 27
+    }
+]
\ No newline at end of file
diff --git a/parse/train/BkVsEMYel/BkVsEMYel_middle.json b/parse/train/BkVsEMYel/BkVsEMYel_middle.json
new file mode 100644
index 0000000000000000000000000000000000000000..879dc25713c7f61c4a16f468403e17acb4edba38
--- /dev/null
+++ b/parse/train/BkVsEMYel/BkVsEMYel_middle.json
@@ -0,0 +1,102006 @@
+{
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+                    "index": 0.5
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+                                    "score": 1.0,
+                                    "content": "analyze convolutional arithmetic circuits, and empirically validate our findings",
+                                    "type": "text"
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+                            "index": 10
+                        },
+                        {
+                            "bbox": [
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "on other types of convolutional networks as well. Correlations are formalized",
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+                        {
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "through the notion of separation rank, which for a given partition of the input,",
+                                    "type": "text"
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+                        },
+                        {
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "measures how far a function is from being separable. We show that a polynomi-",
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+                                    "score": 1.0,
+                                    "content": "ally sized deep network supports exponentially high separation ranks for certain",
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+                                    "score": 1.0,
+                                    "content": "ages. Other pooling schemes lead to different preferences, and this allows tailor-",
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+                                    "score": 1.0,
+                                    "content": "ing the network to data that departs from the usual domain of natural imagery. In",
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+                            ],
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+                        },
+                        {
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "addition to analyzing deep networks, we show that shallow ones support only lin-",
+                                    "type": "text"
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+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
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+                                    "score": 1.0,
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+                                    "content": "arithmetic circuits. These models follow the standard paradigm of locality, weight sharing and pool-",
+                                    "type": "text"
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+                                    "score": 1.0,
+                                    "content": "ing, yet differ from the most conventional convolutional networks in that their point-wise activations",
+                                    "type": "text"
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+                                    "score": 1.0,
+                                    "content": "are linear, with non-linearity originating from product pooling. Recently, Cohen et al. (2016b) an-",
+                                    "type": "text"
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+                                    "score": 1.0,
+                                    "content": "alyzed the depth efficiency of convolutional arithmetic circuits, showing that besides a negligible",
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+                                    "score": 1.0,
+                                    "content": "(zero measure) set, all functions realizable by a deep network require exponential size in order to be",
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+                            ],
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+                        {
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+                                    "score": 1.0,
+                                    "content": "realized (or approximated) by a shallow one. This result, termed complete depth efficiency, stands in",
+                                    "type": "text"
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+                            ],
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+                        {
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+                                    "score": 1.0,
+                                    "content": "contrast to previous depth efficiency results, which merely showed existence of functions efficiently",
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+                                    "content": "realizable by deep networks but not by shallow ones. Besides their analytic advantage, convolu-",
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+                                    "score": 1.0,
+                                    "content": "tional arithmetic circuits are also showing promising empirical performance. In particular, they are",
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+                                    "score": 1.0,
+                                    "content": "equivalent to SimNets – a deep learning architecture that excels in computationally constrained set-",
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+                                    "score": 1.0,
+                                    "content": "tings (Cohen and Shashua (2014); Cohen et al. (2016a)), and in addition, have recently been utilized",
+                                    "type": "text"
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+                            "index": 13
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+                                    "score": 1.0,
+                                    "content": "for classification with missing data (Sharir et al. (2016)). Motivated by these theoretical and practi-",
+                                    "type": "text"
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+                                    "score": 1.0,
+                                    "content": "cal merits, we focus our analysis in this paper on convolutional arithmetic circuits, viewing them as",
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+                                    "score": 1.0,
+                                    "content": "representative of the class of convolutional networks. We empirically validate our conclusions with",
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+                            "index": 16
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+                        {
+                            "bbox": [
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+                                    "score": 1.0,
+                                    "content": "both convolutional arithmetic circuits and convolutional rectifier networks – convolutional networks",
+                                    "type": "text"
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+                            ],
+                            "index": 17
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+                        {
+                            "bbox": [
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "with rectified linear (ReLU, Nair and Hinton (2010)) activation and max or average pooling. Adap-",
+                                    "type": "text"
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+                                    "score": 1.0,
+                                    "content": "tation of the formal analysis to networks of the latter type, similarly to the adaptation of the analysis",
+                                    "type": "text"
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+                        {
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+                                    "score": 1.0,
+                                    "content": "in Cohen et al. (2016b) carried out by Cohen and Shashua (2016), is left for future work.",
+                                    "type": "text"
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+                        }
+                    ],
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+                {
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+                                    "content": "Our analysis approaches the study of inductive bias from the direction of function inputs. Specifi-",
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+                                    "content": "cally, we study the ability of convolutional arithmetic circuits to model correlation between regions",
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+                                    "score": 1.0,
+                                    "content": "of their input. To analyze the correlations of a function, we consider different partitions of input",
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+                                    "score": 1.0,
+                                    "content": "regions into disjoint sets, and ask how far the function is from being separable w.r.t. these parti-",
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+                                    "score": 1.0,
+                                    "content": "tions. Distance from separability is measured through the notion of separation rank (Beylkin and",
+                                    "type": "text"
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+                        {
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+                                    "score": 1.0,
+                                    "content": "Mohlenkamp (2002)), which can be viewed as a surrogate of the",
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+                                    "score": 0.88,
+                                    "content": "L ^ { 2 }",
+                                    "type": "inline_equation"
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+                                {
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+                                    "score": 1.0,
+                                    "content": "distance from the closest sepa-",
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+                                    "score": 1.0,
+                                    "content": "rable function. For a given function and partition of its input, high separation rank implies that the",
+                                    "type": "text"
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+                        {
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+                        {
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+                                    "score": 1.0,
+                                    "content": "with polynomial network size, and which require network to be exponentially large. The standard",
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+                        {
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+                                    "score": 1.0,
+                                    "content": "ones that divide the input into large distinct areas. Other choices lead to different preferences, for",
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+                        {
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+                                    "score": 1.0,
+                                    "content": "titions that split the input symmetrically. We conclude that in terms of modeled correlations, pooling",
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+                                    "score": 1.0,
+                                    "content": "geometry controls the inductive bias, and the particular design commonly employed in practice ori-",
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+                                    "score": 1.0,
+                                    "content": "ents it towards the statistics of natural images (nearby pixels more correlated than ones that are far",
+                                    "type": "text"
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+                        {
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+                                    "score": 1.0,
+                                    "content": "apart). Moreover, when processing data that departs from the usual domain of natural imagery, prior",
+                                    "type": "text"
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+                            ],
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+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "knowledge regarding its statistics can be used to derive respective pooling schemes, and accordingly",
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+                        {
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+                                    "score": 1.0,
+                                    "content": "tailor the inductive bias.",
+                                    "type": "text"
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+                        }
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+                {
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+                                    "content": "is indeed given by eq. 3, simply plug",
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+                                    "score": 1.0,
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+                                    "content": "\\bar { J } = \\{ j _ { 1 } , \\dotsc , j _ { | J | } \\}",
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+                                    "content": "h : ( \\mathbb { R } ^ { s } ) ^ { N } \\to \\mathbb { R }",
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+                                    "score": 1.0,
+                                    "content": ". One may wonder if it is at all possible",
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+                                    "score": 1.0,
+                                    "content": "through such summands, i.e. if the separation rank of",
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+                                    "score": 1.0,
+                                    "content": "is finite. From the theory of",
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+                                    "score": 1.0,
+                                    "content": "tensor products between",
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+                                    "score": 0.87,
+                                    "content": "L ^ { 2 }",
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+                                    "score": 1.0,
+                                    "content": "spaces (see Hackbusch (2012) for a comprehensive coverage), we know",
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+                                    "content": "that any",
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+                                    "content": "h { \\in } L ^ { 2 } ( ( \\mathbb { R } ^ { s } ) ^ { N } )",
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+                                    "score": 0.8,
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+                                    "content": "that is measurable and square-integrable, may be approximated",
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+                                    "score": 1.0,
+                                    "content": "arbitrarily well by summations of the form",
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+                                    "content": "\\begin{array} { r } { \\sum _ { \\nu = 1 } ^ { R } g _ { \\nu } ( \\mathbf { x } _ { i _ { 1 } } , \\dots , \\mathbf { x } _ { i _ { | I | } } ) g _ { \\nu } ^ { \\prime } ( \\mathbf { x } _ { j _ { 1 } } , \\dots , \\mathbf { x } _ { j _ { | J | } } ) } \\end{array}",
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+                                    "score": 1.0,
+                                    "content": ". Exact real-",
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+                                    "score": 1.0,
+                                    "content": "ization however is only guaranteed at the limit",
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+                                    "content": "R \\to \\infty",
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+                                    "score": 1.0,
+                                    "content": ", thus in general the separation rank of",
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+                                    "score": 1.0,
+                                    "content": "need not be finite. Nonetheless, as we show in sec. 5, for the class of functions we are interested in,",
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+                                    "cross_page": true
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+                                    "score": 1.0,
+                                    "content": "e.g. quantum chemistry (Harrison et al. (2003)), particle engineering (Hackbusch (2006)) and ma-",
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+                                    "score": 1.0,
+                                    "content": "chine learning (Beylkin et al. (2009)). If the separation rank of a function w.r.t. a partition of its",
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+                                    "content": "input is equal to 1, the function is separable, meaning it does not model any interaction between",
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+                                    "score": 1.0,
+                                    "content": "appropriate statistic to measure, as a-priori, it may be that",
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+                                    "content": "J Kthe network’s weight settings, and much lower for all the rest. Apparently, as claim 2 below states,",
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+                                    "score": 1.0,
+                                    "content": "this is not the case, and in fact ra",
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+                                    "score": 1.0,
+                                    "content": "is maximal under almost all of the network’s weight",
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+                                    "score": 1.0,
+                                    "content": "settings.",
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+                                    "content": "\\{ \\mathbf { a } ^ { l , \\gamma } \\} _ { l , \\gamma }",
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+                                    "content": "\\mathbf { a } ^ { L , y }",
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+                                    "score": 1.0,
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+                                    "content": "( I , J )",
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+                                    "score": 0.75,
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+                                    "score": 1.0,
+                                    "content": ", rank",
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+                                    "content": "\\mathbb { I } \\boldsymbol { \\mathcal { A } } ^ { y } \\mathbb { I } _ { I , J }",
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "is a function of these weights. This function obtains its maxi-",
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+                                    "score": 1.0,
+                                    "content": "mum almost everywhere (w.r.t. Lebesgue measure).",
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+                                    "score": 1.0,
+                                    "content": "Proof. See app. A.2.",
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+                                    "content": "In this subsection we study correlations modeled by the deep network presented in sec. 3 (fig. 1(a)",
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+                                    "score": 1.0,
+                                    "content": "hidden layers). In accordance with sec. 5.1, we do so",
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+                                    "content": "Recall from eq. 3 the hierarchical decomposition expressing a coefficient tensor",
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+                                    "content": "be an arbitrary partition, i.e.",
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+                                    "content": "I { \\uplus } J = [ N ]",
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+                                    "score": 1.0,
+                                    "content": ". Matricizing the last level of eq. 3 w.r.t.",
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+                        {
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+                                    "score": 1.0,
+                                    "content": ", but rather supports a range of values. We analyze this range by quantifying its maxi-",
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+                        {
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+                                    "score": 1.0,
+                                    "content": "J Kmum, which reflects the strongest correlation that the network can model between the input patches",
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+                            "spans": [
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+                                    "score": 0.66,
+                                    "content": "I",
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+                                {
+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "and those indexed by",
+                                    "type": "text"
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+                                    "score": 0.67,
+                                    "content": "J",
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+                                    "bbox": [
+                                        255,
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+                                    "score": 1.0,
+                                    "content": ". One may wonder if the maximal value of",
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+                                {
+                                    "bbox": [
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+                                    "score": 0.92,
+                                    "content": "r a n k \\ [ \\mathcal { A } ^ { y } ] ] _ { I , J }",
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+                                    "score": 1.0,
+                                    "content": "is the",
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+                            "index": 7
+                        },
+                        {
+                            "bbox": [
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+                            "spans": [
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+                                    "bbox": [
+                                        105,
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+                                        339,
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+                                    "score": 1.0,
+                                    "content": "appropriate statistic to measure, as a-priori, it may be that",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
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+                                    "score": 0.92,
+                                    "content": "r a n k \\ [ \\mathcal { A } ^ { y } ] ] _ { I , J }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "J Kis maximal for very few of",
+                                    "type": "text"
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+                            ],
+                            "index": 8
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+                        {
+                            "bbox": [
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+                                    "score": 1.0,
+                                    "content": "J Kthe network’s weight settings, and much lower for all the rest. Apparently, as claim 2 below states,",
+                                    "type": "text"
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+                            "index": 9
+                        },
+                        {
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "this is not the case, and in fact ra",
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+                                    "bbox": [
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+                                    "score": 0.71,
+                                    "content": "n k \\mathbb { I } A ^ { y } \\mathbb { I } _ { I , J }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "is maximal under almost all of the network’s weight",
+                                    "type": "text"
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+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
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+                            "spans": [
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+                                    "score": 1.0,
+                                    "content": "settings.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        }
+                    ],
+                    "index": 7,
+                    "bbox_fs": [
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+                },
+                {
+                    "type": "text",
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+                                    "score": 1.0,
+                                    "content": "Claim 2. Consider a convolutional arithmetic circuit (fig.",
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+                                    "content": "I ( a ) ,",
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+                                    "score": 1.0,
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+                                    "score": 1.0,
+                                    "content": "sor",
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+                                    "score": 0.85,
+                                    "content": "\\mathcal { A } ^ { y }",
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+                                {
+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "(eq. 2).",
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+                                    "score": 0.83,
+                                    "content": "\\mathcal { A } ^ { y }",
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+                                    "score": 1.0,
+                                    "content": "depends on the network’s linear weights –",
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+                                    "score": 0.87,
+                                    "content": "\\{ \\mathbf { a } ^ { l , \\gamma } \\} _ { l , \\gamma }",
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+                                {
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+                                    "score": 1.0,
+                                    "content": "and",
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+                                    "score": 0.87,
+                                    "content": "\\mathbf { a } ^ { L , y }",
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+                                {
+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": ", thus for a given",
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+                            "index": 13
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+                        {
+                            "bbox": [
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+                            "spans": [
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+                                    "score": 1.0,
+                                    "content": "partition",
+                                    "type": "text"
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+                                {
+                                    "bbox": [
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+                                    "score": 0.92,
+                                    "content": "( I , J )",
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+                                    "score": 1.0,
+                                    "content": "of",
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+                                    "score": 0.75,
+                                    "content": "[ N ]",
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+                                {
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+                                    "score": 1.0,
+                                    "content": ", rank",
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+                                {
+                                    "bbox": [
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+                                    "score": 0.85,
+                                    "content": "\\mathbb { I } \\boldsymbol { \\mathcal { A } } ^ { y } \\mathbb { I } _ { I , J }",
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+                                },
+                                {
+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "is a function of these weights. This function obtains its maxi-",
+                                    "type": "text"
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+                            ],
+                            "index": 14
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+                        {
+                            "bbox": [
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "mum almost everywhere (w.r.t. Lebesgue measure).",
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+                                }
+                            ],
+                            "index": 15
+                        }
+                    ],
+                    "index": 13.5,
+                    "bbox_fs": [
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+                {
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+                    "lines": [
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+                            "bbox": [
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "Proof. See app. A.2.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
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+                    ],
+                    "index": 16,
+                    "bbox_fs": [
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+                                    "content": "5.2 DEEP NETWORK",
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+                                    "score": 1.0,
+                                    "content": "In this subsection we study correlations modeled by the deep network presented in sec. 3 (fig. 1(a)",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
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+                                    "score": 1.0,
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+                                    "score": 0.93,
+                                    "content": "L = \\log _ { 4 } N",
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+                                },
+                                {
+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "hidden layers). In accordance with sec. 5.1, we do so",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
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+                                    "score": 1.0,
+                                    "content": "by characterizing the maximal ranks of coefficient tensor matricizations under different partitions.",
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "Recall from eq. 3 the hierarchical decomposition expressing a coefficient tensor",
+                                    "type": "text"
+                                },
+                                {
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+                                    "content": "realized by the",
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+                                    "score": 1.0,
+                                    "content": ".",
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+                            "index": 22
+                        },
+                        {
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "Let",
+                                    "type": "text"
+                                },
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+                                    "score": 0.92,
+                                    "content": "( I , J )",
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+                                },
+                                {
+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "be an arbitrary partition, i.e.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
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+                                    "score": 0.92,
+                                    "content": "I { \\uplus } J = [ N ]",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        313,
+                                        404,
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+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Matricizing the last level of eq. 3 w.r.t.",
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+                                },
+                                {
+                                    "bbox": [
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+                                {
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+                                    "score": 1.0,
+                                    "content": ",",
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+                            "index": 23
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+                        {
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "while applying the relation in eq. 1, gives:",
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+                                }
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+                        }
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+                                    "score": 1.0,
+                                    "content": "(sec. 5.1), we conclude that the ability of a polynomially sized deep network",
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+                                    "content": "to model correlation between sets of input patches highly depends on the nature of these sets.",
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+                                    "content": "In line with sec. 5.1, this is achieved by characterizing the maximal ranks of coefficient tensor",
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+                                    "content": "Recall from eq. 4 the CP decomposition expressing a coefficient tensor",
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+                                    "score": 1.0,
+                                    "content": "in network size. In light of sec. 5.1 and 5.2, these findings imply that in contrast to the deep net-",
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+                                    "score": 1.0,
+                                    "content": "place. 7 Since all but a negligible set of the functions realizable by the deep network give rise to",
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+                                    "score": 1.0,
+                                    "content": "maximal separation ranks (sec 5.1), we obtain the complete depth efficiency result of Cohen et al.",
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+                                    "score": 1.0,
+                                    "content": "(2016b). However, unlike Cohen et al. (2016b), which did not provide any explanation for the",
+                                    "type": "text"
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+                            ],
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+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "usefulness of functions brought forth by depth, we obtain an insight into their utility – they are able",
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+                                    "content": "to efficiently model strong correlation under favored partitions of the input.",
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+                    ],
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+                                    "content": "6 INDUCTIVE BIAS THROUGH POOLING GEOMETRY",
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+                    ],
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+                                    "content": "7 Convolutional arithmetic circuits as we have defined them (sec. 3) are not universal. In particular, it may",
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+                                    "score": 1.0,
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+                                    "content": "(2016b) for proof that this indeed leads to universality). All results we have established for the original shallow",
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+                            ]
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+                                    "score": 1.0,
+                                    "content": "still linear in its size. This implies that as suggested, depth efficiency indeed holds.",
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+                                    "content": "( I , J ) - \\mathrm { i t }",
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+                                    "score": 1.0,
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+                                    "score": 1.0,
+                                    "content": ", that split many size-4 patch groups,",
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+                                    "score": 1.0,
+                                    "content": ". Since the rank of a coefficient tensor matricization",
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+                                    "score": 1.0,
+                                    "content": "(sec. 5.1), we conclude that the ability of a polynomially sized deep network",
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+                                    "score": 1.0,
+                                    "content": "to model correlation between sets of input patches highly depends on the nature of these sets.",
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+                                    "content": "We now turn to study correlations modeled by the shallow network presented in sec. 3 (fig. 1(b)).",
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+                                    "score": 1.0,
+                                    "content": "In line with sec. 5.1, this is achieved by characterizing the maximal ranks of coefficient tensor",
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+                                    "score": 1.0,
+                                    "content": "Recall from eq. 4 the CP decomposition expressing a coefficient tensor",
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+                                    "score": 1.0,
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+                                    "score": 0.89,
+                                    "content": "\\operatorname* { m i n } \\{ M ^ { \\mathrm { m i n } \\{ | I | , | J | \\} } , r _ { 0 } \\}",
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+                                    "score": 1.0,
+                                    "content": ", meaning that the maximal rank is linear (or less)",
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+                        {
+                            "bbox": [
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+                            "spans": [
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "in network size. In light of sec. 5.1 and 5.2, these findings imply that in contrast to the deep net-",
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+                            "index": 25
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+                            "bbox": [
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+                                    "score": 1.0,
+                                    "content": "work, which with polynomial size supports exponential separation ranks under favored partitions,",
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+                            "index": 26
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+                        {
+                            "bbox": [
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+                                    "score": 1.0,
+                                    "content": "the shallow network treats all partitions (of a given division size) equally, and can only give rise to",
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+                        {
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+                                    "score": 1.0,
+                                    "content": "Suppose now that we would like to use the shallow network to replicate a function realized by a",
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+                        },
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+                            "spans": [
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "network would have to be exponentially large in order to replicate it, i.e. depth efficiency takes",
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+                        {
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+                                    "score": 1.0,
+                                    "content": "place. 7 Since all but a negligible set of the functions realizable by the deep network give rise to",
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+                            ],
+                            "index": 33
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+                        {
+                            "bbox": [
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+                                    "score": 1.0,
+                                    "content": "maximal separation ranks (sec 5.1), we obtain the complete depth efficiency result of Cohen et al.",
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+                            ],
+                            "index": 34
+                        },
+                        {
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "(2016b). However, unlike Cohen et al. (2016b), which did not provide any explanation for the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "usefulness of functions brought forth by depth, we obtain an insight into their utility – they are able",
+                                    "type": "text"
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+                            ],
+                            "index": 36
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+                    ],
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+                                    "content": "6 INDUCTIVE BIAS THROUGH POOLING GEOMETRY",
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+                    ],
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+                                    "type": "text",
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+                                    "score": 1.0,
+                                    "content": "of nodes grouped together in the process of pooling. In compliance with standard convolutional",
+                                    "type": "text",
+                                    "cross_page": true
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+                            ],
+                            "index": 1
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+                                    "score": 1.0,
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+                                    "cross_page": true
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+                                    "score": 1.0,
+                                    "content": ". Under this configuration, the network’s functional description (eq. 2",
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+                                    "content": "patch blocks unevenly, i.e. separate the input to",
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+                                    "score": 1.0,
+                                    "content": "between input regions that are far apart. Had we selected a different pooling regime, the preference",
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+                                    "score": 1.0,
+                                    "content": "of input partition patterns in terms of modeled correlation would change. For example, if pooling",
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+                        },
+                        {
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+                                    "score": 1.0,
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+                                    "score": 1.0,
+                                    "content": "vertical), coarse patterns that divide the input symmetrically, such as the one illustrated on the right",
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+                        {
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+                                    "score": 1.0,
+                                    "content": "of fig. 1(c), would enjoy the possibility of strong correlation, whereas many entangled patterns",
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+                        {
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+                                    "score": 1.0,
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+                                    "score": 1.0,
+                                    "content": "contiguous windows, as commonly employed in practice, lead to a preference that complies with",
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+                                    "content": "our intuition regarding the statistics of natural images (nearby pixels more correlated than distant",
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+                                    "content": "data that departs from the usual domain of natural imagery. We demonstrate this experimentally in",
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+                                    "score": 1.0,
+                                    "content": "in different tasks.",
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+                                    "content": "7 EXPERIMENTS",
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+                                    "content": "efficiently, regardless of the considered input regions. In this section we validate these assertions",
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+                                    "score": 1.0,
+                                    "content": "empirically, not only with convolutional arithmetic circuits (subject of our analyses), but also with",
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+                                    "score": 1.0,
+                                    "content": "convolutional rectifier networks – convolutional networks with ReLU activation and max or average",
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+                                    "score": 1.0,
+                                    "content": "pooling. For conciseness, we defer to app. C some details regarding our implementation. The latter",
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+                                    "score": 1.0,
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+                                    "score": 1.0,
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+                                    "score": 1.0,
+                                    "content": "of fig. 1(c), would enjoy the possibility of strong correlation, whereas many entangled patterns",
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+                                    "score": 1.0,
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+                        {
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+                                    "score": 1.0,
+                                    "content": "contiguous windows, as commonly employed in practice, lead to a preference that complies with",
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+                                    "score": 1.0,
+                                    "content": "our intuition regarding the statistics of natural images (nearby pixels more correlated than distant",
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+                                    "score": 1.0,
+                                    "content": "ones). Other pooling schemes lead to different preferences, and this allows tailoring a network to",
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+                                    "content": "7 EXPERIMENTS",
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+                                    "content": "pooling. For conciseness, we defer to app. C some details regarding our implementation. The latter",
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+                                    "score": 1.0,
+                                    "content": "of pixels in its closure (see app. D for exact definition of the latter). The second score, named",
+                                    "type": "text"
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+                            ],
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+                                    "score": 1.0,
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+                                    "score": 1.0,
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+                                    "score": 1.0,
+                                    "content": "ill-defined). This creates two binary (two-class) classification tasks – one for closedness and one",
+                                    "type": "text"
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+                                    "score": 1.0,
+                                    "content": "for symmetry (see fig. 2 for a sample of images participating in both tasks). Given that closedness",
+                                    "type": "text"
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+                                    "score": 1.0,
+                                    "content": "that relates pixels to their reflections, thus we expect its classification task to demand that a predictor",
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+                                    "content": "pooling windows. The second, dubbed mirror, pools together",
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+                                    "score": 1.0,
+                                    "content": "with missing pixels in its interior (holes). For each image, two continuous scores",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
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+                                    "score": 1.0,
+                                    "content": "in range",
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+                                    "score": 0.69,
+                                    "content": "[ 0 , 1 ]",
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+                                {
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+                                    "score": 1.0,
+                                    "content": "are computed. The first, referred to as closedness, reflects how morphologically closed",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "a blob is, and is defined to be the ratio between the number of pixels in the blob, and the number",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
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+                                    "bbox": [
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+                                        506,
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+                                    ],
+                                    "score": 1.0,
+                                    "content": "of pixels in its closure (see app. D for exact definition of the latter). The second score, named",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
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+                                    "bbox": [
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+                                        506,
+                                        381
+                                    ],
+                                    "score": 1.0,
+                                    "content": "symmetry, reflects the degree to which a blob is left-right symmetric about its center. It is measured",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
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+                            "spans": [
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "by cropping the bounding box around a blob, applying a left-right flip to the latter, and computing the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "ratio between the number of pixels in the intersection of the blob and its reflection, and the number",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
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+                                    "score": 1.0,
+                                    "content": "of pixels in the blob. To generate labeled sets for classification (train and test), we render multiple",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
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+                                    "score": 1.0,
+                                    "content": "images, sort them according to their closedness and symmetry, and for each of the two scores, assign",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "the label “high” to the top",
+                                    "type": "text"
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+                                {
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+                                    "score": 0.85,
+                                    "content": "40 \\%",
+                                    "type": "inline_equation"
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+                                {
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+                                    "score": 1.0,
+                                    "content": "and the label “low” to the bottom",
+                                    "type": "text"
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+                                {
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+                                    "score": 0.86,
+                                    "content": "40 \\%",
+                                    "type": "inline_equation"
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+                                    "score": 1.0,
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+                                    "score": 1.0,
+                                    "content": "ill-defined). This creates two binary (two-class) classification tasks – one for closedness and one",
+                                    "type": "text"
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+                            ],
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+                                    "score": 1.0,
+                                    "content": "for symmetry (see fig. 2 for a sample of images participating in both tasks). Given that closedness",
+                                    "type": "text"
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+                            ],
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+                                    "score": 1.0,
+                                    "content": "is a property of a local nature, we expect its classification task to require a predictor to be able to",
+                                    "type": "text"
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+                                    "type": "text"
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+                                    "score": 1.0,
+                                    "content": "that relates pixels to their reflections, thus we expect its classification task to demand that a predictor",
+                                    "type": "text"
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+                        {
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+                                    "content": "be able to model correlations across distances.",
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+                    ],
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+                                    "score": 1.0,
+                                    "content": "We evaluated the deep convolutional arithmetic circuit considered throughout the paper (fig. 1(a)",
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+                                    "content": "\\left( \\mathbf { x } _ { i } \\right)",
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+                                    "score": 1.0,
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+                                    "content": "Y = 2",
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+                                    "score": 1.0,
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+                                    "score": 1.0,
+                                    "content": "and 128. Fig. 3 shows the results of applying the deep network with both square and mirror pool-",
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+                                    "score": 1.0,
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+                                    "score": 1.0,
+                                    "content": "and 4000 images for testing. As can be seen in the figure, square pooling significantly outperforms",
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+                                        105,
+                                        99,
+                                        385,
+                                        111
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+                                    "score": 1.0,
+                                    "content": "Richard Bellman. Introduction to matrix analysis, volume 960. SIAM, 1970.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        }
+                    ],
+                    "index": 1
+                },
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+                                    "bbox": [
+                                        105,
+                                        115,
+                                        503,
+                                        130
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Gregory Beylkin and Martin J Mohlenkamp. Numerical operator calculus in higher dimensions. Proceedings",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                127,
+                                355,
+                                138
+                            ],
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+                                {
+                                    "bbox": [
+                                        115,
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+                                    "score": 1.0,
+                                    "content": "of the National Academy of Sciences, 99(16):10246–10251, 2002.",
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+                        107,
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+                        504,
+                        165
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+                                105,
+                                143,
+                                506,
+                                158
+                            ],
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+                                    "bbox": [
+                                        105,
+                                        143,
+                                        506,
+                                        158
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Gregory Beylkin, Jochen Garcke, and Martin J Mohlenkamp. Multivariate regression and machine learning",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                116,
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+                                        116,
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+                            "index": 5
+                        }
+                    ],
+                    "index": 4.5
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+                        171,
+                        439,
+                        183
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+                                170,
+                                438,
+                                185
+                            ],
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+                                        170,
+                                        438,
+                                        185
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+                                        117,
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+                                        106,
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+                        }
+                    ],
+                    "index": 15
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+                        505,
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+                                        107,
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+                                        504,
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+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                116,
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+                                    "score": 1.0,
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+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                116,
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+                {
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+                        106,
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+                                        105,
+                                        370,
+                                        505,
+                                        384
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+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                115,
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+                                    "bbox": [
+                                        115,
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+                            "index": 22
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+                        },
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+                            "bbox": [
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+                                    ],
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+                                    "type": "text"
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+                            ],
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+                        }
+                    ],
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+                        },
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+                            "bbox": [
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+                                        115,
+                                        474,
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+                            ],
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+                        }
+                    ],
+                    "index": 27.5
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+                                    "bbox": [
+                                        105,
+                                        490,
+                                        505,
+                                        505
+                                    ],
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+                                    "content": "Robert M Haralick, Stanley R Sternberg, and Xinhua Zhuang. Image analysis using mathematical morphology.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                116,
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+                                        116,
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+                            ],
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+                        }
+                    ],
+                    "index": 29.5
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+                {
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+                        106,
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+                        504,
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+                                106,
+                                519,
+                                505,
+                                531
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+                                    "bbox": [
+                                        106,
+                                        519,
+                                        505,
+                                        531
+                                    ],
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+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                528,
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+                                541
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+                                        115,
+                                        528,
+                                        447,
+                                        541
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+                        }
+                    ],
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+                                        559
+                                    ],
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+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                114,
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+                            "index": 34
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+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
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+                            ],
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+                                        115,
+                                        583,
+                                        506,
+                                        596
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+                                    "type": "text"
+                                }
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+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                593,
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+                                606
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+                        }
+                    ],
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+                            ],
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+                        }
+                    ],
+                    "index": 38
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+                                        105,
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+                        },
+                        {
+                            "bbox": [
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+                            ],
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+                        }
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+                                        503,
+                                        130
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+                                    "content": "Gregory Beylkin and Martin J Mohlenkamp. Numerical operator calculus in higher dimensions. Proceedings",
+                                    "type": "text"
+                                }
+                            ],
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+                        },
+                        {
+                            "bbox": [
+                                115,
+                                127,
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+                        504,
+                        165
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+                                    "bbox": [
+                                        105,
+                                        143,
+                                        506,
+                                        158
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Gregory Beylkin, Jochen Garcke, and Martin J Mohlenkamp. Multivariate regression and machine learning",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                116,
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+                                        116,
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+                                    "type": "text"
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+                        }
+                    ],
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+                        439,
+                        183
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+                                    "type": "text"
+                                }
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+                        },
+                        {
+                            "bbox": [
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+                                        257
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Nadav Cohen, Or Sharir, and Amnon Shashua. Deep simnets. IEEE Conference on Computer Vision and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                254,
+                                249,
+                                266
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        254,
+                                        249,
+                                        266
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Pattern Recognition (CVPR), 2016a.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        }
+                    ],
+                    "index": 11.5,
+                    "bbox_fs": [
+                        105,
+                        244,
+                        505,
+                        266
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        271,
+                        504,
+                        293
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                271,
+                                505,
+                                284
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        271,
+                                        505,
+                                        284
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Nadav Cohen, Or Sharir, and Amnon Shashua. On the expressive power of deep learning: A tensor analysis.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                117,
+                                281,
+                                295,
+                                293
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        117,
+                                        281,
+                                        295,
+                                        293
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Conference On Learning Theory (COLT), 2016b.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        }
+                    ],
+                    "index": 13.5,
+                    "bbox_fs": [
+                        105,
+                        271,
+                        505,
+                        293
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        299,
+                        459,
+                        311
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                299,
+                                459,
+                                312
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        299,
+                                        459,
+                                        312
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Thomas M Cover and Joy A Thomas. Elements of information theory. John Wiley & Sons, 2012.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        }
+                    ],
+                    "index": 15,
+                    "bbox_fs": [
+                        106,
+                        299,
+                        459,
+                        312
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        316,
+                        505,
+                        338
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                107,
+                                317,
+                                504,
+                                328
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        317,
+                                        504,
+                                        328
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Olivier Delalleau and Yoshua Bengio. Shallow vs. deep sum-product networks. In Advances in Neural Infor-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                327,
+                                300,
+                                338
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        327,
+                                        300,
+                                        338
+                                    ],
+                                    "score": 1.0,
+                                    "content": "mation Processing Systems, pages 666–674, 2011.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        }
+                    ],
+                    "index": 16.5,
+                    "bbox_fs": [
+                        107,
+                        317,
+                        504,
+                        338
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        344,
+                        503,
+                        365
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                342,
+                                505,
+                                357
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        342,
+                                        505,
+                                        357
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Carl Eckart and Gale Young. The approximation of one matrix by another of lower rank. Psychometrika, 1(3):",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                354,
+                                175,
+                                365
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        354,
+                                        175,
+                                        365
+                                    ],
+                                    "score": 1.0,
+                                    "content": "211–218, 1936.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        }
+                    ],
+                    "index": 18.5,
+                    "bbox_fs": [
+                        105,
+                        342,
+                        505,
+                        365
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        371,
+                        504,
+                        393
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                370,
+                                505,
+                                384
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        370,
+                                        505,
+                                        384
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Ronen Eldan and Ohad Shamir. The power of depth for feedforward neural networks. arXiv preprint",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                381,
+                                209,
+                                392
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        381,
+                                        209,
+                                        392
+                                    ],
+                                    "score": 1.0,
+                                    "content": "arXiv:1512.03965, 2015.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        }
+                    ],
+                    "index": 20.5,
+                    "bbox_fs": [
+                        105,
+                        370,
+                        505,
+                        392
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        399,
+                        504,
+                        430
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                398,
+                                505,
+                                411
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        398,
+                                        505,
+                                        411
+                                    ],
+                                    "score": 1.0,
+                                    "content": "G.H. Golub and C.F. Van Loan. Matrix Computations. Johns Hopkins Studies in the Mathematical Sciences.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                409,
+                                505,
+                                421
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        409,
+                                        505,
+                                        421
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Johns Hopkins University Press, 2013. ISBN 9781421407944. URL https://books.google.co.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                117,
+                                420,
+                                250,
+                                430
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        117,
+                                        420,
+                                        176,
+                                        430
+                                    ],
+                                    "score": 1.0,
+                                    "content": "il/books?id",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        176,
+                                        420,
+                                        182,
+                                        428
+                                    ],
+                                    "score": 0.4,
+                                    "content": "_ { \\cdot } =",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        183,
+                                        420,
+                                        250,
+                                        430
+                                    ],
+                                    "score": 1.0,
+                                    "content": "X5YfsuCWpxMC.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        }
+                    ],
+                    "index": 23,
+                    "bbox_fs": [
+                        105,
+                        398,
+                        505,
+                        430
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        436,
+                        504,
+                        458
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                435,
+                                505,
+                                449
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        435,
+                                        505,
+                                        449
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Wolfgang Hackbusch. On the efficient evaluation of coalescence integrals in population balance models. Com-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                447,
+                                224,
+                                458
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        447,
+                                        224,
+                                        458
+                                    ],
+                                    "score": 1.0,
+                                    "content": "puting, 78(2):145–159, 2006.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        }
+                    ],
+                    "index": 25.5,
+                    "bbox_fs": [
+                        105,
+                        435,
+                        505,
+                        458
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        463,
+                        503,
+                        485
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                463,
+                                504,
+                                475
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        463,
+                                        504,
+                                        475
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Wolfgang Hackbusch. Tensor Spaces and Numerical Tensor Calculus, volume 42 of Springer Series in Com-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                474,
+                                470,
+                                486
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        474,
+                                        470,
+                                        486
+                                    ],
+                                    "score": 1.0,
+                                    "content": "putational Mathematics. Springer Science & Business Media, Berlin, Heidelberg, February 2012.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        }
+                    ],
+                    "index": 27.5,
+                    "bbox_fs": [
+                        106,
+                        463,
+                        504,
+                        486
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        491,
+                        503,
+                        513
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                490,
+                                505,
+                                505
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        490,
+                                        505,
+                                        505
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Robert M Haralick, Stanley R Sternberg, and Xinhua Zhuang. Image analysis using mathematical morphology.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                501,
+                                421,
+                                513
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        501,
+                                        421,
+                                        513
+                                    ],
+                                    "score": 1.0,
+                                    "content": "IEEE transactions on pattern analysis and machine intelligence, (4):532–550, 1987.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        }
+                    ],
+                    "index": 29.5,
+                    "bbox_fs": [
+                        105,
+                        490,
+                        505,
+                        513
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        518,
+                        504,
+                        541
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                519,
+                                505,
+                                531
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        519,
+                                        505,
+                                        531
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Robert J Harrison, George I Fann, Takeshi Yanai, and Gregory Beylkin. Multiresolution quantum chemistry in",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                528,
+                                447,
+                                541
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        528,
+                                        447,
+                                        541
+                                    ],
+                                    "score": 1.0,
+                                    "content": "multiwavelet bases. In Computational Science-ICCS 2003, pages 103–110. Springer, 2003.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        }
+                    ],
+                    "index": 31.5,
+                    "bbox_fs": [
+                        106,
+                        519,
+                        505,
+                        541
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        546,
+                        504,
+                        568
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                546,
+                                505,
+                                559
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        546,
+                                        505,
+                                        559
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recognition. arXiv",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                557,
+                                241,
+                                567
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        557,
+                                        241,
+                                        567
+                                    ],
+                                    "score": 1.0,
+                                    "content": "preprint arXiv:1512.03385, 2015.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        }
+                    ],
+                    "index": 33.5,
+                    "bbox_fs": [
+                        105,
+                        546,
+                        505,
+                        567
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        573,
+                        506,
+                        605
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                574,
+                                505,
+                                586
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        574,
+                                        505,
+                                        586
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Yangqing Jia, Evan Shelhamer, Jeff Donahue, Sergey Karayev, Jonathan Long, Ross Girshick, Sergio Guadar-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                583,
+                                506,
+                                596
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        583,
+                                        506,
+                                        596
+                                    ],
+                                    "score": 1.0,
+                                    "content": "rama, and Trevor Darrell. Caffe: Convolutional architecture for fast feature embedding. In Proceedings of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                593,
+                                424,
+                                606
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        593,
+                                        424,
+                                        606
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the 22nd ACM international conference on Multimedia, pages 675–678. ACM, 2014.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        }
+                    ],
+                    "index": 36,
+                    "bbox_fs": [
+                        106,
+                        574,
+                        506,
+                        606
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        611,
+                        428,
+                        622
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                611,
+                                428,
+                                623
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        611,
+                                        428,
+                                        623
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Frank Jones. Lebesgue integration on Euclidean space. Jones & Bartlett Learning, 2001.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        }
+                    ],
+                    "index": 38,
+                    "bbox_fs": [
+                        106,
+                        611,
+                        428,
+                        623
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        628,
+                        504,
+                        650
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                627,
+                                505,
+                                641
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        627,
+                                        505,
+                                        641
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Diederik Kingma and Jimmy Ba. Adam: A method for stochastic optimization. arXiv preprint",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                639,
+                                205,
+                                649
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        639,
+                                        205,
+                                        649
+                                    ],
+                                    "score": 1.0,
+                                    "content": "arXiv:1412.6980, 2014.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        }
+                    ],
+                    "index": 39.5,
+                    "bbox_fs": [
+                        105,
+                        627,
+                        505,
+                        649
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        656,
+                        504,
+                        677
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                654,
+                                505,
+                                668
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        654,
+                                        505,
+                                        668
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Tamara G Kolda and Brett W Bader. Tensor Decompositions and Applications. SIAM Review (), 51(3):455–500,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                665,
+                                141,
+                                678
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        665,
+                                        141,
+                                        678
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2009.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        }
+                    ],
+                    "index": 41.5,
+                    "bbox_fs": [
+                        105,
+                        654,
+                        505,
+                        678
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        683,
+                        504,
+                        705
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                684,
+                                505,
+                                695
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        684,
+                                        505,
+                                        695
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Alex Krizhevsky, Ilya Sutskever, and Geoffrey E Hinton. ImageNet Classification with Deep Convolutional",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                693,
+                                466,
+                                705
+                            ],
+                            "spans": [
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+                                    "bbox": [
+                                        115,
+                                        693,
+                                        466,
+                                        705
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Neural Networks. Advances in Neural Information Processing Systems, pages 1106–1114, 2012.",
+                                    "type": "text"
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+                            ],
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+                        }
+                    ],
+                    "index": 43.5,
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+                        684,
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+                    "type": "text",
+                    "bbox": [
+                        106,
+                        711,
+                        506,
+                        732
+                    ],
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+                        {
+                            "bbox": [
+                                106,
+                                710,
+                                505,
+                                723
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        710,
+                                        505,
+                                        723
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Yann LeCun and Yoshua Bengio. Convolutional networks for images, speech, and time series. The handbook",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 45
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                721,
+                                311,
+                                732
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        721,
+                                        311,
+                                        732
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of brain theory and neural networks, 3361(10), 1995.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 46
+                        }
+                    ],
+                    "index": 45.5,
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+                        106,
+                        710,
+                        505,
+                        732
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+                {
+                    "type": "text",
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+                        104,
+                        82,
+                        497,
+                        95
+                    ],
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+                        {
+                            "bbox": [
+                                106,
+                                82,
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+                                96
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+                                {
+                                    "bbox": [
+                                        106,
+                                        82,
+                                        497,
+                                        96
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Yann LeCun, Yoshua Bengio, and Geoffrey Hinton. Deep learning. Nature, 521(7553):436–444, May 2015.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        }
+                    ],
+                    "index": 0
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+                    "type": "text",
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+                        107,
+                        101,
+                        503,
+                        122
+                    ],
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+                        {
+                            "bbox": [
+                                105,
+                                100,
+                                505,
+                                113
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        100,
+                                        505,
+                                        113
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Hrushikesh Mhaskar, Qianli Liao, and Tomaso Poggio. Learning real and boolean functions: When is deep",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                111,
+                                335,
+                                122
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        111,
+                                        335,
+                                        122
+                                    ],
+                                    "score": 1.0,
+                                    "content": "better than shallow. arXiv preprint arXiv:1603.00988, 2016.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        }
+                    ],
+                    "index": 1.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        128,
+                        504,
+                        150
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                128,
+                                506,
+                                141
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        128,
+                                        506,
+                                        141
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Guido F Montufar, Razvan Pascanu, Kyunghyun Cho, and Yoshua Bengio. On the number of linear regions of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                139,
+                                491,
+                                150
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        139,
+                                        491,
+                                        150
+                                    ],
+                                    "score": 1.0,
+                                    "content": "deep neural networks. In Advances in Neural Information Processing Systems, pages 2924–2932, 2014.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        }
+                    ],
+                    "index": 3.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        156,
+                        503,
+                        178
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                107,
+                                157,
+                                505,
+                                168
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        157,
+                                        505,
+                                        168
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Vinod Nair and Geoffrey E Hinton. Rectified linear units improve restricted boltzmann machines. In Proceed-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                167,
+                                472,
+                                179
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        167,
+                                        472,
+                                        179
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ings of the 27th International Conference on Machine Learning (ICML-10), pages 807–814, 2010.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        }
+                    ],
+                    "index": 5.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        184,
+                        503,
+                        206
+                    ],
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+                        {
+                            "bbox": [
+                                106,
+                                185,
+                                505,
+                                196
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        185,
+                                        505,
+                                        196
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Razvan Pascanu, Guido Montufar, and Yoshua Bengio. On the number of inference regions of deep feed",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                194,
+                                431,
+                                206
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        194,
+                                        431,
+                                        206
+                                    ],
+                                    "score": 1.0,
+                                    "content": "forward networks with piece-wise linear activations. arXiv preprint arXiv, 1312, 2013.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        }
+                    ],
+                    "index": 7.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        212,
+                        504,
+                        234
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                213,
+                                505,
+                                224
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        213,
+                                        505,
+                                        224
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Tomaso Poggio, Fabio Anselmi, and Lorenzo Rosasco. I-theory on depth vs width: hierarchical function",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                223,
+                                435,
+                                234
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        223,
+                                        435,
+                                        234
+                                    ],
+                                    "score": 1.0,
+                                    "content": "composition. Technical report, Center for Brains, Minds and Machines (CBMM), 2015.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        }
+                    ],
+                    "index": 9.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        240,
+                        448,
+                        252
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                240,
+                                447,
+                                253
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        240,
+                                        447,
+                                        253
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Walter Rudin. Functional analysis. international series in pure and applied mathematics, 1991.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        }
+                    ],
+                    "index": 11
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        258,
+                        505,
+                        279
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                257,
+                                505,
+                                270
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        257,
+                                        505,
+                                        270
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Or Sharir, Ronen Tamari, Nadav Cohen, and Amnon Shashua. Tensorial mixture models. arXiv preprint",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                268,
+                                209,
+                                279
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        268,
+                                        209,
+                                        279
+                                    ],
+                                    "score": 1.0,
+                                    "content": "arXiv:1610.04167, 2016.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        }
+                    ],
+                    "index": 12.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        286,
+                        503,
+                        307
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                285,
+                                504,
+                                299
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        285,
+                                        504,
+                                        299
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Karen Simonyan and Andrew Zisserman. Very deep convolutional networks for large-scale image recognition.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                296,
+                                258,
+                                307
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        296,
+                                        258,
+                                        307
+                                    ],
+                                    "score": 1.0,
+                                    "content": "arXiv preprint arXiv:1409.1556, 2014.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        }
+                    ],
+                    "index": 14.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        313,
+                        503,
+                        345
+                    ],
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+                        {
+                            "bbox": [
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+                                313,
+                                505,
+                                326
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+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        313,
+                                        505,
+                                        326
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Nitish Srivastava, Geoffrey E Hinton, Alex Krizhevsky, Ilya Sutskever, and Ruslan Salakhutdinov. Dropout:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                325,
+                                505,
+                                335
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        325,
+                                        505,
+                                        335
+                                    ],
+                                    "score": 1.0,
+                                    "content": "a simple way to prevent neural networks from overfitting. Journal of Machine Learning Research, 15(1):",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                117,
+                                334,
+                                184,
+                                345
+                            ],
+                            "spans": [
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+                                    "bbox": [
+                                        117,
+                                        334,
+                                        184,
+                                        345
+                                    ],
+                                    "score": 1.0,
+                                    "content": "1929–1958, 2014.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        }
+                    ],
+                    "index": 17
+                },
+                {
+                    "type": "text",
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+                        352,
+                        504,
+                        373
+                    ],
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+                        {
+                            "bbox": [
+                                105,
+                                351,
+                                506,
+                                364
+                            ],
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+                                {
+                                    "bbox": [
+                                        105,
+                                        351,
+                                        506,
+                                        364
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Christian Szegedy, Wei Liu, Yangqing Jia, Pierre Sermanet, Scott Reed, Dragomir Anguelov, Dumitru Erhan,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                362,
+                                458,
+                                374
+                            ],
+                            "spans": [
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+                                    "bbox": [
+                                        116,
+                                        362,
+                                        458,
+                                        374
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Vincent Vanhoucke, and Andrew Rabinovich. Going Deeper with Convolutions. CVPR, 2015.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        }
+                    ],
+                    "index": 19.5
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+                                    "bbox": [
+                                        105,
+                                        379,
+                                        505,
+                                        392
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Matus Telgarsky. Representation benefits of deep feedforward networks. arXiv preprint arXiv:1509.08101,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
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+                        760
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+                                299,
+                                750,
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+                                764
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+                                        299,
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+                                        96
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+                            ],
+                            "index": 0
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+                        107,
+                        101,
+                        503,
+                        122
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+                            "bbox": [
+                                105,
+                                100,
+                                505,
+                                113
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        100,
+                                        505,
+                                        113
+                                    ],
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+                            ],
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+                        {
+                            "bbox": [
+                                116,
+                                111,
+                                335,
+                                122
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+                                        116,
+                                        111,
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+                        }
+                    ],
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+                        504,
+                        150
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+                                    "bbox": [
+                                        105,
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+                                        506,
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+                            ],
+                            "index": 3
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+                                116,
+                                139,
+                                491,
+                                150
+                            ],
+                            "spans": [
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+                                    "bbox": [
+                                        116,
+                                        139,
+                                        491,
+                                        150
+                                    ],
+                                    "score": 1.0,
+                                    "content": "deep neural networks. In Advances in Neural Information Processing Systems, pages 2924–2932, 2014.",
+                                    "type": "text"
+                                }
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+                            "index": 4
+                        }
+                    ],
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+                        128,
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+                    ]
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+                    "type": "text",
+                    "bbox": [
+                        108,
+                        156,
+                        503,
+                        178
+                    ],
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+                            "bbox": [
+                                107,
+                                157,
+                                505,
+                                168
+                            ],
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+                                    "bbox": [
+                                        107,
+                                        157,
+                                        505,
+                                        168
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Vinod Nair and Geoffrey E Hinton. Rectified linear units improve restricted boltzmann machines. In Proceed-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                167,
+                                472,
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+                        }
+                    ],
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+                        157,
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+                        184,
+                        503,
+                        206
+                    ],
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+                                    "bbox": [
+                                        106,
+                                        185,
+                                        505,
+                                        196
+                                    ],
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+                            "index": 7
+                        },
+                        {
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+                                115,
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+                                        115,
+                                        194,
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+                        }
+                    ],
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+                        234
+                    ],
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+                                    "bbox": [
+                                        106,
+                                        213,
+                                        505,
+                                        224
+                                    ],
+                                    "score": 1.0,
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+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                223,
+                                435,
+                                234
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        223,
+                                        435,
+                                        234
+                                    ],
+                                    "score": 1.0,
+                                    "content": "composition. Technical report, Center for Brains, Minds and Machines (CBMM), 2015.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        }
+                    ],
+                    "index": 9.5,
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+                        106,
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+                        505,
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+                    "type": "text",
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+                        106,
+                        240,
+                        448,
+                        252
+                    ],
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+                        {
+                            "bbox": [
+                                106,
+                                240,
+                                447,
+                                253
+                            ],
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+                                    "bbox": [
+                                        106,
+                                        240,
+                                        447,
+                                        253
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Walter Rudin. Functional analysis. international series in pure and applied mathematics, 1991.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        }
+                    ],
+                    "index": 11,
+                    "bbox_fs": [
+                        106,
+                        240,
+                        447,
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+                                        505,
+                                        270
+                                    ],
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+                                    "content": "Or Sharir, Ronen Tamari, Nadav Cohen, and Amnon Shashua. Tensorial mixture models. arXiv preprint",
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+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                115,
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+                        },
+                        {
+                            "bbox": [
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+                                    "bbox": [
+                                        115,
+                                        296,
+                                        258,
+                                        307
+                                    ],
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+                            "index": 15
+                        }
+                    ],
+                    "index": 14.5,
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+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                325,
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+                                        115,
+                                        325,
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+                            ],
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+                        },
+                        {
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+                                    "type": "text"
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+                            ],
+                            "index": 18
+                        }
+                    ],
+                    "index": 17,
+                    "bbox_fs": [
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+                                        351,
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+                                        364
+                                    ],
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+                            ],
+                            "index": 19
+                        },
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+                                        116,
+                                        362,
+                                        458,
+                                        374
+                                    ],
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+                            "index": 20
+                        }
+                    ],
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+                        },
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+                                    "content": "measure is defined over sets in a Euclidean space, and may be interpreted as quantifying their “volume”. For",
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+                                    "score": 1.0,
+                                    "content": "example, the Lebesgue measure of a unit hypercube is one, of the entire space is infinity, and of a finite set of",
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+                                    "score": 1.0,
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+                                    "score": 1.0,
+                                    "content": "of points in which it does not occur has Lebesgue measure zero, i.e. is negligible. An important result we will",
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+                                    "content": "make use of (proven in Caron and Traynor (2005) for example) is the following. Given a polynomial defined",
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+                                    "score": 1.0,
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+                                    "content": "Heading on to the proof, we recall from sec. 3 that the entries of the coefficient tensor",
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+                                    "score": 1.0,
+                                    "content": "is non-singular. The corresponding minor, i.e. the determinant of the sub-matrix",
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+                                    "score": 1.0,
+                                    "content": "which is not identically zero. In light of the above, this polynomial",
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+                                    "score": 0.9,
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+                                    "content": ". This equality holds for the specific weight setting we defined",
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+                                    "content": ", implies that the second to last levels of",
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+                                    "content": "[ \\mathcal { A } ^ { y } ] ] _ { I , J } = \\underset { t = 1 } { \\overset { N / 4 } { \\odot } } [ \\left[ \\phi ^ { 1 , 1 } \\right] ] _ { I _ { 1 , t } , J _ { 1 , t } }",
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+                                    "content": "Applying the rank-multiplicative property of the Kronecker product, and plugging in eq. 20, we obtain:",
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+                                    "content": "r a n k \\ [ \\boldsymbol { A } ^ { y } \\ ] _ { I , J } = \\prod _ { t = 1 } ^ { N / 4 } r a n k \\bigl [ \\boldsymbol { \\phi } ^ { 1 , 1 } \\bigr ] \\bigr | _ { I _ { 1 , t } , J _ { 1 , t } } = \\operatorname* { m i n } \\bigl \\{ r _ { 0 } , M \\bigr \\} ^ { S }",
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+                                    "content": ". This equality holds for the specific weight setting we defined",
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+                                    "score": 1.0,
+                                    "content": "in eq. 19. Maximizing over all weight settings gives the sought after lower bound:",
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+                                    "content": "\\mathbb { [ } \\phi ^ { l , \\gamma } \\ ] _ { I _ { l , k } , J _ { l , k } }",
+                                    "type": "inline_equation"
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+                                {
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+                                    "score": 1.0,
+                                    "content": "is no greater than",
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+                                    "content": "c ^ { l , k }",
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+                                    "score": 1.0,
+                                    "content": ", regardless of the chosen weight setting. For the base case",
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+                                    "content": "l = 1",
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+                                    "content": "Jwe have:",
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+                                    "content": "conveyed in sec. 4. When the separation rank of a function w.r.t. a partition of its input is equal to 1, the function",
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+                                    "content": "is separable, meaning it does not model any interaction between sides of the partition. We argued that the higher",
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+                                    "score": 1.0,
+                                    "content": "between sides of the partition. In the current appendix we formalize this argument, by relating separation rank",
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+                                    "score": 1.0,
+                                    "content": "distance from the set of separable functions. We begin by defining and characterizing a normalized",
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+                                    "score": 1.0,
+                                    "content": "circuits is derived (app. B.3), based on the lower bound for their separation ranks established in sec. 5.2.",
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+                            "index": 24
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+                                    "score": 1.0,
+                                    "content": "of matrices. In line with sec. 5, an assumption throughout this appendix is that all functions in question are",
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+                                    "score": 1.0,
+                                    "content": "over the respective Euclidean space), and in app. B.3, we",
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+                                    "score": 1.0,
+                                    "content": "also make use of the fact that representation functions",
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+                                    "content": "( f _ { \\theta _ { d } } )",
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+                                    "content": "of a convolutional arithmetic circuit can be regarded",
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+                                    "score": 1.0,
+                                    "content": "as linearly independent (see sec. 5.1). Finally, for convenience, we now fix",
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+                                    "content": "circuits is derived (app. B.3), based on the lower bound for their separation ranks established in sec. 5.2.",
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+                                    "content": "As a first step in deriving eq. 23, we show that",
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+                                    "content": "\\| h \\| ^ { 2 } = \\sigma _ { 1 } ^ { 2 } ( A ) + \\cdot \\cdot \\cdot + \\sigma _ { \\operatorname* { m i n } \\{ m , m ^ { \\prime } \\} } ^ { 2 } ( A ) \\colon",
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+                                    "content": "\\begin{array} { r l r } { \\mathrm { d } t ^ { 2 } } & { = } & { \\int \\boldsymbol { \\mu } ^ { \\nu } ( \\mathbf { S } _ { \\mu \\nu } - \\mathbf { S } _ { \\nu \\mu } ) \\mathrm { d } \\mathbf { S } _ { \\nu \\mu } \\mathrm { d } t ^ { 2 } , } \\\\ & { \\in \\int \\left( \\sum _ { s ^ { \\prime } = - 1 } ^ { \\infty } \\sum _ { \\nu ^ { \\prime } = 1 } ^ { \\infty } A _ { \\mu \\nu } - \\boldsymbol { S } _ { \\nu \\mu } \\right) \\mathrm { d } s , } \\\\ & { \\in \\mathbb { R } ^ { 3 } \\sum _ { \\nu \\in \\mathcal { S } _ { \\mu \\nu } } \\sum _ { \\nu ^ { \\prime } = 1 } ^ { \\infty } A _ { \\mu \\nu } - \\boldsymbol { S } _ { \\nu \\mu } \\mathrm { d } s , } \\\\ & { \\in \\mathbb { R } ^ { 3 } \\sum _ { \\nu \\in \\mathcal { S } _ { \\mu \\nu } } \\sum _ { \\nu ^ { \\prime } = 1 } ^ { \\infty } A _ { \\mu \\nu } \\mathrm { d } s , } \\\\ & { \\in \\mathbb { R } ^ { 3 } \\sum _ { \\nu \\in \\mathcal { S } _ { \\mu \\nu } } \\sum _ { \\nu ^ { \\prime } = 1 } ^ { \\infty } A _ { \\mu \\nu } \\mathrm { d } s , } \\\\ & { \\in \\mathbb { R } ^ { 3 } \\sum _ { \\nu \\in \\mathcal { S } _ { \\mu \\nu } } \\sum _ { \\nu ^ { \\prime } = 1 } ^ { \\infty } A _ { \\mu \\nu } \\mathrm { d } s , } \\\\ & { = } & { \\int \\mathrm { e } ^ { \\mathrm { i } ( s ) } , } \\\\ &  \\frac { \\sum _ { s ^ { \\prime } = 1 } ^ { \\infty } \\sum _ { \\nu ^ { \\prime } = 1 } ^ { \\infty } \\sum _ { \\nu ^ { \\prime } = 1 } ^ { \\infty } A _ { \\mu \\nu ^ { \\prime } } \\mathrm { d } s , } \\\\ & { } & { \\mathrm { e } ^ { \\mathrm { i } ( s ) } , } \\\\ &  \\frac  \\sum _ { s ^ { \\prime } = 1 } ^ { \\infty } \\sum _ { \\nu ^ { \\prime } = 1 } ^ { \\infty } \\sum _ { \\nu ^ { \\prime } = 1 } ^ { \\infty } \\sum _ { \\nu ^ { \\prime } = 1 } ^ { \\infty } \\sum _ { \\nu ^ { \\prime } = 1 } ^ { \\infty } \\sum _ { \\nu ^ { \\prime } = 1 } ^ { \\infty } \\sum _ { \\nu ^ { \\prime } = 1 } ^ { \\infty } \\sum _ { \\nu ^ { \\prime } = 1 } ^ { \\infty } A _ { \\mu \\nu ^ { \\prime } } \\mathrm \\end{array}",
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+                                    "score": 1.0,
+                                    "content": "and Thomas (2012) for a comprehensive introduction). Both measures quantify the interaction that a nor-",
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+                                    "content": ". Second, the notion of distance in mu-",
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+                                    "content": "\\{ \\phi _ { \\mu } \\} _ { \\mu = 1 } ^ { m } , \\{ \\phi _ { \\mu ^ { \\prime } } ^ { \\prime } \\} _ { \\mu ^ { \\prime } = 1 } ^ { m ^ { \\prime } }",
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+                                    "content": "L ^ { 2 } ( ( \\mathbb { R } ^ { s } ) ^ { | I | } ) , L ^ { 2 } ( ( \\mathbb { R } ^ { s } ) ^ { | J | } )",
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+                                    "score": 1.0,
+                                    "content": "respectively. We refer to such expression as an orthonormal",
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+                                    "score": 1.0,
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+                                    "content": "\\delta ^ { \\prime } \\in s p a n \\{ \\phi _ { 1 } ^ { \\prime } \\ldots \\phi _ { m ^ { \\prime } } ^ { \\prime } \\} ^ { \\perp }",
+                                    "type": "inline_equation"
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+                                    "content": "\\begin{array} { r } { g ^ { \\prime } = \\sum _ { \\mu ^ { \\prime } = 1 } ^ { m ^ { \\prime } } \\alpha _ { \\mu ^ { \\prime } } ^ { \\prime } \\cdot \\phi _ { \\mu ^ { \\prime } } ^ { \\prime } + \\delta ^ { \\prime } } \\end{array}",
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+                                    "content": ". Fact 2 in app. A.1 indicates",
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+                                    "content": "that the function given by",
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+                                    "score": 0.92,
+                                    "content": "( \\mathbf { x } _ { 1 } , \\ldots , \\mathbf { x } _ { N } ) { \\mapsto } g ( \\mathbf { x } _ { i _ { 1 } } , \\ldots , \\mathbf { x } _ { i _ { | I | } } ) g ^ { \\prime } ( \\mathbf { x } _ { j _ { 1 } } , \\ldots , \\mathbf { x } _ { j _ { | J | } } )",
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+                                    "content": "L ^ { 2 } ( ( \\mathbb { R } ^ { s } ) ^ { N } )",
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+                                    "content": ". We may",
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+                                    "content": "express it as follows:",
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+                                    "content": "\\begin{array} { r l r } { g ( { \\bf x } _ { i _ { 1 } } , \\ldots , { \\bf x } _ { i _ { | I | } } ) g ^ { \\prime } ( { \\bf x } _ { j _ { 1 } } , \\ldots , { \\bf x } _ { j _ { | J | } } ) } & { = } & { \\sum _ { \\mu = 1 } ^ { m } \\sum _ { \\mu ^ { \\prime } = 1 } ^ { m ^ { \\prime } } \\alpha _ { \\mu } \\alpha _ { \\mu ^ { \\prime } } ^ { \\prime } \\cdot \\phi _ { \\mu } ( { \\bf x } _ { i _ { 1 } } , \\ldots , { \\bf x } _ { i _ { | I | } } ) \\phi _ { \\mu ^ { \\prime } } ^ { \\prime } ( { \\bf x } _ { j _ { 1 } } , \\ldots , { \\bf x } _ { j _ { | J | } } ) } \\\\ & { } & { + \\left( \\sum _ { \\mu = 1 } ^ { m } \\alpha _ { \\mu } \\cdot \\phi _ { \\mu } ( { \\bf x } _ { i _ { 1 } } , \\ldots , { \\bf x } _ { i _ { | I | } } ) \\right) \\cdot \\delta ^ { \\prime } ( { \\bf x } _ { j _ { 1 } } , \\ldots , { \\bf x } _ { j _ { | J | } } ) } \\\\ & { } & { + \\delta ( { \\bf x } _ { i _ { 1 } } , \\ldots , { \\bf x } _ { i _ { | I | } } ) \\cdot \\left( \\sum _ { \\mu ^ { \\prime } = 1 } ^ { m ^ { \\prime } } \\alpha _ { \\mu ^ { \\prime } } ^ { \\prime } \\cdot \\phi _ { \\mu ^ { \\prime } } ^ { \\prime } ( { \\bf x } _ { j _ { 1 } } , \\ldots , { \\bf x } _ { j _ { | J | } } ) \\right) } \\\\ & { } & { + \\delta ( { \\bf x } _ { i _ { 1 } } , \\ldots , { \\bf x } _ { i _ { | I | } } ) \\delta ^ { \\prime } ( { \\bf x } _ { j _ { 1 } } , \\ldots , { \\bf x } _ { j _ { | J | } } ) } \\end{array}",
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+                                    "content": "According to fact 3 in app. A.1, the second, third and fourth terms on the right hand side of the above are orthog-",
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+                                    "content": "s \\bar { p } a n \\{ ( { \\bf x } _ { 1 } , \\ldots , \\hat { \\bf x } _ { N } ) { \\mapsto } { \\phi } _ { \\mu } ( { \\bf x } _ { i _ { 1 } } , \\ldots , { \\bf x } _ { i _ { | I | } } ) { \\phi } _ { \\mu ^ { \\prime } } ^ { \\prime } ( { \\bf x } _ { j _ { 1 } } , \\ldots , { \\bf x } _ { j _ { | J | } } ) \\} _ { \\mu \\in [ m ] , \\mu ^ { \\prime } \\in [ m ^ { \\prime } ] } ,",
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+                                    "score": 1.0,
+                                    "content": ". Denote their summation",
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+                                    "content": "\\mathcal { E } ( \\mathbf { x } _ { 1 } , \\ldots , \\mathbf { x } _ { N } )",
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": ", and subtract the overall function from",
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+                                    "content": "(given by eq. 22):",
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+                                    "content": "\\begin{array} { r l } & { h ( { \\mathbf x } _ { 1 } , \\ldots , { \\mathbf x } _ { N } ) - g ( { \\mathbf x } _ { i _ { 1 } } , \\ldots , { \\mathbf x } _ { i _ { | I | } } ) g ^ { \\prime } ( { \\mathbf x } _ { j _ { 1 } } , \\ldots , { \\mathbf x } _ { j _ { | J | } } ) } \\\\ & { \\qquad = \\sum _ { \\mu = 1 } ^ { m } \\sum _ { \\mu ^ { \\prime } = 1 } ^ { m ^ { \\prime } } A _ { \\mu , \\mu ^ { \\prime } } \\cdot \\phi _ { \\mu } ( { \\mathbf x } _ { i _ { 1 } } , \\ldots , { \\mathbf x } _ { i _ { | I | } } ) \\phi _ { \\mu ^ { \\prime } } ^ { \\prime } ( { \\mathbf x } _ { j _ { 1 } } , \\ldots , { \\mathbf x } _ { j _ { | J | } } ) } \\\\ & { \\qquad - \\sum _ { \\mu = 1 } ^ { m } \\sum _ { \\mu ^ { \\prime } = 1 } ^ { m ^ { \\prime } } \\alpha _ { \\mu } \\alpha _ { \\mu ^ { \\prime } } ^ { \\prime } \\cdot \\phi _ { \\mu } ( { \\mathbf x } _ { i _ { 1 } } , \\ldots , { \\mathbf x } _ { i _ { | I | } } ) \\phi _ { \\mu ^ { \\prime } } ^ { \\prime } ( { \\mathbf x } _ { j _ { 1 } } , \\ldots , { \\mathbf x } _ { j _ { | J | } } ) - \\mathcal { E } ( { \\mathbf x } _ { 1 } , \\ldots , { \\mathbf x } _ { N } ) } \\\\ & { \\qquad = \\sum _ { \\mu = 1 } ^ { m } \\sum _ { \\mu ^ { \\prime } = 1 } ^ { m ^ { \\prime } } ( A _ { \\mu , \\mu ^ { \\prime } } - \\alpha _ { \\mu } \\alpha _ { \\mu ^ { \\prime } } ^ { \\prime } ) \\cdot \\phi _ { \\mu } ( { \\mathbf x } _ { i _ { 1 } } , \\ldots , { \\mathbf x } _ { i _ { | I | } } ) \\phi _ { \\mu ^ { \\prime } } ^ { \\prime } ( { \\mathbf x } _ { j _ { 1 } } , \\ldots , { \\mathbf x } _ { j _ { | J | } } ) - \\mathcal { E } ( { \\mathbf x } _ { 1 } , \\ldots , { \\mathbf x } _ { N } ) } \\end{array}",
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+                                    "content": "Since the two terms in the latter expression are orthogonal to one another, we have:",
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+                                    "content": "Applying a sequence of steps as in eq. 24 to the first term in the second line of the above, we obtain:",
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+                                    "content": "\\delta ^ { \\prime }",
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+                                    "content": "are the zero functions, implying that:",
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+                                    "content": "(Eckart and Young (1936)). From this we conclude that:",
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+                                    "content": ". We thus have the infimum over all possible",
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+                                    "content": "Recall that we would like to derive the formula in eq. 23 for",
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+                                    "content": "separable decomposition in eq. 22. Taking square root of the equalities established in eq. 24 and 25, and",
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+                                    "content": "(eq. 21), we obtain the sought after result.",
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+                                    "content": "Applying a sequence of steps as in eq. 24 to the first term in the second line of the above, we obtain:",
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+                                    "content": "are the zero functions, implying that:",
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+                            ],
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+                        },
+                        {
+                            "bbox": [
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+                                    "score": 1.0,
+                                    "content": "is the squared Frobenius distance between the matrix",
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+                                    "score": 1.0,
+                                    "content": "and the rank-1 matrix",
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+                                    "score": 0.86,
+                                    "content": "\\pmb { \\alpha } \\pmb { \\alpha } ^ { \\prime \\top }",
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+                                    "content": "\\mathbf { \\Delta } _ { \\mathbf { { \\alpha } } \\mathbf { { \\alpha } } } ^ { \\prime }",
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+                                    "content": "\\alpha _ { 1 } \\ldots \\alpha _ { m }",
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+                                    "content": "\\alpha _ { 1 } ^ { \\prime } \\ldots \\alpha _ { m ^ { \\prime } } ^ { \\prime }",
+                                    "type": "inline_equation"
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+                                    "score": 1.0,
+                                    "content": "respectively. This squared distance is greater than or equal",
+                                    "type": "text"
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+                                    "score": 1.0,
+                                    "content": "to the sum of squares over the second to last singular values of",
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+                                    "content": ", and moreover, the inequality holds with",
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+                                    "score": 1.0,
+                                    "content": "equality for proper choices of",
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+                                    "content": "_ { \\pmb { \\alpha } }",
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+                                    "content": "\\mathbf { \\Delta } _ { \\mathbf { { \\alpha } } \\mathbf { { \\alpha } } } ^ { \\prime }",
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+                                    "score": 1.0,
+                                    "content": "(Eckart and Young (1936)). From this we conclude that:",
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+                                    "content": "\\scriptstyle \\sum _ { \\mu = 1 } ^ { m } \\alpha _ { \\mu } \\cdot \\phi _ { \\mu }",
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+                                    "content": ". Plugging this into eq. 26, we obtain:",
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+                                    "content": ". Additionally, we denote the function",
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+                                    "score": 1.0,
+                                    "content": ", which according to fact 2 in app. A.1 belongs to",
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+                                    "score": 1.0,
+                                    "content": ". Now, recall the definition of matriciza-",
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+                                    "score": 1.0,
+                                    "content": "tion given in sec. 2, and consider",
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+                                    "content": "their definitions, (3) makes use of Fubini’s theorem (see Jones (2001)), (5) relies on the (temporary) as-",
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+                                    "content": ", thus there exist orthonormal functiatrix between the bases – the matrix de the original representation functions",
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+                                    "content": "\\begin{array} { r } { \\varphi _ { c } = \\sum _ { d = 1 } ^ { M } F _ { c , d } \\cdot f _ { \\theta _ { d } } } \\end{array}",
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+                                {
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+                                    "score": 1.0,
+                                    "content": "Using the latter, the lower bound in eq. 31 applies, and there exists a setting for the linear weights of the",
+                                    "type": "text"
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+                                    "content": "\\{ \\mathbf { a } ^ { l , \\gamma } \\} _ { l , \\gamma } , \\mathbf { a } ^ { L , y }",
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+                                    "content": ", such that",
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+                                    "score": 0.93,
+                                    "content": "D ( \\bar { h } _ { y } ; I , \\bar { J } ) \\ge \\sqrt { 1 - \\operatorname* { m i n } \\{ r _ { 0 } , M \\} ^ { - S } }",
+                                    "type": "inline_equation"
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+                                {
+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": ". Recalling the structure of convolu-",
+                                    "type": "text"
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+                            "index": 17
+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "tional arithmetic circuits (fig. 1(a)), one readily sees that if we return to the original representation functions",
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+                                    "type": "inline_equation"
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+                                {
+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": ", while multiplying conv weights in hidden layer 0 by",
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+                                    "score": 0.86,
+                                    "content": "F ^ { \\top }",
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+                                    "score": 1.0,
+                                    "content": "(i.e. mapping",
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+                                    "score": 0.87,
+                                    "content": "\\mathbf { a } ^ { 0 , \\gamma } { \\mapsto } F ^ { \\top } \\mathbf { a } ^ { 0 , \\gamma } ,",
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+                                    "score": 1.0,
+                                    "content": "), the overall",
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+                                    "content": "function",
+                                    "type": "text"
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+                                    "score": 0.87,
+                                    "content": "h _ { y }",
+                                    "type": "inline_equation"
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+                                {
+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "remains unchanged, and in particular",
+                                    "type": "text"
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "score": 0.91,
+                                    "content": "D ( h _ { y } ; I , J ) \\ge \\sqrt { 1 - \\operatorname* { m i n } \\{ r _ { 0 } , M \\} ^ { - S } }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "still holds. We con-",
+                                    "type": "text"
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+                        {
+                            "bbox": [
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+                            "spans": [
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "clude that the lower bound in eq. 31 applies, even if representation functions are not orthonormal.",
+                                    "type": "text"
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+                        }
+                    ],
+                    "index": 16
+                },
+                {
+                    "type": "text",
+                    "bbox": [
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "To summarize, we translated the lower bound from sec. 5.2 on the maximal separation rank realized by a deep",
+                                    "type": "text"
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+                                    "content": "L ^ { 2 }",
+                                    "type": "inline_equation"
+                                },
+                                {
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+                                    "score": 1.0,
+                                    "content": "distance from separable",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "functions (eq. 31). This, along with the translation of upper bounds facilitated in app. B.2, implies that the",
+                                    "type": "text"
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+                            "index": 24
+                        },
+                        {
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "analysis carried out in the paper, which studies correlations modeled by convolutional networks through the",
+                                    "type": "text"
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+                        },
+                        {
+                            "bbox": [
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+                            "spans": [
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+                                    "bbox": [
+                                        105,
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+                                    "score": 1.0,
+                                    "content": "notion of separation rank, may equivalently be framed in terms of normalized",
+                                    "type": "text"
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+                                    "score": 0.87,
+                                    "content": "L ^ { 2 }",
+                                    "type": "inline_equation"
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+                                {
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+                                    "type": "text"
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+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "functions. We note however that there is one particular aspect in our original analysis that does not carry through",
+                                    "type": "text"
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+                            ],
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+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "the translation. Namely, in sec. 5.1 it was shown that separation ranks realized by convolutional arithmetic",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
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+                                    "content": "a network is non-trivial, and forms a subject for future research.",
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+                                    "content": "C IMPLEMENTATION DETAILS",
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+                                    "score": 1.0,
+                                    "content": "decreasing by a factor of 10 after 12000 iterations (38.4 epochs). We did not use dropout (Srivastava et al.",
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+                                    "content": "J Kforms: it is either a non-zero (row/column) vector, or it is a matrix holding 1 in several entries and 0 in all the",
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+                                    "content": ", thus there exist orthonormal functiatrix between the bases – the matrix de the original representation functions",
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+                                    "content": "Using the latter, the lower bound in eq. 31 applies, and there exists a setting for the linear weights of the",
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+                                    "score": 0.93,
+                                    "content": "D ( \\bar { h } _ { y } ; I , \\bar { J } ) \\ge \\sqrt { 1 - \\operatorname* { m i n } \\{ r _ { 0 } , M \\} ^ { - S } }",
+                                    "type": "inline_equation"
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+                                {
+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": ". Recalling the structure of convolu-",
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+                        {
+                            "bbox": [
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+                                    "score": 1.0,
+                                    "content": "tional arithmetic circuits (fig. 1(a)), one readily sees that if we return to the original representation functions",
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+                                    "score": 1.0,
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+                                    "content": "\\mathbf { a } ^ { 0 , \\gamma } { \\mapsto } F ^ { \\top } \\mathbf { a } ^ { 0 , \\gamma } ,",
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+                                    "score": 1.0,
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+                                    "content": "function",
+                                    "type": "text"
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+                                    "content": "h _ { y }",
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "remains unchanged, and in particular",
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+                                    "score": 0.91,
+                                    "content": "D ( h _ { y } ; I , J ) \\ge \\sqrt { 1 - \\operatorname* { m i n } \\{ r _ { 0 } , M \\} ^ { - S } }",
+                                    "type": "inline_equation"
+                                },
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+                                    "score": 1.0,
+                                    "content": "still holds. We con-",
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+                            "spans": [
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "clude that the lower bound in eq. 31 applies, even if representation functions are not orthonormal.",
+                                    "type": "text"
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+                            "index": 21
+                        }
+                    ],
+                    "index": 16,
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+                                    "score": 1.0,
+                                    "content": "To summarize, we translated the lower bound from sec. 5.2 on the maximal separation rank realized by a deep",
+                                    "type": "text"
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+                                    "content": "L ^ { 2 }",
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+                                    "score": 1.0,
+                                    "content": "distance from separable",
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+                                    "score": 1.0,
+                                    "content": "functions (eq. 31). This, along with the translation of upper bounds facilitated in app. B.2, implies that the",
+                                    "type": "text"
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+                        },
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+                                    "score": 1.0,
+                                    "content": "analysis carried out in the paper, which studies correlations modeled by convolutional networks through the",
+                                    "type": "text"
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+                                    "score": 1.0,
+                                    "content": "notion of separation rank, may equivalently be framed in terms of normalized",
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+                                    "type": "text"
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+                        {
+                            "bbox": [
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "functions. We note however that there is one particular aspect in our original analysis that does not carry through",
+                                    "type": "text"
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+                            ],
+                            "index": 27
+                        },
+                        {
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+                            "spans": [
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+                                    "bbox": [
+                                        106,
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+                                    "score": 1.0,
+                                    "content": "the translation. Namely, in sec. 5.1 it was shown that separation ranks realized by convolutional arithmetic",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
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+                            "spans": [
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "circuits are maximal almost always, i.e. for all linear weight settings but a set of (Lebesgue) measure zero. Put",
+                                    "type": "text"
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+                            ],
+                            "index": 29
+                        },
+                        {
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+                            "spans": [
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+                                    "score": 1.0,
+                                    "content": "differently, for a given partition",
+                                    "type": "text"
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+                                {
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+                                    "score": 0.92,
+                                    "content": "( I , J )",
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+                                {
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+                                    "score": 1.0,
+                                    "content": ", the maximal separation rank brought forth by a network characterizes",
+                                    "type": "text"
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+                            ],
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+                        },
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+                                    "score": 1.0,
+                                    "content": "almost all functions realized by it. An equivalent statement does not hold with the continuous measure of",
+                                    "type": "text"
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+                                    "type": "text"
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+                                {
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+                                    "content": "4. Remove pixels introduced in padding",
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+                                    "score": 1.0,
+                                    "content": "D MORPHOLOGICAL CLOSURE",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        }
+                    ],
+                    "index": 0
+                },
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "The synthetic dataset used in our experiments (sec. 7) consists of binary images displaying different shapes",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
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+                                    "bbox": [
+                                        106,
+                                        114,
+                                        505,
+                                        126
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(blobs). One of the tasks facilitated by this dataset is the detection of morphologically closed blobs, i.e. of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
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+                                125,
+                                505,
+                                137
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+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        125,
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+                                        137
+                                    ],
+                                    "score": 1.0,
+                                    "content": "images that are relatively similar to their morphological closure. The procedure we followed for computing the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                135,
+                                265,
+                                147
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        135,
+                                        265,
+                                        147
+                                    ],
+                                    "score": 1.0,
+                                    "content": "morphological closure of a binary image is:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        }
+                    ],
+                    "index": 2.5,
+                    "bbox_fs": [
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+                },
+                {
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+                    "bbox": [
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "1. Pad the given image with background (0 value) pixels",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5,
+                            "is_list_start_line": true,
+                            "is_list_end_line": true
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+                                    "content": "2. Morphological dilation: simultaneously turn on (set to 1) all pixels that have a (left, right, top or",
+                                    "type": "text"
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+                            ],
+                            "index": 6,
+                            "is_list_start_line": true
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+                                    "score": 1.0,
+                                    "content": "bottom) neighbor originally active (holding 1)",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7,
+                            "is_list_end_line": true
+                        },
+                        {
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+                            ],
+                            "spans": [
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+                                    "bbox": [
+                                        129,
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+                                        505,
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+                                    ],
+                                    "score": 1.0,
+                                    "content": "3. Morphological erosion: simultaneously turn off (set to 0) all pixels that have a (left, right, top or",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8,
+                            "is_list_start_line": true
+                        },
+                        {
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+                            "spans": [
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+                                    "bbox": [
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+                                        315,
+                                        215
+                                    ],
+                                    "score": 1.0,
+                                    "content": "bottom) neighbor currently inactive (holding 0)",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
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+                            ],
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+                                    "bbox": [
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+                                        216,
+                                        279,
+                                        229
+                                    ],
+                                    "score": 1.0,
+                                    "content": "4. Remove pixels introduced in padding",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10,
+                            "is_list_start_line": true,
+                            "is_list_end_line": true
+                        }
+                    ],
+                    "index": 7.5,
+                    "bbox_fs": [
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+                        229
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+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        235,
+                                        505,
+                                        249
+                                    ],
+                                    "score": 1.0,
+                                    "content": "It is not difficult to see that any pixel active in the original image is necessarily active in its closure. Moreover,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
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+                            "spans": [
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "pixels that are originally inactive yet are surrounded by active ones will also be turned on in the closure, hence",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
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+                                267
+                            ],
+                            "spans": [
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+                                    "bbox": [
+                                        106,
+                                        256,
+                                        505,
+                                        267
+                                    ],
+                                    "score": 1.0,
+                                    "content": "the effect of “gap filling”. Finally, we note that the particular sequence of steps described above represents the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
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+                                267,
+                                505,
+                                278
+                            ],
+                            "spans": [
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+                                    "bbox": [
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+                                        267,
+                                        505,
+                                        278
+                                    ],
+                                    "score": 1.0,
+                                    "content": "most basic form of morphological closure. The interested reader is referred to Haralick et al. (1987) for a much",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
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+                                    "bbox": [
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+                                        277,
+                                        232,
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+                                    ],
+                                    "score": 1.0,
+                                    "content": "more comprehensive introduction.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        }
+                    ],
+                    "index": 13,
+                    "bbox_fs": [
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+                }
+            ]
+        }
+    ],
+    "_backend": "pipeline",
+    "_version_name": "2.2.2"
+}
\ No newline at end of file
diff --git a/parse/train/BkVsEMYel/BkVsEMYel_model.json b/parse/train/BkVsEMYel/BkVsEMYel_model.json
new file mode 100644
index 0000000000000000000000000000000000000000..e067b781622df1e2b8ce8457b7b42cee9ad576ae
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diff --git a/parse/train/BkmM8Dceg/BkmM8Dceg.md b/parse/train/BkmM8Dceg/BkmM8Dceg.md
new file mode 100644
index 0000000000000000000000000000000000000000..e97dbcf0349ee152a0693eb09d599960df636840
--- /dev/null
+++ b/parse/train/BkmM8Dceg/BkmM8Dceg.md
@@ -0,0 +1,322 @@
+# WARPED CONVOLUTIONS: EFFICIENT INVARIANCE TO SPATIAL TRANSFORMATIONS
+
+João F. Henriques & Andrea Vedaldi   
+Visual Geometry Group   
+University of Oxford   
+{joao,vedaldi}@robots.ox.ac.uk
+
+# ABSTRACT
+
+Convolutional Neural Networks (CNNs) are extremely efficient, since they exploit the inherent translation-invariance of natural images. However, translation is just one of a myriad of useful spatial transformations. Can the same efficiency be attained when considering other spatial invariances? Such generalized convolutions have been considered in the past, but at a high computational cost. We present a construction that is simple and exact, yet has the same computational complexity that standard convolutions enjoy. It consists of a constant image warp followed by a simple convolution, which are standard blocks in deep learning toolboxes. With a carefully crafted warp, the resulting architecture can be made equivariant to a wide range of 2-parameters spatial transformations. We show encouraging results in realistic scenarios, including the estimation of vehicle poses in the Google Earth dataset (rotation and scale), and face poses in Annotated Facial Landmarks in the Wild (3D rotations under perspective).
+
+# 1 INTRODUCTION
+
+A crucial aspect of current deep learning architectures is the encoding of invariances. This fact is epitomized in the success of convolutional neural networks (CNN), where equivariance to image translation is key: translating the input results in a translated output. When invariances are present in the data, encoding them explicitly in an architecture provides an important source of regularization, which allows to reduce the amount of training data required for learning. Invariances may also be used to improve the efficiency of implementations; for instance, a convolutional layer requires orders of magnitude less memory and also less computation compared to an equivalent fully-connected layer.
+
+The success of CNNs indicates that translation invariance is an important property of images. However, this does not explain why translation equivariant operators work well for image understanding. The common interpretation is that such operators are matched to the statistics of natural images, which are well known to be translation invariant (Hyvärinen et al., 2009). However, natural image statistics are also (largely) invariant to other transformations such as isotropic scaling and rotation, which suggests that alternative neural network designs may also work well with images. Furthermore, in specific applications, invariances other than translation may be more appropriate.
+
+Therefore, it is natural to consider generalizing convolutional architectures to other image transformations, and this has been the subject of extensive study (Kanazawa et al., 2014; Bruna et al., 2013; Cohen & Welling, 2016). Unfortunately these approaches do not possess the same memory and speed benefits that CNNs enjoy. The reason is that, ultimately, they have to transform (warp) an image or filter several times (Kanazawa et al., 2014; Marcos et al., 2016; Dieleman et al., 2015), incurring a high computational burden. Another approach is to consider a basis of filters (analogous to eigen-images) encoding the desired invariance (Cohen & Welling, 2014; Bruna et al., 2013; Cohen & Welling, 2016), which requires more storage than a convolutional filter.
+
+Although they are able to handle transformations with many pose parameters, in practice most recent proposals are limited to very coarsely discretized transformations, such as horizontal/vertical flips and $9 0 ^ { \circ }$ rotations (Dieleman et al., 2015; Cohen & Welling, 2014).
+
+In this work we propose a generalization of CNNs that overcomes these disadvantages. Our main result shows that a linear layer with equivariance w.r.t. a large class of 2-parameters transformations can always be implemented efficiently, using a standard convolution in a warped image space. The image warp can be implemented using bilinear resampling, a simple and fast operation that has been popularized by spatial transformer networks (Jaderberg et al., 2015), and is part of most deep learning toolboxes. Unlike previous proposals, the proposed warped convolutions can handle continuous transformations, such as fine rotation and scaling.
+
+This makes generalized convolution easily implementable in neural networks, including using fast convolution algorithms on GPU hardware, such as Winograd (Lavin, 2015) or the Fast Fourier Transform (Lyons, 2010). We present these notions in the simplest possible way (sections 2 to 4), but we note that they can be derived in broader generality from well know concepts of group theory (section 4.2).
+
+# 2 GENERALIZING CONVOLUTION
+
+# 2.1 CONVOLUTIONS OF CONTINUOUS IMAGES
+
+We start by looking at the basic building block of CNNs, i.e. the convolution operator. This operator computes the inner product of an image $\boldsymbol { I } \in \mathbb { R } ^ { m \times n }$ with a translated version of the filter $\boldsymbol { F } \in \mathbb { R } ^ { r \times s }$ , producing a new image as output:
+
+$$
+H _ { j } = \sum _ { k } I _ { k } F _ { k + j } ,
+$$
+
+where $k$ ${ \mathfrak { a } } , { \mathfrak { j } } \in \mathbb { Z } ^ { 2 }$ are two-dimensional vectors of indexes, and the summation ranges inside the extents of both arrays.1 To handle continuous deformations of the input, it is more natural to express eq. 1 as an integral over continuous rather than discrete inputs:
+
+$$
+H ( u ; I ) = \int I ( x ) F ( x + u ) d x ,
+$$
+
+where $I ( x )$ and $F ( x )$ are continuous functions over a bounded 2D region $\Omega \subset \mathbb { R } ^ { 2 }$ , that is: $I , F :$ $\Omega \to \mathbb { R }$ . The real-valued 2D vectors $x \in \Omega$ now play the role of the indexes $k \in  { \mathbb { Z } } ^ { 2 }$ . Equation 2 reduces to the discrete case of eq. 1 if we define $I ( x )$ and $F ( x )$ as the sum of delta functions on grids. Intermediate values can be obtained by interpolation, such as bilinear (which amounts to convolution of the delta functions with a triangle filter (Jaderberg et al., 2015)). Importantly, such continuous images can be deformed by very rich continuous transformations of the input coordinates, whereas strictly discrete operations would be more limiting.
+
+Over the next sections it will be more convenient to translate the image $I$ instead of the filter $F$ . This alternative form of eq. 2 is obtained by replacing $x + u  x$ :
+
+$$
+H ( u ; I ) = \int I ( x - u ) F ( x ) d x .
+$$
+
+# 2.2 BEYOND IMAGE TRANSLATIONS
+
+The standard convolution operator of eq. 3 can be interpreted as applying the filter to translated versions of the image. Translations can be replaced by other transformations as follows (Henriques et al., 2014):
+
+$$
+H ( t ; I ) = \int I ( t ( x ) ) F ( x ) d x , \quad t \in G
+$$
+
+where $G$ is a set of transformation functions $t : \Omega \to \Omega$ (assumed to be invertible). Intuitively, this generalized convolution performs an exhaustive search for a pattern, at many different poses (Henriques et al., 2014; Kanazawa et al., 2014). The interest in this definition lies in the fact that it makes convolution equivariant (Lenc & Vedaldi, 2015):
+
+Lemma 1 (Equivariance). Consider the generalized convolution operator $H ( t ; I )$ of eq. 4. Generalized convolution “commutes” with any transformation $q \in G$ of the image:
+
+$$
+H ( t ; I \circ q ) = H ( q \circ t ; I ) .
+$$
+
+Proof. One has immediately $\begin{array} { r } { H ( t ; I \circ q ) = \int I ( q ( t ( x ) ) ) F ( x ) d x = H ( q \circ t ; I ) . } \end{array}$
+
+A notable case is when transformations have an additive parametrization $t : \Omega \times \mathbb { R } ^ { 2 } \to \Omega$ , with $( x , u ) \mapsto t _ { u } ( x )$ and $t _ { u } \circ t _ { v } = t _ { u + v }$ . In this case, the equivariance relation can be written as
+
+$$
+H ( u ; I \circ t _ { v } ) = H ( v + u ; I ) .
+$$
+
+In particular, standard convolution is obtained when $t _ { u } ( x ) = x - u$ is the translation operator. In this case, the lemma above simply states that any translation of the input of the convolution results in a corresponding translation of the output.
+
+In section 5, we will look in more detail at a few concrete examples of transformations other than translations. Although we will not do so explicitly, in this construction it is also possible to let one or more dimensions of the parameter space $\mathbb { R } ^ { \bar { 2 } }$ be given modulus a period $Q$ , in the sense of replacing $\mathbb { R }$ with $\mathbb { R } / \mathbb { Z } ( Q )$ ; the latter is required to parameterise transformations such as rotation.
+
+# 3 COMPUTATIONAL EFFICIENCY
+
+Unfortunately, what eq. 4 gains us in generality, it loses in both performance and ease of implementation. Most works in computer vision that looked at filtering under generalized transformations (e.g. scale pyramids (Kanazawa et al., 2014) or rotated filter banks (Marcos et al., 2016; Cohen & Welling, 2014; 2016; Henriques et al., 2014)) compute eq. 4 directly by evaluating a large number of transformations $t \in G$ . This entails warping (transforming) either the image or the filter once per transformation $t$ , which can be expensive.
+
+Opting to transform the filter instead of the image can be advantageous, since it is smaller in size. On the other hand, the filter and its domain then become spatially-varying, which foregoes the benefit of the regular, predictable, and local pattern of computations in standard convolution. It precludes the use of fast convolution routines such as Winograd’s algorithm (Lavin, 2015), or the Fast Fourier Transform (Lyons, 2010), which has lower computational complexity than exhaustive search (eq. 3).
+
+In practice, most recent works focus on very coarse transformations that do not change the filter support and can be implemented strictly via permutations, like horizontal/vertical flips and $9 0 ^ { \circ }$ rotations (Dieleman et al., 2015; Cohen & Welling, 2014). Such difficulties explain why generalized convolutions are not as widespread as CNNs.
+
+In section 4 we will show that, for an important class of transformations, including the ones considered in previous works (such as Kanazawa et al. (2014); Cohen & Welling (2014); Marcos et al. (2016)) it is possible to perform generalized convolution by composing a single warp with a standard convolution, instead of several warps. Thus, we are able to take full advantage of modern convolution implementations (Lavin, 2015; Lyons, 2010), including those with lower computational complexity.
+
+# 4 MAIN RESULT
+
+Our main contribution is to show that the generalized convolution operator of eq. 4 can be implemented efficiently by a standard convolution, by pre-warping the input image and filter appropriately. The warp is the same for any image, depending solely on the nature of the relevant transformations, and can be written in closed form. This result, given in theorem 1, allows us to implement very efficient generalized convolutions using simple computational blocks, as shown in section 4.1. We name this method warped convolution.
+
+The strongest assumption is that transformations must have an additive parametrization. By this, we mean that there exists a bijection $t _ { u } : \Omega \to \Omega$ such that, for any $u , v \in \mathbb { R } ^ { 2 }$ , parameters compose additively $t _ { u } \circ t _ { v } = t _ { u + v }$ . The second assumption is that there exists a pivot point $x _ { 0 } \in \Omega$ such that $u \mapsto t _ { u } ( x _ { 0 } )$ defines a bijection $\mathbb { R } ^ { 2 } \to \Omega$ from the parameter space to the real plane. The latter requirements means that any point $x \in \Omega$ can be “reached” by transforming $x _ { 0 }$ under a suitable $t _ { u }$ . We then have that:
+
+Theorem 1. Consider the generalized convolution of eq. 4. Assume that the transformation is additive $( t _ { u } \circ t _ { v } = t _ { u + v . }$ ). Assume also that, for a fixed pivot point $x _ { 0 }$ , the function $u \mapsto t _ { u } ( x _ { 0 } )$ is bijective. Then we can rewrite generalized convolution (eq. 4) as the standard convolution
+
+$$
+H ( u ; I ) = \int \hat { I } ( u + v ) \hat { F } ( v ) d v ,
+$$
+
+where $\hat { I }$ and $\hat { F }$ are the warped image and filter given by:
+
+$$
+\hat { I } ( u ) = I ( t _ { u } ( x _ { 0 } ) ) , \qquad \hat { F } ( u ) = F ( t _ { u } ( x _ { 0 } ) ) \left| \frac { d t _ { u } ( x _ { 0 } ) } { d u } \right| .
+$$
+
+Proof. We use the variable substitution $x = t _ { v } ( x _ { 0 } )$ in eq. 4. Then:
+
+$$
+\begin{array} { l } { H ( u ; I ) = \displaystyle \int I ( t _ { u } ( x ) ) F ( x ) d x } \\ { \displaystyle = \int I ( t _ { u } ( t _ { v } ( x _ { 0 } ) ) ) F ( t _ { v } ( x _ { 0 } ) ) \left| \frac { d t _ { v } ( x _ { 0 } ) } { d v } \right| d v } \\ { \displaystyle = \int \underbrace { I ( t _ { u + v } ( x _ { 0 } ) ) } _ { \hat { I } ( u + v ) } \underbrace { F ( t _ { v } ( x _ { 0 } ) ) \left| \frac { d t _ { v } ( x _ { 0 } ) } { d v } \right| } _ { \hat { F } ( v ) } d v } \\ { \displaystyle = \int \hat { I } ( u + v ) \hat { F } ( v ) d v . } \end{array}
+$$
+
+The warp that is applied to both inputs in eq. 7 can be interpreted as follows. We start with an arbitrary pivot point $x _ { 0 }$ in the image and them sample other points by repeatedly applying the transformation $t _ { u } ( x _ { 0 } )$ to the pivot (by varying $u$ ). When discretized, this sampling is performed over a 2D grid of parameters $u$ . Finally, sampling the input at these points (for example, by bilinear interpolation) yields the warped input.
+
+An illustration is given in fig. 1, for various transformations (each one is discussed in more detail in section 5). The red dot shows the pivot point $x _ { 0 }$ , and the two arrows pointing away from it show the two directions of increasing $u$ values (recall that transformation parameters are two-dimensional). The grids were generated by sampling $u$ at regular intervals. Note that the warp grids are independent of the image contents – they can be computed once offline and then applied to any image.
+
+The last factor in eq. 7 is the determinant of the Jacobian of the image transformation $t$ . It rescales the image values to account for the stretching and shrinking of space due to non-linear warps. It can also be computed offline, and its application amounts to an element-wise product by a constant array. A generalization using group theory is discussed in section 4.2.
+
+# 4.1 PRACTICAL CONSIDERATIONS
+
+There are a few interesting aspects that simplify the use of theorem 1 in practice.
+
+First, since in most applications the filter $F$ is learned, we are free to ignore the constant warp and Jacobian in eq. 7 (which amounts to a simple reparametrization), and learn $\hat { F }$ directly. In practice, this means that we warp only the input image $I$ to obtain $\hat { I }$ , and then perform a standard convolution with a filter $\hat { F }$ . The learned warped filter $\hat { F }$ has a one-to-one correspondence to an image-space filter $F$ by means of eq. 7, although there is no real need to build the latter explicitly.
+
+Second, we can choose either one or two spatial transformations for the generalized convolution (e.g. scale and rotation, simultaneously). The reason is that the input image is 2D, so the parameterspace after warping is also 2D. The choice is not arbitrary though: the two transformations must commute, in order to respect additivity. This will be the case of the pairs we study in section 5.
+
+# Algorithm 1 Warped convolution.
+
+Grid generation (offline)
+
+• Apply the spatial transformation $t$ repeatedly to a pivot point $x _ { 0 }$ , using a 2D grid of parameters $\stackrel { \cdot } { u } = \{ \bar { ( } u _ { 1 } + i \delta _ { 1 } , u _ { 2 } + j \delta _ { 2 } ) : i = 0 , \ldots , m , j = 0 , \bar { \ldots } , n \}$ , obtaining the 2D warp grid $t _ { u } ( x _ { 0 } )$ .
+
+Warped convolution
+
+1. Resample input image $I$ using the warp grid $t _ { u } ( x _ { 0 } )$ , by bilinear interpolation.
+
+2. Convolve the warped image $\hat { I }$ with filter $\hat { F }$ .
+
+By theorem 1, these steps are equivalent to a generalized convolution, which performs an exhaustive search across the pose-space of transformation $t$ , but at a much lower computational cost.
+
+# 4.2 RELATIONSHIP TO GROUP THEORY
+
+This section relates our results, which have been presented using a simple formalism and in a restricted setting, to a more general approach based on group theory (Folland, 1995).
+
+To this end, let $G$ be a group of transformations. Under very mild conditions (the group has to be locally compact and Hausdorff), there exists a unique measure on the group, the Haar measure, which is invariant to the group action, in the sense that, given a measurable function ${ \tilde { I } } : G \to$ $\mathbb { R }$ , then $\begin{array} { r } { \int \tilde { I } ( g ^ { \prime } g ) d g = \int \overline { { \tilde { I } } } ( g ) \dot { } d g } \end{array}$ . Using this measure, one can define generalized convolution as $\begin{array} { r } { ( \tilde { I } * \tilde { F } ) ( t ) = \int _ { G } \tilde { I } ( t g ) \tilde { F } ( g ^ { - 1 } ) d g } \end{array}$ . This resembles our definition (4), although image and filter are defined on the group $G$ instead of the spatial domain $\mathbb { R } ^ { 2 }$ . Lemma 1 translates immediately to this case (Folland, 1995).
+
+In order to extend Theorem 1, we need to make this general but abstract construction concrete. Here one assumes that the group acts transitively on a subset $X \subset \mathbb { R } ^ { 2 }$ (which means that any point $x \in X$ can be written as $x = g x _ { 0 }$ , for a fixed point $x _ { 0 } \in X$ and a suitable transformation $g \in G$ ). Then one can define the image as $\tilde { I } ( g ) = I ( g \bar { ( } x _ { 0 } ) )$ , where $I$ is a function of the spatial domain $X$ instead of the group $G$ , and likewise for the filter. Next, it is necessary to explicitly calculate the integral over $G$ . If the group is an Abelian (commutative) Lie group, then one can show that there exists a map $\exp : V \to G$ , the exponential map, defined on a vector space $V$ . Under commutativity, this map is also additive, in the sense that $\exp ( u ) \exp ( v ) = \exp ( u + v )$ . The structure of $V$ depends on the specific group, but under such restrictive conditions, it is a torus, which allows the calculation of $\textstyle \int { \tilde { I } } ( { \bar { g } } ) d g$ as $\begin{array} { r } { \int \tilde { I } ( \exp ( u ) x _ { 0 } ) d u . } \end{array}$ .
+
+Finally, in order to swap integration over the group parameters with integration over space, one assumes that $x \ = \ \exp ( u ) x _ { 0 }$ defines a smooth bijection $V \  \ X$ , so that it is possible to use the change of variable $\dot { u }  u ( x )$ where $\mathrm { e x p } ( u ( x ) ) x _ { 0 } = x$ . This allows writing the integral as $\begin{array} { r } { \int { \tilde { I } } ( \exp ( u ) x _ { 0 } ) d u = \int I ( x ) \left| d u / d x \right| d x } \end{array}$ . Note that this Jacobian is the inverse of the one found in (1) due to the fact that we started by defining our convolution using $I$ instead of $\tilde { I }$ .
+
+# 5 EXAMPLES OF SPATIAL TRANSFORMATIONS
+
+We now give some concrete examples of pairs of spatial transformations that obey the conditions of theorem 1, and can be useful in practice.
+
+# 5.1 SCALE AND ASPECT RATIO
+
+Detection tasks require predicting the extent of an object as a bounding box. While the location can be found accurately by a standard CNN, which is equivariant to translation, the size prediction could similarly benefit from equivariance to horizontal and vertical scale (equivalently, scale and aspect ratio).
+
+Such a spatial transformation, from which a warp can be constructed, is given by:
+
+![](images/60788d1a003ce7fcae165868e8ad44de46e7af62c507569ccf0f4de9f35dc344.jpg)  
+Figure 1: First row: Sampling grids that define the warps associated with different spatial transformations. Second row: An example image (a) after warping with each grid (b-d). Third row: A small translation is applied to each warped image, which is then mapped back to the original space (by an inverse warp). Translation in one axis of the appropriate warped space is equivalent to (b) horizontal scaling; (c) planar rotation; (d) 3D rotation around the vertical axis.
+
+$$
+t _ { u } ( x ) = { \left[ \begin{array} { l } { x _ { 1 } s ^ { u _ { 1 } } } \\ { x _ { 2 } s ^ { u _ { 2 } } } \end{array} \right] }
+$$
+
+The $s$ constant controls the total degree of scaling applied. Notice that the output must be exponential in the scale parameters $u$ ; this ensures the additive structure required by theorem 1: $t _ { u } ( \bar { t } _ { v } ( x ) ) =$ $t _ { u + v } ( x )$ . The resulting warp grid can be visualized in fig. 1-b. In this case, the domain of the image must be $\Omega \in \mathbb { R } _ { + } ^ { 2 }$ , since a pivot $x _ { 0 }$ in one quadrant cannot reach another quadrant by any amount of (positive) scaling.
+
+# 5.2 SCALE AND ROTATION (LOG-POLAR WARP)
+
+Planar scale and rotation are perhaps the most obvious spatial transformations in images, and are a natural test case for works on spatial transformations (Kanazawa et al., 2014; Marcos et al., 2016). Rotating a point $x$ by $u _ { 1 }$ radians and scaling it by $u _ { 2 }$ , around the origin, can be performed with
+
+$$
+t _ { u } ( x ) = \left[ \begin{array} { l } { s ^ { u _ { 2 } } \left\| x \right\| \cos ( \mathrm { a t a n } _ { 2 } ( x _ { 2 } , x _ { 1 } ) + u _ { 1 } ) } \\ { s ^ { u _ { 2 } } \left\| x \right\| \sin ( \mathrm { a t a n } _ { 2 } ( x _ { 2 } , x _ { 1 } ) + u _ { 1 } ) } \end{array} \right] ,
+$$
+
+where atan $^ 2$ is the standard 4-quadrant inverse tangent function (atan2). The domain in this case must exclude the origin $( \Omega \in \dot { \mathbb { R } } ^ { 2 } \setminus \{ 0 \} )$ , since a pivot $x _ { 0 } = 0$ cannot reach any other points in the image by rotation or scaling.
+
+![](images/411e48b00e252ab8e9ec8948af96a700f5774ade8b1cca75c0faf68a96fea41e.jpg)  
+Figure 2: Equivariant pose estimation strategy used in the experiments (section 6). With an appropriate warp and a standard CNN, the shaded block becomes equivalent to a generalized CNN (by theorem 1), which performs exhaustive searches across pose-space instead of image-space.
+
+The resulting warp grid can be visualized in fig. 1-c. It is interesting to observe that it corresponds exactly to the log-polar domain, which is used in the signal processing literature to perform correlation across scale and rotation (Tzimiropoulos et al., 2010; Reddy & Chatterji, 1996). In fact, it was the source of inspiration for this work, which can be seen as a generalization of the log-polar domain to other spatial transformations.
+
+# 5.3 3D SPHERE ROTATION UNDER PERSPECTIVE
+
+We will now tackle a more difficult spatial transformation, in an attempt to demonstrate the generality of theorem 1. The transformations we will consider are yaw and pitch rotations in 3D space, as seen by a perspective camera. In the experiments (section 6) we will show how to apply it to face pose estimation.
+
+In order to maintain additivity, the rotated 3D points must remain on the surface of a sphere. We consider a simplified camera and world model, whose only hyperparameters are a focal length $f$ , the radius of a sphere $r$ , and its distance from the camera center $d$ . The equations for the spatial transformation corresponding to yaw and pitch rotation under this model are in appendix A.
+
+The corresponding warp grid can be seen in fig. 1-d. It can be observed that the grid corresponds to what we would expect of a 3D rendering of a sphere with a discrete mesh. An intuitive picture of the effect of the warp grid in such cases is that it wraps the 2D image around the surface of the 3D object, so that translation in the warped space corresponds to moving between vertexes of the 3D geometry.
+
+# 6 EXPERIMENTS
+
+# 6.1 ARCHITECTURE
+
+As mentioned in section 2.2, generalized convolution performs an exhaustive search for patterns across spatial transformations, by varying pose parameters. For tasks where invariance to that transformation is important, it is usual to pool the detection responses across all poses (Marcos et al., 2016; Kanazawa et al., 2014).
+
+In the experiments, however, we will test the framework in pose prediction tasks. As such, we do not want to pool the detection responses (e.g. with a max operation) but rather find the pose with the strongest response (i.e., an argmax operation). To perform this operation in a differentiable manner, we implement a soft argmax operation, defined as follows:
+
+$$
+s _ { 1 } ( a ) = \sum _ { i j } ^ { m n } \frac { i } { m } \sigma _ { i j } ( a ) , \qquad s _ { 2 } ( a ) = \sum _ { i j } ^ { m n } \frac { j } { n } \sigma _ { i j } ( a ) ,
+$$
+
+where $\sigma ( a ) \in \mathbb { R } ^ { m \times n }$ is the softmax over all spatial locations, and $\sigma _ { i j } ( a )$ indexes the element at $( i , j )$ . The outputs are the two spatial coordinates of the maximum value, $s ( a ) \in \mathbb { R } ^ { 2 }$ .
+
+Our base architecture then consists of the following blocks, outlined in fig. 2. First, the input image is warped with a pre-generated grid, according to section 4. The warped image is then processed by a standard CNN, which is now equivariant to the spatial transformation that was used to generate the warp grid. A soft argmax (eq. 10) then finds the maximum over pose-space. To ensure the pose prediction is well registered to the reference coordinate system, a learnable scale and bias are applied to the outputs. Training proceeds by minimizing the $L ^ { 1 }$ loss between the predicted pose and ground truth pose.
+
+Table 1: Results of scale and rotation pose estimation of vehicles in the Google Earth dataset.   
+
+<table><tr><td></td><td>CNN+FC</td><td>CNN+softargmax</td><td> Warped CNN</td></tr><tr><td>Rotation error (degrees)</td><td>28.87</td><td>30.6</td><td>26.44</td></tr><tr><td>Scale error (px)</td><td>17.51</td><td>5.783</td><td>5.4</td></tr></table>
+
+![](images/db8ba0448a92bfa2d818168ec5f182ee517f7c3a909c68da0c90758eb10407fb.jpg)  
+Figure 3: Example pose estimates (rotation and scale) on the Google Earth dataset (Section 6.2).
+
+# 6.2 GOOGLE EARTH
+
+For the first task in our experiments, we will consider aerial photos of vehicles, which have been used in several works that deal with rotation invariance (Liu et al., 2014; Schmidt & Roth, 2012; Henriques et al., 2014).
+
+Dataset. The Google Earth dataset (Heitz & Koller, 2008) contains bounding box annotations, supplemented with angle annotations from (Henriques et al., 2014), for 697 vehicles in 15 large images. We use the first 10 for training and the rest for validation. Going beyond these previous works, we focus on the estimation of both rotation and scale parameters. The object scale is taken to be the diagonal length of the bounding box.
+
+Implementation. A $4 8 \times 4 8$ image around each vehicle is cropped and downscaled by $50 \%$ , and then fed to a network for pose prediction. The proposed method, Warped CNN, follows the architecture of section 6.1 (visualized in fig. 2). The CNN block contains 3 convolutional layers with $5 \times 5$ filters, with 20, 50 and 1 output channels respectively. Recall that the output of the CNN block is a single-channel response map over 2D pose-space, which in this case consists of rotation and scale. Between the convolutional layers there are $3 \times 3$ max-pooling operators, with a stride of 2, and a ReLU before the last layer. All networks are trained for 20 epochs with SGD, using hyperparameters chosen by cross-validation.
+
+Baselines and results. The results of the experiments are presented in table 1, which shows angular and scale error in the validation set. Qualitative results are shown in fig. 3. To verify whether the proposed warped convolution is indeed responsible for a boost in performance, rather than other architectural details, we compare it against a number of baselines with different components removed. The first baseline, CNN $^ +$ softargmax, consists of the same architecture but without the warp (section 5.2). This is a standard CNN, with the soft argmax at the end. Since CNNs are equivariant to translation, rather than scale and rotation, we observe a drop in performance. For the second baseline, $\mathrm { C N N + F C }$ , we replace the soft argmax with a fully-connected layer, to allow a prediction that is not equivariant with translation. The FC layer improves the angular error, but not the scale error. The proposed Warped CNN has a similar (slightly lower) capacity to the $\mathrm { C N N + F C }$ baseline, but we see it achieve better performance, since its architectural equivariance seems to be better matched to the data distribution.
+
+Table 2: Results of yaw and pitch pose estimation of faces on the AFLW dataset.   
+
+<table><tr><td></td><td>CNN+FC</td><td>STN+FC</td><td> STN+softargmax</td><td> Warped CNN</td></tr><tr><td>Yaw err. (deg.)</td><td>13.87</td><td>16.92</td><td>15.01</td><td>10.65</td></tr><tr><td>Pitch err. (deg.)</td><td>7.23</td><td>10.17</td><td>6.88</td><td>6.351</td></tr></table>
+
+# 6.3 FACES
+
+We now turn to face pose estimation in unconstrained photos, which requires handling more complex 3D rotations under perspective.
+
+Dataset. For this task we use the Annotated Facial Landmarks in the Wild (AFLW) dataset (Koestinger et al., 2011). It contains about 25K faces found in Flickr photos, and includes yaw (left-right) and pitch (up-down) annotations. We removed 933 faces with yaw larger than 90 degrees (i.e., facing away from the camera), resulting in a set of 24,384 samples. $20 \%$ of the faces were set aside for validation.
+
+Implementation. The region in each face’s bounding box is resized to a $6 4 \times 6 4$ image, which is then processed by the network. Recall that our simplified 3D model of yaw and pitch rotation (section 5.3) assumes a spherical geometry. Although a person’s head roughly follows a spherical shape, the sample images are centered around the face, not the head. As such, we use an affine Spatial Transformer Network (STN) (Jaderberg et al., 2015) as a first step, to center the image correctly. Similarly, because the optimal camera parameters $( f , r$ and $d$ ) are difficult to set by hand, we let the network learn them, by computing their derivatives numerically (which has a low overhead, since they are scalars). The rest of the network follows the same diagram as before (fig. 2). The main CNN has 4 convolutional layers, the first two with $5 \times 5$ filters, the others being $9 \times 9$ . The numbers of output channels are 20, 50, 20 and 1, respectively. A $3 \times 3$ max-pooling with a stride of 2 is performed after the first layer, and there are ReLU non-linearities between the others. As for the STN, it has 3 convolutional layers $\mathrm { ( 5 \times 5 ) }$ , with 20, 50 and 6 output channels respectively, and $3 \times 3$ max-pooling (stride 2) between them.
+
+Baselines and results. The angular error of the proposed equivariant pose estimation, Warped CNN, is shown in table 2, along with a number of baselines. Qualitative results are shown in fig. 4. The goal of these experiments is to demonstrate that it is possible to achieve equivariance to complex 3D rotations. We also wish to disentangle the performance benefits of the warped convolution from the other architectural aspects. The first baseline, $\mathrm { S T N + s }$ oftargmax, is the same as the proposed method, but without the warp. The large performance drop indicates that the spherical model incorporates important domain knowledge, which is ignored by a translation-equivariant STN. To allow nonequivariant models, we also test two other baselines where the softargmax is replaced with a fullyconnected (FC) layer. The $\mathrm { S T N + F C }$ includes an affine Spatial Transformer, while the $\mathrm { C N N + F C }$ does not, corresponding to a standard CNN of equivalent capacity. We observe that neither the FC or the STN components can account up for the performance of the warped convolution, which better exploits the natural 3D rotation equivariance of the data.
+
+# 7 CONCLUSIONS
+
+In this work we show that it is possible to reuse highly optimized convolutional blocks, which are equivariant to image translation, and coax them to exhibit equivariance to other operators, including 3D transformations. This is achieved by a simple warp of the input image, implemented with off-the-shelf components of deep networks, and can be used for image recognition tasks involving a large range of image transformations. Compared to other works, warped convolutions are simpler, relying on highly optimized convolution routines, and can flexibly handle many types of continuous transformations. Studying generalizations that support more than two parameters seems like a fruitful direction for future work. In addition to the practical aspects, our analysis offers some insights into the fundamental relationships between arbitrary image transformations and convolutional architectures.
+
+![](images/fb41b34c37d9d1158c9e5bd2cc84338546aa9a736b99811dd4154caf38a83c9a.jpg)  
+Figure 4: Example pose estimates (yaw and pitch) on the AFLW dataset (Section 6.3).
+
+# REFERENCES
+
+Joan Bruna, Arthur Szlam, and Yann LeCun. Learning stable group invariant representations with convolutional networks. arXiv preprint arXiv:1301.3537, 2013.
+
+Taco Cohen and Max Welling. Learning the Irreducible Representations of Commutative Lie Groups. In Proceedings of the 31st International Conference on Machine Learning (ICML-14), 2014.
+
+Taco Cohen and Max Welling. Group equivariant convolutional networks. In Proceedings of the 33rd International Conference on Machine Learning (ICML-16), 2016.
+
+Sander Dieleman, Kyle W Willett, and Joni Dambre. Rotation-invariant convolutional neural networks for galaxy morphology prediction. Monthly notices of the royal astronomical society, 450 (2):1441–1459, 2015.
+
+Gerald B Folland. A course in abstract harmonic analysis. 1995.
+
+Geremy Heitz and Daphne Koller. Learning spatial context: Using stuff to find things. In European Conference on Computer Vision, pp. 30–43. Springer, 2008.
+
+J. F. Henriques, P. Martins, R. Caseiro, and J. Batista. Fast training of pose detectors in the fourier domain. In Advances in Neural Information Processing Systems, 2014.
+
+Aapo Hyvärinen, Jarmo Hurri, and Patrick O Hoyer. Natural Image Statistics: A Probabilistic Approach to Early Computational Vision., volume 39. Springer Science & Business Media, 2009.
+
+Max Jaderberg, Karen Simonyan, Andrew Zisserman, et al. Spatial transformer networks. In Advances in Neural Information Processing Systems, pp. 2017–2025, 2015.
+
+Angjoo Kanazawa, Abhishek Sharma, and David Jacobs. Locally scale-invariant convolutional neural networks. arXiv preprint arXiv:1412.5104, 2014.
+
+Martin Koestinger, Paul Wohlhart, Peter M. Roth, and Horst Bischof. Annotated facial landmarks in the wild: A large-scale, real-world database for facial landmark localization. In First IEEE International Workshop on Benchmarking Facial Image Analysis Technologies, 2011.
+
+Andrew Lavin. Fast algorithms for convolutional neural networks. arXiv preprint arXiv:1509.09308, 2015.
+
+Karel Lenc and Andrea Vedaldi. Understanding image representations by measuring their equivariance and equivalence. In Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 991–999, 2015.
+
+Kun Liu, Henrik Skibbe, Thorsten Schmidt, Thomas Blein, Klaus Palme, Thomas Brox, and Olaf Ronneberger. Rotation-Invariant HOG Descriptors Using Fourier Analysis in Polar and Spherical Coordinates. International Journal of Computer Vision, 106(3):342–364, February 2014. ISSN 0920-5691, 1573-1405. doi: 10.1007/s11263-013-0634-z.
+
+Richard G Lyons. Understanding digital signal processing. Pearson Education, 2010.
+
+Diego Marcos, Michele Volpi, and Devis Tuia. Learning rotation invariant convolutional filters for texture classification. arXiv preprint arXiv:1604.06720, 2016.
+
+B. Srinivasa Reddy and Biswanath N. Chatterji. An FFT-based technique for translation, rotation, and scale-invariant image registration. IEEE Transactions on Image Processing, 5(8):1266–1271, 1996.
+
+Uwe Schmidt and Stefan Roth. Learning rotation-aware features: From invariant priors to equivariant descriptors. In Computer Vision and Pattern Recognition (CVPR), 2012 IEEE Conference on, pp. 2050–2057, 2012.
+
+Georgios Tzimiropoulos, Vasileios Argyriou, Stefanos Zafeiriou, and Tania Stathaki. Robust FFTbased scale-invariant image registration with image gradients. IEEE Transactions on Pattern Analysis and Machine Intelligence, 32(10):1899–1906, 2010.
+
+# A SPATIAL TRANSFORMATION FOR 3D SPHERE ROTATION UNDER PERSPECTIVE
+
+Our simplified model consists of a perspective camera with focal length $f$ and all other camera parameters equal to identity, at a distance $d$ from a centered sphere of radius $r$ (see fig. 1-d).
+
+A 2D point $x$ in image-space corresponds to the 3D point
+
+$$
+p = ( x _ { 1 } , x _ { 2 } , f ) .
+$$
+
+Raycasting it along the $z$ axis, it will intersect the sphere surface at the 3D point
+
+$$
+q = { \frac { p } { \| p \| } } \left( k - { \sqrt { k ^ { 2 } - d ^ { 2 } + r ^ { 2 } } } \right) , k = { \frac { f d } { \| p \| } } .
+$$
+
+If the argument of the square-root is negative, the ray does not intersect the sphere and so the point transformation is undefined. This means that the domain of the image $\Omega$ should be restricted to the sphere region. In practice, in such cases we simply leave the point unmodified.
+
+Then, the yaw and pitch coordinates of the point $q$ on the surface of the sphere are
+
+$$
+\phi _ { 1 } = \cos ^ { - 1 } \left( - \frac { q _ { 2 } } { r } \right) , \phi _ { 2 } = \mathrm { a t a n _ { 2 } } \left( - \frac { q _ { 1 } } { d - q _ { 3 } } \right) .
+$$
+
+These polar coordinates are now rotated by the spatial transformation parameters, $\phi ^ { \prime } = \phi + u$
+
+Converting the polar coordinates back to a 3D point $q ^ { \prime }$
+
+$$
+\begin{array} { r } { q ^ { \prime } = \left[ \begin{array} { c } { r \sin \phi _ { 1 } ^ { \prime } \sin \phi _ { 2 } ^ { \prime } } \\ { - r \cos \phi _ { 1 } ^ { \prime } } \\ { r \sin \phi _ { 1 } ^ { \prime } \cos \phi _ { 2 } ^ { \prime } - d } \end{array} \right] . } \end{array}
+$$
+
+Finally, projection of $q ^ { \prime }$ into image-space yields
+
+$$
+t _ { u } ( x ) = - { \frac { f } { q _ { 3 } ^ { \prime } } } \left[ \begin{array} { c } { { q _ { 1 } ^ { \prime } } } \\ { { q _ { 2 } ^ { \prime } } } \end{array} \right] .
+$$
\ No newline at end of file
diff --git a/parse/train/BkmM8Dceg/BkmM8Dceg_content_list.json b/parse/train/BkmM8Dceg/BkmM8Dceg_content_list.json
new file mode 100644
index 0000000000000000000000000000000000000000..b2007e5e9fc213e48ae1e068d0c239fe896669d8
--- /dev/null
+++ b/parse/train/BkmM8Dceg/BkmM8Dceg_content_list.json
@@ -0,0 +1,1635 @@
+[
+    {
+        "type": "text",
+        "text": "WARPED CONVOLUTIONS: EFFICIENT INVARIANCE TO SPATIAL TRANSFORMATIONS ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            98,
+            823,
+            146
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "João F. Henriques & Andrea Vedaldi   \nVisual Geometry Group   \nUniversity of Oxford   \n{joao,vedaldi}@robots.ox.ac.uk ",
+        "bbox": [
+            184,
+            169,
+            478,
+            226
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "ABSTRACT ",
+        "text_level": 1,
+        "bbox": [
+            454,
+            262,
+            544,
+            277
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Convolutional Neural Networks (CNNs) are extremely efficient, since they exploit the inherent translation-invariance of natural images. However, translation is just one of a myriad of useful spatial transformations. Can the same efficiency be attained when considering other spatial invariances? Such generalized convolutions have been considered in the past, but at a high computational cost. We present a construction that is simple and exact, yet has the same computational complexity that standard convolutions enjoy. It consists of a constant image warp followed by a simple convolution, which are standard blocks in deep learning toolboxes. With a carefully crafted warp, the resulting architecture can be made equivariant to a wide range of 2-parameters spatial transformations. We show encouraging results in realistic scenarios, including the estimation of vehicle poses in the Google Earth dataset (rotation and scale), and face poses in Annotated Facial Landmarks in the Wild (3D rotations under perspective). ",
+        "bbox": [
+            233,
+            295,
+            764,
+            476
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
+        "bbox": [
+            178,
+            507,
+            336,
+            523
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "A crucial aspect of current deep learning architectures is the encoding of invariances. This fact is epitomized in the success of convolutional neural networks (CNN), where equivariance to image translation is key: translating the input results in a translated output. When invariances are present in the data, encoding them explicitly in an architecture provides an important source of regularization, which allows to reduce the amount of training data required for learning. Invariances may also be used to improve the efficiency of implementations; for instance, a convolutional layer requires orders of magnitude less memory and also less computation compared to an equivalent fully-connected layer. ",
+        "bbox": [
+            174,
+            541,
+            825,
+            651
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "The success of CNNs indicates that translation invariance is an important property of images. However, this does not explain why translation equivariant operators work well for image understanding. The common interpretation is that such operators are matched to the statistics of natural images, which are well known to be translation invariant (Hyvärinen et al., 2009). However, natural image statistics are also (largely) invariant to other transformations such as isotropic scaling and rotation, which suggests that alternative neural network designs may also work well with images. Furthermore, in specific applications, invariances other than translation may be more appropriate. ",
+        "bbox": [
+            174,
+            659,
+            825,
+            756
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Therefore, it is natural to consider generalizing convolutional architectures to other image transformations, and this has been the subject of extensive study (Kanazawa et al., 2014; Bruna et al., 2013; Cohen & Welling, 2016). Unfortunately these approaches do not possess the same memory and speed benefits that CNNs enjoy. The reason is that, ultimately, they have to transform (warp) an image or filter several times (Kanazawa et al., 2014; Marcos et al., 2016; Dieleman et al., 2015), incurring a high computational burden. Another approach is to consider a basis of filters (analogous to eigen-images) encoding the desired invariance (Cohen & Welling, 2014; Bruna et al., 2013; Cohen & Welling, 2016), which requires more storage than a convolutional filter. ",
+        "bbox": [
+            174,
+            763,
+            825,
+            875
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Although they are able to handle transformations with many pose parameters, in practice most recent proposals are limited to very coarsely discretized transformations, such as horizontal/vertical flips and $9 0 ^ { \\circ }$ rotations (Dieleman et al., 2015; Cohen & Welling, 2014). ",
+        "bbox": [
+            176,
+            882,
+            823,
+            922
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "In this work we propose a generalization of CNNs that overcomes these disadvantages. Our main result shows that a linear layer with equivariance w.r.t. a large class of 2-parameters transformations can always be implemented efficiently, using a standard convolution in a warped image space. The image warp can be implemented using bilinear resampling, a simple and fast operation that has been popularized by spatial transformer networks (Jaderberg et al., 2015), and is part of most deep learning toolboxes. Unlike previous proposals, the proposed warped convolutions can handle continuous transformations, such as fine rotation and scaling. ",
+        "bbox": [
+            173,
+            103,
+            825,
+            202
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "This makes generalized convolution easily implementable in neural networks, including using fast convolution algorithms on GPU hardware, such as Winograd (Lavin, 2015) or the Fast Fourier Transform (Lyons, 2010). We present these notions in the simplest possible way (sections 2 to 4), but we note that they can be derived in broader generality from well know concepts of group theory (section 4.2). ",
+        "bbox": [
+            174,
+            208,
+            825,
+            279
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2 GENERALIZING CONVOLUTION ",
+        "text_level": 1,
+        "bbox": [
+            178,
+            297,
+            464,
+            314
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2.1 CONVOLUTIONS OF CONTINUOUS IMAGES ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            329,
+            504,
+            343
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "We start by looking at the basic building block of CNNs, i.e. the convolution operator. This operator computes the inner product of an image $\\boldsymbol { I } \\in \\mathbb { R } ^ { m \\times n }$ with a translated version of the filter $\\boldsymbol { F } \\in \\mathbb { R } ^ { r \\times s }$ , producing a new image as output: ",
+        "bbox": [
+            176,
+            354,
+            823,
+            397
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "equation",
+        "img_path": "images/d66687c82b23f584b74fc1586f926c8608ecfcedd91fe2ee364b6171447e398c.jpg",
+        "text": "$$\nH _ { j } = \\sum _ { k } I _ { k } F _ { k + j } ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            436,
+            396,
+            562,
+            429
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "where $k$ ${ \\mathfrak { a } } , { \\mathfrak { j } } \\in \\mathbb { Z } ^ { 2 }$ are two-dimensional vectors of indexes, and the summation ranges inside the extents of both arrays.1 To handle continuous deformations of the input, it is more natural to express eq. 1 as an integral over continuous rather than discrete inputs: ",
+        "bbox": [
+            174,
+            433,
+            825,
+            476
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "equation",
+        "img_path": "images/1aac3ddd9e603b228f74471fb49e534750cac869c5ebec337c39afd1194fb627.jpg",
+        "text": "$$\nH ( u ; I ) = \\int I ( x ) F ( x + u ) d x ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            388,
+            481,
+            607,
+            513
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "where $I ( x )$ and $F ( x )$ are continuous functions over a bounded 2D region $\\Omega \\subset \\mathbb { R } ^ { 2 }$ , that is: $I , F :$ $\\Omega \\to \\mathbb { R }$ . The real-valued 2D vectors $x \\in \\Omega$ now play the role of the indexes $k \\in  { \\mathbb { Z } } ^ { 2 }$ . Equation 2 reduces to the discrete case of eq. 1 if we define $I ( x )$ and $F ( x )$ as the sum of delta functions on grids. Intermediate values can be obtained by interpolation, such as bilinear (which amounts to convolution of the delta functions with a triangle filter (Jaderberg et al., 2015)). Importantly, such continuous images can be deformed by very rich continuous transformations of the input coordinates, whereas strictly discrete operations would be more limiting. ",
+        "bbox": [
+            173,
+            520,
+            825,
+            619
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Over the next sections it will be more convenient to translate the image $I$ instead of the filter $F$ . This alternative form of eq. 2 is obtained by replacing $x + u  x$ : ",
+        "bbox": [
+            174,
+            625,
+            821,
+            654
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "equation",
+        "img_path": "images/c53784700ff0cd400b5498931f64a21a8843276f3b0dc1f7c736466ccb3b073a.jpg",
+        "text": "$$\nH ( u ; I ) = \\int I ( x - u ) F ( x ) d x .\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2.2 BEYOND IMAGE TRANSLATIONS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            707,
+            436,
+            720
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "The standard convolution operator of eq. 3 can be interpreted as applying the filter to translated versions of the image. Translations can be replaced by other transformations as follows (Henriques et al., 2014): ",
+        "bbox": [
+            174,
+            732,
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+            773
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "equation",
+        "img_path": "images/c9c58d1ae40c35730ca04373a89d28c133f2745bd59ccf00fcbaaff8a2edf31a.jpg",
+        "text": "$$\nH ( t ; I ) = \\int I ( t ( x ) ) F ( x ) d x , \\quad t \\in G\n$$",
+        "text_format": "latex",
+        "bbox": [
+            367,
+            772,
+            632,
+            804
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "where $G$ is a set of transformation functions $t : \\Omega \\to \\Omega$ (assumed to be invertible). Intuitively, this generalized convolution performs an exhaustive search for a pattern, at many different poses (Henriques et al., 2014; Kanazawa et al., 2014). The interest in this definition lies in the fact that it makes convolution equivariant (Lenc & Vedaldi, 2015): ",
+        "bbox": [
+            174,
+            806,
+            825,
+            863
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Lemma 1 (Equivariance). Consider the generalized convolution operator $H ( t ; I )$ of eq. 4. Generalized convolution “commutes” with any transformation $q \\in G$ of the image: ",
+        "bbox": [
+            171,
+            103,
+            823,
+            132
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/215391eb24c08504dcb2ff688bd3ec840e2bb91efb68e7d7e2e094d96e759c4e.jpg",
+        "text": "$$\nH ( t ; I \\circ q ) = H ( q \\circ t ; I ) .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            411,
+            140,
+            584,
+            156
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Proof. One has immediately $\\begin{array} { r } { H ( t ; I \\circ q ) = \\int I ( q ( t ( x ) ) ) F ( x ) d x = H ( q \\circ t ; I ) . } \\end{array}$ ",
+        "bbox": [
+            171,
+            171,
+            700,
+            189
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "A notable case is when transformations have an additive parametrization $t : \\Omega \\times \\mathbb { R } ^ { 2 } \\to \\Omega$ , with $( x , u ) \\mapsto t _ { u } ( x )$ and $t _ { u } \\circ t _ { v } = t _ { u + v }$ . In this case, the equivariance relation can be written as ",
+        "bbox": [
+            171,
+            205,
+            823,
+            234
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/0661afcf0ae6cdffe78a17ebec2cc568e97a6684c79ffdac14e7bb3a10dd40d5.jpg",
+        "text": "$$\nH ( u ; I \\circ t _ { v } ) = H ( v + u ; I ) .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            401,
+            242,
+            596,
+            258
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In particular, standard convolution is obtained when $t _ { u } ( x ) = x - u$ is the translation operator. In this case, the lemma above simply states that any translation of the input of the convolution results in a corresponding translation of the output. ",
+        "bbox": [
+            174,
+            266,
+            826,
+            309
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In section 5, we will look in more detail at a few concrete examples of transformations other than translations. Although we will not do so explicitly, in this construction it is also possible to let one or more dimensions of the parameter space $\\mathbb { R } ^ { \\bar { 2 } }$ be given modulus a period $Q$ , in the sense of replacing $\\mathbb { R }$ with $\\mathbb { R } / \\mathbb { Z } ( Q )$ ; the latter is required to parameterise transformations such as rotation. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3 COMPUTATIONAL EFFICIENCY ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Unfortunately, what eq. 4 gains us in generality, it loses in both performance and ease of implementation. Most works in computer vision that looked at filtering under generalized transformations (e.g. scale pyramids (Kanazawa et al., 2014) or rotated filter banks (Marcos et al., 2016; Cohen & Welling, 2014; 2016; Henriques et al., 2014)) compute eq. 4 directly by evaluating a large number of transformations $t \\in G$ . This entails warping (transforming) either the image or the filter once per transformation $t$ , which can be expensive. ",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Opting to transform the filter instead of the image can be advantageous, since it is smaller in size. On the other hand, the filter and its domain then become spatially-varying, which foregoes the benefit of the regular, predictable, and local pattern of computations in standard convolution. It precludes the use of fast convolution routines such as Winograd’s algorithm (Lavin, 2015), or the Fast Fourier Transform (Lyons, 2010), which has lower computational complexity than exhaustive search (eq. 3). ",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In practice, most recent works focus on very coarse transformations that do not change the filter support and can be implemented strictly via permutations, like horizontal/vertical flips and $9 0 ^ { \\circ }$ rotations (Dieleman et al., 2015; Cohen & Welling, 2014). Such difficulties explain why generalized convolutions are not as widespread as CNNs. ",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In section 4 we will show that, for an important class of transformations, including the ones considered in previous works (such as Kanazawa et al. (2014); Cohen & Welling (2014); Marcos et al. (2016)) it is possible to perform generalized convolution by composing a single warp with a standard convolution, instead of several warps. Thus, we are able to take full advantage of modern convolution implementations (Lavin, 2015; Lyons, 2010), including those with lower computational complexity. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "4 MAIN RESULT ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Our main contribution is to show that the generalized convolution operator of eq. 4 can be implemented efficiently by a standard convolution, by pre-warping the input image and filter appropriately. The warp is the same for any image, depending solely on the nature of the relevant transformations, and can be written in closed form. This result, given in theorem 1, allows us to implement very efficient generalized convolutions using simple computational blocks, as shown in section 4.1. We name this method warped convolution. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The strongest assumption is that transformations must have an additive parametrization. By this, we mean that there exists a bijection $t _ { u } : \\Omega \\to \\Omega$ such that, for any $u , v \\in \\mathbb { R } ^ { 2 }$ , parameters compose additively $t _ { u } \\circ t _ { v } = t _ { u + v }$ . The second assumption is that there exists a pivot point $x _ { 0 } \\in \\Omega$ such that $u \\mapsto t _ { u } ( x _ { 0 } )$ defines a bijection $\\mathbb { R } ^ { 2 } \\to \\Omega$ from the parameter space to the real plane. The latter requirements means that any point $x \\in \\Omega$ can be “reached” by transforming $x _ { 0 }$ under a suitable $t _ { u }$ . We then have that: ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Theorem 1. Consider the generalized convolution of eq. 4. Assume that the transformation is additive $( t _ { u } \\circ t _ { v } = t _ { u + v . }$ ). Assume also that, for a fixed pivot point $x _ { 0 }$ , the function $u \\mapsto t _ { u } ( x _ { 0 } )$ is bijective. Then we can rewrite generalized convolution (eq. 4) as the standard convolution ",
+        "bbox": [
+            173,
+            148,
+            825,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/63ea9bdacd1b511cbcc2248b2a9f69d17af3e02ea4e53ea964c348c91ef9e3a1.jpg",
+        "text": "$$\nH ( u ; I ) = \\int \\hat { I } ( u + v ) \\hat { F } ( v ) d v ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            392,
+            195,
+            604,
+            228
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where $\\hat { I }$ and $\\hat { F }$ are the warped image and filter given by: ",
+        "bbox": [
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+            233,
+            545,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/36c0607d4677e46cf89b622989f83fa21343507de331febd605abe36a9587f7c.jpg",
+        "text": "$$\n\\hat { I } ( u ) = I ( t _ { u } ( x _ { 0 } ) ) , \\qquad \\hat { F } ( u ) = F ( t _ { u } ( x _ { 0 } ) ) \\left| \\frac { d t _ { u } ( x _ { 0 } ) } { d u } \\right| .\n$$",
+        "text_format": "latex",
+        "bbox": [
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+            252,
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+            287
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Proof. We use the variable substitution $x = t _ { v } ( x _ { 0 } )$ in eq. 4. Then: ",
+        "bbox": [
+            173,
+            300,
+            611,
+            315
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/f62b9951c65fe6aab37827b2ea6e20108c56f377a9d664ff0d612ef222aa99ff.jpg",
+        "text": "$$\n\\begin{array} { l } { H ( u ; I ) = \\displaystyle \\int I ( t _ { u } ( x ) ) F ( x ) d x } \\\\ { \\displaystyle = \\int I ( t _ { u } ( t _ { v } ( x _ { 0 } ) ) ) F ( t _ { v } ( x _ { 0 } ) ) \\left| \\frac { d t _ { v } ( x _ { 0 } ) } { d v } \\right| d v } \\\\ { \\displaystyle = \\int \\underbrace { I ( t _ { u + v } ( x _ { 0 } ) ) } _ { \\hat { I } ( u + v ) } \\underbrace { F ( t _ { v } ( x _ { 0 } ) ) \\left| \\frac { d t _ { v } ( x _ { 0 } ) } { d v } \\right| } _ { \\hat { F } ( v ) } d v } \\\\ { \\displaystyle = \\int \\hat { I } ( u + v ) \\hat { F } ( v ) d v . } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            321,
+            320,
+            676,
+            479
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The warp that is applied to both inputs in eq. 7 can be interpreted as follows. We start with an arbitrary pivot point $x _ { 0 }$ in the image and them sample other points by repeatedly applying the transformation $t _ { u } ( x _ { 0 } )$ to the pivot (by varying $u$ ). When discretized, this sampling is performed over a 2D grid of parameters $u$ . Finally, sampling the input at these points (for example, by bilinear interpolation) yields the warped input. ",
+        "bbox": [
+            174,
+            511,
+            825,
+            582
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "An illustration is given in fig. 1, for various transformations (each one is discussed in more detail in section 5). The red dot shows the pivot point $x _ { 0 }$ , and the two arrows pointing away from it show the two directions of increasing $u$ values (recall that transformation parameters are two-dimensional). The grids were generated by sampling $u$ at regular intervals. Note that the warp grids are independent of the image contents – they can be computed once offline and then applied to any image. ",
+        "bbox": [
+            174,
+            588,
+            825,
+            659
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The last factor in eq. 7 is the determinant of the Jacobian of the image transformation $t$ . It rescales the image values to account for the stretching and shrinking of space due to non-linear warps. It can also be computed offline, and its application amounts to an element-wise product by a constant array. A generalization using group theory is discussed in section 4.2. ",
+        "bbox": [
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+            665,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4.1 PRACTICAL CONSIDERATIONS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            737,
+            421,
+            752
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "There are a few interesting aspects that simplify the use of theorem 1 in practice. ",
+        "bbox": [
+            176,
+            763,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "First, since in most applications the filter $F$ is learned, we are free to ignore the constant warp and Jacobian in eq. 7 (which amounts to a simple reparametrization), and learn $\\hat { F }$ directly. In practice, this means that we warp only the input image $I$ to obtain $\\hat { I }$ , and then perform a standard convolution with a filter $\\hat { F }$ . The learned warped filter $\\hat { F }$ has a one-to-one correspondence to an image-space filter $F$ by means of eq. 7, although there is no real need to build the latter explicitly. ",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Second, we can choose either one or two spatial transformations for the generalized convolution (e.g. scale and rotation, simultaneously). The reason is that the input image is 2D, so the parameterspace after warping is also 2D. The choice is not arbitrary though: the two transformations must commute, in order to respect additivity. This will be the case of the pairs we study in section 5. ",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Algorithm 1 Warped convolution. ",
+        "text_level": 1,
+        "bbox": [
+            176,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Grid generation (offline) ",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "• Apply the spatial transformation $t$ repeatedly to a pivot point $x _ { 0 }$ , using a 2D grid of parameters $\\stackrel { \\cdot } { u } = \\{ \\bar { ( } u _ { 1 } + i \\delta _ { 1 } , u _ { 2 } + j \\delta _ { 2 } ) : i = 0 , \\ldots , m , j = 0 , \\bar { \\ldots } , n \\}$ , obtaining the 2D warp grid $t _ { u } ( x _ { 0 } )$ . ",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Warped convolution ",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "1. Resample input image $I$ using the warp grid $t _ { u } ( x _ { 0 } )$ , by bilinear interpolation. ",
+        "bbox": [
+            209,
+            213,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "2. Convolve the warped image $\\hat { I }$ with filter $\\hat { F }$ . ",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "By theorem 1, these steps are equivalent to a generalized convolution, which performs an exhaustive search across the pose-space of transformation $t$ , but at a much lower computational cost. ",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.2 RELATIONSHIP TO GROUP THEORY ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            314,
+            452,
+            328
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "This section relates our results, which have been presented using a simple formalism and in a restricted setting, to a more general approach based on group theory (Folland, 1995). ",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "To this end, let $G$ be a group of transformations. Under very mild conditions (the group has to be locally compact and Hausdorff), there exists a unique measure on the group, the Haar measure, which is invariant to the group action, in the sense that, given a measurable function ${ \\tilde { I } } : G \\to$ $\\mathbb { R }$ , then $\\begin{array} { r } { \\int \\tilde { I } ( g ^ { \\prime } g ) d g = \\int \\overline { { \\tilde { I } } } ( g ) \\dot { } d g } \\end{array}$ . Using this measure, one can define generalized convolution as $\\begin{array} { r } { ( \\tilde { I } * \\tilde { F } ) ( t ) = \\int _ { G } \\tilde { I } ( t g ) \\tilde { F } ( g ^ { - 1 } ) d g } \\end{array}$ . This resembles our definition (4), although image and filter are defined on the group $G$ instead of the spatial domain $\\mathbb { R } ^ { 2 }$ . Lemma 1 translates immediately to this case (Folland, 1995). ",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "In order to extend Theorem 1, we need to make this general but abstract construction concrete. Here one assumes that the group acts transitively on a subset $X \\subset \\mathbb { R } ^ { 2 }$ (which means that any point $x \\in X$ can be written as $x = g x _ { 0 }$ , for a fixed point $x _ { 0 } \\in X$ and a suitable transformation $g \\in G$ ). Then one can define the image as $\\tilde { I } ( g ) = I ( g \\bar { ( } x _ { 0 } ) )$ , where $I$ is a function of the spatial domain $X$ instead of the group $G$ , and likewise for the filter. Next, it is necessary to explicitly calculate the integral over $G$ . If the group is an Abelian (commutative) Lie group, then one can show that there exists a map $\\exp : V \\to G$ , the exponential map, defined on a vector space $V$ . Under commutativity, this map is also additive, in the sense that $\\exp ( u ) \\exp ( v ) = \\exp ( u + v )$ . The structure of $V$ depends on the specific group, but under such restrictive conditions, it is a torus, which allows the calculation of $\\textstyle \\int { \\tilde { I } } ( { \\bar { g } } ) d g$ as $\\begin{array} { r } { \\int \\tilde { I } ( \\exp ( u ) x _ { 0 } ) d u . } \\end{array}$ . ",
+        "bbox": [
+            173,
+            488,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Finally, in order to swap integration over the group parameters with integration over space, one assumes that $x \\ = \\ \\exp ( u ) x _ { 0 }$ defines a smooth bijection $V \\  \\ X$ , so that it is possible to use the change of variable $\\dot { u }  u ( x )$ where $\\mathrm { e x p } ( u ( x ) ) x _ { 0 } = x$ . This allows writing the integral as $\\begin{array} { r } { \\int { \\tilde { I } } ( \\exp ( u ) x _ { 0 } ) d u = \\int I ( x ) \\left| d u / d x \\right| d x } \\end{array}$ . Note that this Jacobian is the inverse of the one found in (1) due to the fact that we started by defining our convolution using $I$ instead of $\\tilde { I }$ . ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "5 EXAMPLES OF SPATIAL TRANSFORMATIONS ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We now give some concrete examples of pairs of spatial transformations that obey the conditions of theorem 1, and can be useful in practice. ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "5.1 SCALE AND ASPECT RATIO ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            819,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Detection tasks require predicting the extent of an object as a bounding box. While the location can be found accurately by a standard CNN, which is equivariant to translation, the size prediction could similarly benefit from equivariance to horizontal and vertical scale (equivalently, scale and aspect ratio). ",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Such a spatial transformation, from which a warp can be constructed, is given by: ",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/60788d1a003ce7fcae165868e8ad44de46e7af62c507569ccf0f4de9f35dc344.jpg",
+        "image_caption": [
+            "Figure 1: First row: Sampling grids that define the warps associated with different spatial transformations. Second row: An example image (a) after warping with each grid (b-d). Third row: A small translation is applied to each warped image, which is then mapped back to the original space (by an inverse warp). Translation in one axis of the appropriate warped space is equivalent to (b) horizontal scaling; (c) planar rotation; (d) 3D rotation around the vertical axis. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+            98,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "img_path": "images/2d30af2a4b23b48bb60e4ef9cc351f77c45fee152af7976aafd5c3c199090dea.jpg",
+        "text": "$$\nt _ { u } ( x ) = { \\left[ \\begin{array} { l } { x _ { 1 } s ^ { u _ { 1 } } } \\\\ { x _ { 2 } s ^ { u _ { 2 } } } \\end{array} \\right] }\n$$",
+        "text_format": "latex",
+        "bbox": [
+            431,
+            606,
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+            641
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "The $s$ constant controls the total degree of scaling applied. Notice that the output must be exponential in the scale parameters $u$ ; this ensures the additive structure required by theorem 1: $t _ { u } ( \\bar { t } _ { v } ( x ) ) =$ $t _ { u + v } ( x )$ . The resulting warp grid can be visualized in fig. 1-b. In this case, the domain of the image must be $\\Omega \\in \\mathbb { R } _ { + } ^ { 2 }$ , since a pivot $x _ { 0 }$ in one quadrant cannot reach another quadrant by any amount of (positive) scaling. ",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5.2 SCALE AND ROTATION (LOG-POLAR WARP) ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            744,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Planar scale and rotation are perhaps the most obvious spatial transformations in images, and are a natural test case for works on spatial transformations (Kanazawa et al., 2014; Marcos et al., 2016). Rotating a point $x$ by $u _ { 1 }$ radians and scaling it by $u _ { 2 }$ , around the origin, can be performed with ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "img_path": "images/c12bc61daeb8c4068f35af6a7e6dcd729d9df9dbb649a577448644364e368d24.jpg",
+        "text": "$$\nt _ { u } ( x ) = \\left[ \\begin{array} { l } { s ^ { u _ { 2 } } \\left\\| x \\right\\| \\cos ( \\mathrm { a t a n } _ { 2 } ( x _ { 2 } , x _ { 1 } ) + u _ { 1 } ) } \\\\ { s ^ { u _ { 2 } } \\left\\| x \\right\\| \\sin ( \\mathrm { a t a n } _ { 2 } ( x _ { 2 } , x _ { 1 } ) + u _ { 1 } ) } \\end{array} \\right] ,\n$$",
+        "text_format": "latex",
+        "bbox": [
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+            833,
+            656,
+            868
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where atan $^ 2$ is the standard 4-quadrant inverse tangent function (atan2). The domain in this case must exclude the origin $( \\Omega \\in \\dot { \\mathbb { R } } ^ { 2 } \\setminus \\{ 0 \\} )$ , since a pivot $x _ { 0 } = 0$ cannot reach any other points in the image by rotation or scaling. ",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/411e48b00e252ab8e9ec8948af96a700f5774ade8b1cca75c0faf68a96fea41e.jpg",
+        "image_caption": [
+            "Figure 2: Equivariant pose estimation strategy used in the experiments (section 6). With an appropriate warp and a standard CNN, the shaded block becomes equivalent to a generalized CNN (by theorem 1), which performs exhaustive searches across pose-space instead of image-space. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            266,
+            103,
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+            142
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "The resulting warp grid can be visualized in fig. 1-c. It is interesting to observe that it corresponds exactly to the log-polar domain, which is used in the signal processing literature to perform correlation across scale and rotation (Tzimiropoulos et al., 2010; Reddy & Chatterji, 1996). In fact, it was the source of inspiration for this work, which can be seen as a generalization of the log-polar domain to other spatial transformations. ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "5.3 3D SPHERE ROTATION UNDER PERSPECTIVE ",
+        "text_level": 1,
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+        "text": "We will now tackle a more difficult spatial transformation, in an attempt to demonstrate the generality of theorem 1. The transformations we will consider are yaw and pitch rotations in 3D space, as seen by a perspective camera. In the experiments (section 6) we will show how to apply it to face pose estimation. ",
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+        "type": "text",
+        "text": "In order to maintain additivity, the rotated 3D points must remain on the surface of a sphere. We consider a simplified camera and world model, whose only hyperparameters are a focal length $f$ , the radius of a sphere $r$ , and its distance from the camera center $d$ . The equations for the spatial transformation corresponding to yaw and pitch rotation under this model are in appendix A. ",
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+        "type": "text",
+        "text": "The corresponding warp grid can be seen in fig. 1-d. It can be observed that the grid corresponds to what we would expect of a 3D rendering of a sphere with a discrete mesh. An intuitive picture of the effect of the warp grid in such cases is that it wraps the 2D image around the surface of the 3D object, so that translation in the warped space corresponds to moving between vertexes of the 3D geometry. ",
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+        "text": "6 EXPERIMENTS ",
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+        "text": "6.1 ARCHITECTURE ",
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+        "type": "text",
+        "text": "As mentioned in section 2.2, generalized convolution performs an exhaustive search for patterns across spatial transformations, by varying pose parameters. For tasks where invariance to that transformation is important, it is usual to pool the detection responses across all poses (Marcos et al., 2016; Kanazawa et al., 2014). ",
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+        "text": "In the experiments, however, we will test the framework in pose prediction tasks. As such, we do not want to pool the detection responses (e.g. with a max operation) but rather find the pose with the strongest response (i.e., an argmax operation). To perform this operation in a differentiable manner, we implement a soft argmax operation, defined as follows: ",
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+        "img_path": "images/37776009230040da7cad487e5ed5747cc940e28dac129b7bb622cfd1f71dfbd0.jpg",
+        "text": "$$\ns _ { 1 } ( a ) = \\sum _ { i j } ^ { m n } \\frac { i } { m } \\sigma _ { i j } ( a ) , \\qquad s _ { 2 } ( a ) = \\sum _ { i j } ^ { m n } \\frac { j } { n } \\sigma _ { i j } ( a ) ,\n$$",
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+        "type": "text",
+        "text": "where $\\sigma ( a ) \\in \\mathbb { R } ^ { m \\times n }$ is the softmax over all spatial locations, and $\\sigma _ { i j } ( a )$ indexes the element at $( i , j )$ . The outputs are the two spatial coordinates of the maximum value, $s ( a ) \\in \\mathbb { R } ^ { 2 }$ . ",
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+        "text": "Our base architecture then consists of the following blocks, outlined in fig. 2. First, the input image is warped with a pre-generated grid, according to section 4. The warped image is then processed by a standard CNN, which is now equivariant to the spatial transformation that was used to generate the warp grid. A soft argmax (eq. 10) then finds the maximum over pose-space. To ensure the pose prediction is well registered to the reference coordinate system, a learnable scale and bias are applied to the outputs. Training proceeds by minimizing the $L ^ { 1 }$ loss between the predicted pose and ground truth pose. ",
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+        "table_caption": [
+            "Table 1: Results of scale and rotation pose estimation of vehicles in the Google Earth dataset. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>CNN+FC</td><td>CNN+softargmax</td><td> Warped CNN</td></tr><tr><td>Rotation error (degrees)</td><td>28.87</td><td>30.6</td><td>26.44</td></tr><tr><td>Scale error (px)</td><td>17.51</td><td>5.783</td><td>5.4</td></tr></table>",
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+        "img_path": "images/db8ba0448a92bfa2d818168ec5f182ee517f7c3a909c68da0c90758eb10407fb.jpg",
+        "image_caption": [
+            "Figure 3: Example pose estimates (rotation and scale) on the Google Earth dataset (Section 6.2). "
+        ],
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+        "type": "text",
+        "text": "6.2 GOOGLE EARTH",
+        "text_level": 1,
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+        "type": "text",
+        "text": "For the first task in our experiments, we will consider aerial photos of vehicles, which have been used in several works that deal with rotation invariance (Liu et al., 2014; Schmidt & Roth, 2012; Henriques et al., 2014). ",
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+        "type": "text",
+        "text": "Dataset. The Google Earth dataset (Heitz & Koller, 2008) contains bounding box annotations, supplemented with angle annotations from (Henriques et al., 2014), for 697 vehicles in 15 large images. We use the first 10 for training and the rest for validation. Going beyond these previous works, we focus on the estimation of both rotation and scale parameters. The object scale is taken to be the diagonal length of the bounding box. ",
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+    {
+        "type": "text",
+        "text": "Implementation. A $4 8 \\times 4 8$ image around each vehicle is cropped and downscaled by $50 \\%$ , and then fed to a network for pose prediction. The proposed method, Warped CNN, follows the architecture of section 6.1 (visualized in fig. 2). The CNN block contains 3 convolutional layers with $5 \\times 5$ filters, with 20, 50 and 1 output channels respectively. Recall that the output of the CNN block is a single-channel response map over 2D pose-space, which in this case consists of rotation and scale. Between the convolutional layers there are $3 \\times 3$ max-pooling operators, with a stride of 2, and a ReLU before the last layer. All networks are trained for 20 epochs with SGD, using hyperparameters chosen by cross-validation. ",
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+    {
+        "type": "text",
+        "text": "Baselines and results. The results of the experiments are presented in table 1, which shows angular and scale error in the validation set. Qualitative results are shown in fig. 3. To verify whether the proposed warped convolution is indeed responsible for a boost in performance, rather than other architectural details, we compare it against a number of baselines with different components removed. The first baseline, CNN $^ +$ softargmax, consists of the same architecture but without the warp (section 5.2). This is a standard CNN, with the soft argmax at the end. Since CNNs are equivariant to translation, rather than scale and rotation, we observe a drop in performance. For the second baseline, $\\mathrm { C N N + F C }$ , we replace the soft argmax with a fully-connected layer, to allow a prediction that is not equivariant with translation. The FC layer improves the angular error, but not the scale error. The proposed Warped CNN has a similar (slightly lower) capacity to the $\\mathrm { C N N + F C }$ baseline, but we see it achieve better performance, since its architectural equivariance seems to be better matched to the data distribution. ",
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+        "type": "table",
+        "img_path": "images/bf93d6e3f74a317490197552af8bed33a05296e8f8bcae07c592ca6123689bd4.jpg",
+        "table_caption": [
+            "Table 2: Results of yaw and pitch pose estimation of faces on the AFLW dataset. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>CNN+FC</td><td>STN+FC</td><td> STN+softargmax</td><td> Warped CNN</td></tr><tr><td>Yaw err. (deg.)</td><td>13.87</td><td>16.92</td><td>15.01</td><td>10.65</td></tr><tr><td>Pitch err. (deg.)</td><td>7.23</td><td>10.17</td><td>6.88</td><td>6.351</td></tr></table>",
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "6.3 FACES ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We now turn to face pose estimation in unconstrained photos, which requires handling more complex 3D rotations under perspective. ",
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+    {
+        "type": "text",
+        "text": "Dataset. For this task we use the Annotated Facial Landmarks in the Wild (AFLW) dataset (Koestinger et al., 2011). It contains about 25K faces found in Flickr photos, and includes yaw (left-right) and pitch (up-down) annotations. We removed 933 faces with yaw larger than 90 degrees (i.e., facing away from the camera), resulting in a set of 24,384 samples. $20 \\%$ of the faces were set aside for validation. ",
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+        "page_idx": 8
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+    {
+        "type": "text",
+        "text": "Implementation. The region in each face’s bounding box is resized to a $6 4 \\times 6 4$ image, which is then processed by the network. Recall that our simplified 3D model of yaw and pitch rotation (section 5.3) assumes a spherical geometry. Although a person’s head roughly follows a spherical shape, the sample images are centered around the face, not the head. As such, we use an affine Spatial Transformer Network (STN) (Jaderberg et al., 2015) as a first step, to center the image correctly. Similarly, because the optimal camera parameters $( f , r$ and $d$ ) are difficult to set by hand, we let the network learn them, by computing their derivatives numerically (which has a low overhead, since they are scalars). The rest of the network follows the same diagram as before (fig. 2). The main CNN has 4 convolutional layers, the first two with $5 \\times 5$ filters, the others being $9 \\times 9$ . The numbers of output channels are 20, 50, 20 and 1, respectively. A $3 \\times 3$ max-pooling with a stride of 2 is performed after the first layer, and there are ReLU non-linearities between the others. As for the STN, it has 3 convolutional layers $\\mathrm { ( 5 \\times 5 ) }$ , with 20, 50 and 6 output channels respectively, and $3 \\times 3$ max-pooling (stride 2) between them. ",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Baselines and results. The angular error of the proposed equivariant pose estimation, Warped CNN, is shown in table 2, along with a number of baselines. Qualitative results are shown in fig. 4. The goal of these experiments is to demonstrate that it is possible to achieve equivariance to complex 3D rotations. We also wish to disentangle the performance benefits of the warped convolution from the other architectural aspects. The first baseline, $\\mathrm { S T N + s }$ oftargmax, is the same as the proposed method, but without the warp. The large performance drop indicates that the spherical model incorporates important domain knowledge, which is ignored by a translation-equivariant STN. To allow nonequivariant models, we also test two other baselines where the softargmax is replaced with a fullyconnected (FC) layer. The $\\mathrm { S T N + F C }$ includes an affine Spatial Transformer, while the $\\mathrm { C N N + F C }$ does not, corresponding to a standard CNN of equivalent capacity. We observe that neither the FC or the STN components can account up for the performance of the warped convolution, which better exploits the natural 3D rotation equivariance of the data. ",
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+        "page_idx": 8
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+    {
+        "type": "text",
+        "text": "7 CONCLUSIONS ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 8
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+    {
+        "type": "text",
+        "text": "In this work we show that it is possible to reuse highly optimized convolutional blocks, which are equivariant to image translation, and coax them to exhibit equivariance to other operators, including 3D transformations. This is achieved by a simple warp of the input image, implemented with off-the-shelf components of deep networks, and can be used for image recognition tasks involving a large range of image transformations. Compared to other works, warped convolutions are simpler, relying on highly optimized convolution routines, and can flexibly handle many types of continuous transformations. Studying generalizations that support more than two parameters seems like a fruitful direction for future work. In addition to the practical aspects, our analysis offers some insights into the fundamental relationships between arbitrary image transformations and convolutional architectures. ",
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+        "image_caption": [
+            "Figure 4: Example pose estimates (yaw and pitch) on the AFLW dataset (Section 6.3). "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "REFERENCES ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            308,
+            287,
+            324
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Joan Bruna, Arthur Szlam, and Yann LeCun. Learning stable group invariant representations with convolutional networks. arXiv preprint arXiv:1301.3537, 2013. ",
+        "bbox": [
+            174,
+            332,
+            823,
+            359
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Taco Cohen and Max Welling. Learning the Irreducible Representations of Commutative Lie Groups. In Proceedings of the 31st International Conference on Machine Learning (ICML-14), 2014. ",
+        "bbox": [
+            174,
+            369,
+            825,
+            411
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Taco Cohen and Max Welling. Group equivariant convolutional networks. In Proceedings of the 33rd International Conference on Machine Learning (ICML-16), 2016. ",
+        "bbox": [
+            174,
+            421,
+            821,
+            450
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Sander Dieleman, Kyle W Willett, and Joni Dambre. Rotation-invariant convolutional neural networks for galaxy morphology prediction. Monthly notices of the royal astronomical society, 450 (2):1441–1459, 2015. ",
+        "bbox": [
+            173,
+            458,
+            825,
+            502
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Gerald B Folland. A course in abstract harmonic analysis. 1995. ",
+        "bbox": [
+            173,
+            511,
+            598,
+            526
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Geremy Heitz and Daphne Koller. Learning spatial context: Using stuff to find things. In European Conference on Computer Vision, pp. 30–43. Springer, 2008. ",
+        "bbox": [
+            176,
+            535,
+            823,
+            564
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "J. F. Henriques, P. Martins, R. Caseiro, and J. Batista. Fast training of pose detectors in the fourier domain. In Advances in Neural Information Processing Systems, 2014. ",
+        "bbox": [
+            173,
+            573,
+            823,
+            603
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Aapo Hyvärinen, Jarmo Hurri, and Patrick O Hoyer. Natural Image Statistics: A Probabilistic Approach to Early Computational Vision., volume 39. Springer Science & Business Media, 2009. ",
+        "bbox": [
+            174,
+            611,
+            823,
+            641
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Max Jaderberg, Karen Simonyan, Andrew Zisserman, et al. Spatial transformer networks. In Advances in Neural Information Processing Systems, pp. 2017–2025, 2015. ",
+        "bbox": [
+            173,
+            648,
+            825,
+            679
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Angjoo Kanazawa, Abhishek Sharma, and David Jacobs. Locally scale-invariant convolutional neural networks. arXiv preprint arXiv:1412.5104, 2014. ",
+        "bbox": [
+            173,
+            688,
+            823,
+            717
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Martin Koestinger, Paul Wohlhart, Peter M. Roth, and Horst Bischof. Annotated facial landmarks in the wild: A large-scale, real-world database for facial landmark localization. In First IEEE International Workshop on Benchmarking Facial Image Analysis Technologies, 2011. ",
+        "bbox": [
+            176,
+            726,
+            825,
+            768
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Andrew Lavin. Fast algorithms for convolutional neural networks. arXiv preprint arXiv:1509.09308, 2015. ",
+        "bbox": [
+            169,
+            777,
+            823,
+            806
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Karel Lenc and Andrea Vedaldi. Understanding image representations by measuring their equivariance and equivalence. In Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 991–999, 2015. ",
+        "bbox": [
+            174,
+            815,
+            823,
+            858
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Kun Liu, Henrik Skibbe, Thorsten Schmidt, Thomas Blein, Klaus Palme, Thomas Brox, and Olaf Ronneberger. Rotation-Invariant HOG Descriptors Using Fourier Analysis in Polar and Spherical Coordinates. International Journal of Computer Vision, 106(3):342–364, February 2014. ISSN 0920-5691, 1573-1405. doi: 10.1007/s11263-013-0634-z. ",
+        "bbox": [
+            174,
+            867,
+            825,
+            922
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Richard G Lyons. Understanding digital signal processing. Pearson Education, 2010. ",
+        "bbox": [
+            171,
+            103,
+            735,
+            119
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Diego Marcos, Michele Volpi, and Devis Tuia. Learning rotation invariant convolutional filters for texture classification. arXiv preprint arXiv:1604.06720, 2016. ",
+        "bbox": [
+            171,
+            127,
+            823,
+            156
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "B. Srinivasa Reddy and Biswanath N. Chatterji. An FFT-based technique for translation, rotation, and scale-invariant image registration. IEEE Transactions on Image Processing, 5(8):1266–1271, 1996. ",
+        "bbox": [
+            174,
+            165,
+            823,
+            207
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Uwe Schmidt and Stefan Roth. Learning rotation-aware features: From invariant priors to equivariant descriptors. In Computer Vision and Pattern Recognition (CVPR), 2012 IEEE Conference on, pp. 2050–2057, 2012. ",
+        "bbox": [
+            174,
+            215,
+            823,
+            258
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Georgios Tzimiropoulos, Vasileios Argyriou, Stefanos Zafeiriou, and Tania Stathaki. Robust FFTbased scale-invariant image registration with image gradients. IEEE Transactions on Pattern Analysis and Machine Intelligence, 32(10):1899–1906, 2010. ",
+        "bbox": [
+            174,
+            268,
+            825,
+            310
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "A SPATIAL TRANSFORMATION FOR 3D SPHERE ROTATION UNDER PERSPECTIVE ",
+        "text_level": 1,
+        "bbox": [
+            173,
+            102,
+            732,
+            136
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Our simplified model consists of a perspective camera with focal length $f$ and all other camera parameters equal to identity, at a distance $d$ from a centered sphere of radius $r$ (see fig. 1-d). ",
+        "bbox": [
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+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "A 2D point $x$ in image-space corresponds to the 3D point ",
+        "bbox": [
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+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "equation",
+        "img_path": "images/31b2b0a184906950d991c80ce2aae529f41484f0295cf85ed81183c4f31b7898.jpg",
+        "text": "$$\np = ( x _ { 1 } , x _ { 2 } , f ) .\n$$",
+        "text_format": "latex",
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+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Raycasting it along the $z$ axis, it will intersect the sphere surface at the 3D point ",
+        "bbox": [
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+        "page_idx": 11
+    },
+    {
+        "type": "equation",
+        "img_path": "images/65e033401ece94284d9a8c2e47819810b432e434dece1e0248f03118b89e64cd.jpg",
+        "text": "$$\nq = { \\frac { p } { \\| p \\| } } \\left( k - { \\sqrt { k ^ { 2 } - d ^ { 2 } + r ^ { 2 } } } \\right) , k = { \\frac { f d } { \\| p \\| } } .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            352,
+            279,
+            645,
+            313
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "If the argument of the square-root is negative, the ray does not intersect the sphere and so the point transformation is undefined. This means that the domain of the image $\\Omega$ should be restricted to the sphere region. In practice, in such cases we simply leave the point unmodified. ",
+        "bbox": [
+            174,
+            321,
+            825,
+            364
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Then, the yaw and pitch coordinates of the point $q$ on the surface of the sphere are ",
+        "bbox": [
+            173,
+            371,
+            712,
+            386
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "equation",
+        "img_path": "images/eef936dd424937eaf2ee8049bccbb30bbd6a80d89ead27a210e329c8de5152f5.jpg",
+        "text": "$$\n\\phi _ { 1 } = \\cos ^ { - 1 } \\left( - \\frac { q _ { 2 } } { r } \\right) , \\phi _ { 2 } = \\mathrm { a t a n _ { 2 } } \\left( - \\frac { q _ { 1 } } { d - q _ { 3 } } \\right) .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            339,
+            401,
+            658,
+            436
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "These polar coordinates are now rotated by the spatial transformation parameters, $\\phi ^ { \\prime } = \\phi + u$ ",
+        "bbox": [
+            173,
+            446,
+            789,
+            463
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Converting the polar coordinates back to a 3D point $q ^ { \\prime }$ ",
+        "bbox": [
+            173,
+            468,
+            532,
+            483
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "equation",
+        "img_path": "images/c31db84264a5f137aa8076f7b4f5b20fa78965ee3c84fec0a39ee035046b4fa2.jpg",
+        "text": "$$\n\\begin{array} { r } { q ^ { \\prime } = \\left[ \\begin{array} { c } { r \\sin \\phi _ { 1 } ^ { \\prime } \\sin \\phi _ { 2 } ^ { \\prime } } \\\\ { - r \\cos \\phi _ { 1 } ^ { \\prime } } \\\\ { r \\sin \\phi _ { 1 } ^ { \\prime } \\cos \\phi _ { 2 } ^ { \\prime } - d } \\end{array} \\right] . } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            397,
+            500,
+            601,
+            545
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Finally, projection of $q ^ { \\prime }$ into image-space yields ",
+        "bbox": [
+            174,
+            555,
+            488,
+            571
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "equation",
+        "img_path": "images/9121d7cb1fbc46d052286b9a607a4800601ac9121a4351b6b000ffc46db5e8eb.jpg",
+        "text": "$$\nt _ { u } ( x ) = - { \\frac { f } { q _ { 3 } ^ { \\prime } } } \\left[ \\begin{array} { c } { { q _ { 1 } ^ { \\prime } } } \\\\ { { q _ { 2 } ^ { \\prime } } } \\end{array} \\right] .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            423,
+            587,
+            575,
+            622
+        ],
+        "page_idx": 11
+    }
+]
\ No newline at end of file
diff --git a/parse/train/BkmM8Dceg/BkmM8Dceg_middle.json b/parse/train/BkmM8Dceg/BkmM8Dceg_middle.json
new file mode 100644
index 0000000000000000000000000000000000000000..ad45786e9492bdc367907e4a775ab03b882ee61c
--- /dev/null
+++ b/parse/train/BkmM8Dceg/BkmM8Dceg_middle.json
@@ -0,0 +1,31160 @@
+{
+    "pdf_info": [
+        {
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "WARPED CONVOLUTIONS: EFFICIENT INVARIANCE TO",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "SPATIAL TRANSFORMATIONS",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        }
+                    ],
+                    "index": 0.5
+                },
+                {
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "João F. Henriques & Andrea Vedaldi",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
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+                                    "score": 1.0,
+                                    "content": "Visual Geometry Group",
+                                    "type": "text"
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+                            ],
+                            "index": 3
+                        },
+                        {
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+                                157,
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+                                {
+                                    "bbox": [
+                                        112,
+                                        157,
+                                        199,
+                                        169
+                                    ],
+                                    "score": 1.0,
+                                    "content": "University of Oxford",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                113,
+                                169,
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "{joao,vedaldi}@robots.ox.ac.uk",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        }
+                    ],
+                    "index": 3.5
+                },
+                {
+                    "type": "title",
+                    "bbox": [
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+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
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+                                222
+                            ],
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+                                    "bbox": [
+                                        276,
+                                        207,
+                                        336,
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+                                    "score": 1.0,
+                                    "content": "ABSTRACT",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "type": "text",
+                    "bbox": [
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+                        377
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
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+                                247
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        142,
+                                        235,
+                                        469,
+                                        247
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Convolutional Neural Networks (CNNs) are extremely efficient, since they exploit",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "the inherent translation-invariance of natural images. However, translation is just",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
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+                                269
+                            ],
+                            "spans": [
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+                                    "bbox": [
+                                        142,
+                                        257,
+                                        469,
+                                        269
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+                                    "score": 1.0,
+                                    "content": "one of a myriad of useful spatial transformations. Can the same efficiency be at-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
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+                                469,
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+                            ],
+                            "spans": [
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+                                    "bbox": [
+                                        141,
+                                        268,
+                                        469,
+                                        279
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tained when considering other spatial invariances? Such generalized convolutions",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
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+                                291
+                            ],
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "have been considered in the past, but at a high computational cost. We present a",
+                                    "type": "text"
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+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
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+                                290,
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+                                302
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "construction that is simple and exact, yet has the same computational complexity",
+                                    "type": "text"
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+                            "index": 12
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+                        {
+                            "bbox": [
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+                                    "bbox": [
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+                                        313
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+                                    "score": 1.0,
+                                    "content": "that standard convolutions enjoy. It consists of a constant image warp followed",
+                                    "type": "text"
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+                            "index": 13
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+                        {
+                            "bbox": [
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+                                    "score": 1.0,
+                                    "content": "by a simple convolution, which are standard blocks in deep learning toolboxes.",
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+                            "index": 14
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+                                    "score": 1.0,
+                                    "content": "With a carefully crafted warp, the resulting architecture can be made equivariant",
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+                        {
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+                                    "score": 1.0,
+                                    "content": "to a wide range of 2-parameters spatial transformations. We show encouraging re-",
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+                            ],
+                            "index": 16
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+                        {
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+                                    "score": 1.0,
+                                    "content": "sults in realistic scenarios, including the estimation of vehicle poses in the Google",
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+                            "index": 17
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+                        {
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+                                    "score": 1.0,
+                                    "content": "in the Wild (3D rotations under perspective).",
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+                            "index": 19
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+                                    "score": 1.0,
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+                            "index": 20
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+                    ],
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+                },
+                {
+                    "type": "text",
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "A crucial aspect of current deep learning architectures is the encoding of invariances. This fact",
+                                    "type": "text"
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+                        },
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+                            "bbox": [
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+                            ],
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+                        {
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "translation is key: translating the input results in a translated output. When invariances are present in",
+                                    "type": "text"
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+                                    "score": 1.0,
+                                    "content": "the data, encoding them explicitly in an architecture provides an important source of regularization,",
+                                    "type": "text"
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+                            "index": 24
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+                                    "score": 1.0,
+                                    "content": "which allows to reduce the amount of training data required for learning. Invariances may also be",
+                                    "type": "text"
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+                            ],
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+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "used to improve the efficiency of implementations; for instance, a convolutional layer requires orders",
+                                    "type": "text"
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+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "of magnitude less memory and also less computation compared to an equivalent fully-connected",
+                                    "type": "text"
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+                            "index": 27
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+                        {
+                            "bbox": [
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+                                    "score": 1.0,
+                                    "content": "layer.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        }
+                    ],
+                    "index": 24.5
+                },
+                {
+                    "type": "text",
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+                                    "score": 1.0,
+                                    "content": "The success of CNNs indicates that translation invariance is an important property of images. How-",
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+                        },
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+                                    "score": 1.0,
+                                    "content": "ever, this does not explain why translation equivariant operators work well for image understanding.",
+                                    "type": "text"
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+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
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+                                    "score": 1.0,
+                                    "content": "The common interpretation is that such operators are matched to the statistics of natural images,",
+                                    "type": "text"
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+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "which are well known to be translation invariant (Hyvärinen et al., 2009). However, natural image",
+                                    "type": "text"
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+                                    "score": 1.0,
+                                    "content": ". Finally, sampling the input at these points (for example, by bilinear",
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+                                    "score": 1.0,
+                                    "content": "at regular intervals. Note that the warp grids are independent",
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+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
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+                                    "score": 1.0,
+                                    "content": "of the image contents – they can be computed once offline and then applied to any image.",
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+                                    "content": "can also be computed offline, and its application amounts to an element-wise product by a constant",
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+                                    "score": 1.0,
+                                    "content": "has a one-to-one correspondence to an image-space filter",
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+                                    "content": "by means of eq. 7, although there is no real need to build the latter explicitly.",
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+                                    "score": 1.0,
+                                    "content": "section 5). The red dot shows the pivot point",
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+                                    "score": 1.0,
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+                                    "score": 1.0,
+                                    "content": "at regular intervals. Note that the warp grids are independent",
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+                                    "score": 1.0,
+                                    "content": "of the image contents – they can be computed once offline and then applied to any image.",
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+                                    "score": 1.0,
+                                    "content": "be a group of transformations. Under very mild conditions (the group has to",
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+                                    "score": 1.0,
+                                    "content": "which is invariant to the group action, in the sense that, given a measurable function",
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+                                    "content": "{ \\tilde { I } } : G \\to",
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+                                    "content": "\\mathbb { R }",
+                                    "type": "inline_equation"
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+                                    "content": "\\begin{array} { r } { \\int \\tilde { I } ( g ^ { \\prime } g ) d g = \\int \\overline { { \\tilde { I } } } ( g ) \\dot { } d g } \\end{array}",
+                                    "type": "inline_equation"
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+                                    "score": 1.0,
+                                    "content": ". Using this measure, one can define generalized convolution as",
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+                                    "score": 1.0,
+                                    "content": ". This resembles our definition (4), although image and filter are",
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+                                    "score": 1.0,
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+                                    "content": ". If the group is an Abelian (commutative) Lie group, then one can show that there exists a",
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+                                    "score": 1.0,
+                                    "content": "be a group of transformations. Under very mild conditions (the group has to",
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+                                    "type": "inline_equation"
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+                                    "score": 1.0,
+                                    "content": "We now turn to face pose estimation in unconstrained photos, which requires handling more complex",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
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+                                    "score": 1.0,
+                                    "content": "3D rotations under perspective.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        }
+                    ],
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+                },
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+                                    "score": 1.0,
+                                    "content": "Dataset. For this task we use the Annotated Facial Landmarks in the Wild (AFLW) dataset",
+                                    "type": "text"
+                                }
+                            ],
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+                                    "score": 1.0,
+                                    "content": "(Koestinger et al., 2011). It contains about 25K faces found in Flickr photos, and includes yaw",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
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+                                    "score": 1.0,
+                                    "content": "(left-right) and pitch (up-down) annotations. We removed 933 faces with yaw larger than 90 degrees",
+                                    "type": "text"
+                                }
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+                                    "content": "(i.e., facing away from the camera), resulting in a set of 24,384 samples.",
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+                                },
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+                                    "score": 0.85,
+                                    "content": "20 \\%",
+                                    "type": "inline_equation"
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+                                    "score": 1.0,
+                                    "content": "of the faces were set",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "aside for validation.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        }
+                    ],
+                    "index": 9
+                },
+                {
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+                                    "type": "inline_equation"
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+                                    "score": 1.0,
+                                    "content": "is then processed by the network. Recall that our simplified 3D model of yaw and pitch rotation",
+                                    "type": "text"
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+                            ],
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+                        {
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+                                    "score": 1.0,
+                                    "content": "(section 5.3) assumes a spherical geometry. Although a person’s head roughly follows a spherical",
+                                    "type": "text"
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+                            ],
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+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "shape, the sample images are centered around the face, not the head. As such, we use an affine",
+                                    "type": "text"
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+                                    "score": 1.0,
+                                    "content": "Spatial Transformer Network (STN) (Jaderberg et al., 2015) as a first step, to center the image",
+                                    "type": "text"
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+                            "index": 16
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+                                    "score": 1.0,
+                                    "content": "correctly. Similarly, because the optimal camera parameters",
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+                                    "score": 0.44,
+                                    "content": "( f , r",
+                                    "type": "inline_equation"
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+                                {
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+                                    "type": "inline_equation"
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+                                    "score": 1.0,
+                                    "content": ") are difficult to set by",
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+                                    "score": 1.0,
+                                    "content": "hand, we let the network learn them, by computing their derivatives numerically (which has a low",
+                                    "type": "text"
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+                            ],
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+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "overhead, since they are scalars). The rest of the network follows the same diagram as before (fig. 2).",
+                                    "type": "text"
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+                                    "score": 1.0,
+                                    "content": "The main CNN has 4 convolutional layers, the first two with",
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+                                    "score": 0.89,
+                                    "content": "5 \\times 5",
+                                    "type": "inline_equation"
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+                                {
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+                                    "score": 1.0,
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+                                    "score": 1.0,
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+                                    "score": 1.0,
+                                    "content": "numbers of output channels are 20, 50, 20 and 1, respectively. A",
+                                    "type": "text"
+                                },
+                                {
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+                                    "type": "inline_equation"
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+                                    "score": 1.0,
+                                    "content": "of 2 is performed after the first layer, and there are ReLU non-linearities between the others. As for",
+                                    "type": "text"
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+                                    "score": 0.87,
+                                    "content": "\\mathrm { ( 5 \\times 5 ) }",
+                                    "type": "inline_equation"
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+                                {
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+                                    "score": 1.0,
+                                    "content": ", with 20, 50 and 6 output channels respectively, and",
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+                                    "score": 0.88,
+                                    "content": "3 \\times 3",
+                                    "type": "inline_equation"
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+                                {
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+                                    "score": 1.0,
+                                    "content": "max-pooling (stride 2) between them.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        }
+                    ],
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+                },
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+                                    "type": "text"
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+                            ],
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+                                    "type": "text"
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+                        {
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+                                    "score": 1.0,
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+                                    "type": "text"
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+                                    "score": 0.3,
+                                    "content": "\\mathrm { S T N + s }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "oftargmax, is the same as the proposed method,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
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+                            "spans": [
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "but without the warp. The large performance drop indicates that the spherical model incorporates",
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+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "important domain knowledge, which is ignored by a translation-equivariant STN. To allow non-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "equivariant models, we also test two other baselines where the softargmax is replaced with a fully-",
+                                    "type": "text"
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+                            ],
+                            "index": 32
+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "connected (FC) layer. The",
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+                                    "bbox": [
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+                                    "score": 0.73,
+                                    "content": "\\mathrm { S T N + F C }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "includes an affine Spatial Transformer, while the",
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+                                    "score": 0.77,
+                                    "content": "\\mathrm { C N N + F C }",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "does not, corresponding to a standard CNN of equivalent capacity. We observe that neither the FC",
+                                    "type": "text"
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+                            ],
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+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "or the STN components can account up for the performance of the warped convolution, which better",
+                                    "type": "text"
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+                            ],
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+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "exploits the natural 3D rotation equivariance of the data.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        }
+                    ],
+                    "index": 30.5
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+                                    "score": 1.0,
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+                                    "score": 1.0,
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+                                    "content": "\\mathrm { C N N + F C }",
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+                            "index": 33
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+                        {
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+                                    "score": 1.0,
+                                    "content": "does not, corresponding to a standard CNN of equivalent capacity. We observe that neither the FC",
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+                        {
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+                                    "score": 1.0,
+                                    "content": "or the STN components can account up for the performance of the warped convolution, which better",
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+                                    "content": "REFERENCES",
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+                                    "score": 1.0,
+                                    "content": "Joan Bruna, Arthur Szlam, and Yann LeCun. Learning stable group invariant representations with",
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+                            ],
+                            "index": 5
+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "convolutional networks. arXiv preprint arXiv:1301.3537, 2013.",
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+                                293,
+                                506,
+                                306
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        293,
+                                        506,
+                                        306
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Taco Cohen and Max Welling. Learning the Irreducible Representations of Commutative Lie",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                303,
+                                505,
+                                317
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        303,
+                                        505,
+                                        317
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Groups. In Proceedings of the 31st International Conference on Machine Learning (ICML-14),",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                313,
+                                144,
+                                327
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        313,
+                                        144,
+                                        327
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2014.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        }
+                    ],
+                    "index": 8
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        334,
+                        503,
+                        357
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                334,
+                                505,
+                                347
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        334,
+                                        505,
+                                        347
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Taco Cohen and Max Welling. Group equivariant convolutional networks. In Proceedings of the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                344,
+                                403,
+                                357
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        344,
+                                        403,
+                                        357
+                                    ],
+                                    "score": 1.0,
+                                    "content": "33rd International Conference on Machine Learning (ICML-16), 2016.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        }
+                    ],
+                    "index": 10.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        363,
+                        505,
+                        398
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                364,
+                                505,
+                                376
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        364,
+                                        505,
+                                        376
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Sander Dieleman, Kyle W Willett, and Joni Dambre. Rotation-invariant convolutional neural net-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                375,
+                                506,
+                                389
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        375,
+                                        506,
+                                        389
+                                    ],
+                                    "score": 1.0,
+                                    "content": "works for galaxy morphology prediction. Monthly notices of the royal astronomical society, 450",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                386,
+                                206,
+                                398
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        386,
+                                        206,
+                                        398
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(2):1441–1459, 2015.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        }
+                    ],
+                    "index": 13
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        405,
+                        366,
+                        417
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                405,
+                                366,
+                                418
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        405,
+                                        366,
+                                        418
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Gerald B Folland. A course in abstract harmonic analysis. 1995.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        }
+                    ],
+                    "index": 15
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        424,
+                        504,
+                        447
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                423,
+                                505,
+                                439
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        423,
+                                        505,
+                                        439
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Geremy Heitz and Daphne Koller. Learning spatial context: Using stuff to find things. In European",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                435,
+                                357,
+                                448
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        435,
+                                        357,
+                                        448
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Conference on Computer Vision, pp. 30–43. Springer, 2008.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        }
+                    ],
+                    "index": 16.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        454,
+                        504,
+                        478
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                454,
+                                505,
+                                467
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        454,
+                                        505,
+                                        467
+                                    ],
+                                    "score": 1.0,
+                                    "content": "J. F. Henriques, P. Martins, R. Caseiro, and J. Batista. Fast training of pose detectors in the fourier",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                465,
+                                403,
+                                478
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        465,
+                                        403,
+                                        478
+                                    ],
+                                    "score": 1.0,
+                                    "content": "domain. In Advances in Neural Information Processing Systems, 2014.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        }
+                    ],
+                    "index": 18.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        484,
+                        504,
+                        508
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                485,
+                                506,
+                                498
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        485,
+                                        506,
+                                        498
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Aapo Hyvärinen, Jarmo Hurri, and Patrick O Hoyer. Natural Image Statistics: A Probabilistic",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                496,
+                                505,
+                                509
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        496,
+                                        505,
+                                        509
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Approach to Early Computational Vision., volume 39. Springer Science & Business Media, 2009.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        }
+                    ],
+                    "index": 20.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        514,
+                        505,
+                        538
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                515,
+                                505,
+                                528
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        515,
+                                        505,
+                                        528
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Max Jaderberg, Karen Simonyan, Andrew Zisserman, et al. Spatial transformer networks. In Ad-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                526,
+                                410,
+                                538
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        526,
+                                        410,
+                                        538
+                                    ],
+                                    "score": 1.0,
+                                    "content": "vances in Neural Information Processing Systems, pp. 2017–2025, 2015.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        }
+                    ],
+                    "index": 22.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        545,
+                        504,
+                        568
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                544,
+                                505,
+                                557
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        544,
+                                        505,
+                                        557
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Angjoo Kanazawa, Abhishek Sharma, and David Jacobs. Locally scale-invariant convolutional",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                556,
+                                344,
+                                568
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        556,
+                                        344,
+                                        568
+                                    ],
+                                    "score": 1.0,
+                                    "content": "neural networks. arXiv preprint arXiv:1412.5104, 2014.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        }
+                    ],
+                    "index": 24.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        575,
+                        505,
+                        609
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                575,
+                                505,
+                                587
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        575,
+                                        505,
+                                        587
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Martin Koestinger, Paul Wohlhart, Peter M. Roth, and Horst Bischof. Annotated facial landmarks",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                587,
+                                505,
+                                598
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        587,
+                                        505,
+                                        598
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in the wild: A large-scale, real-world database for facial landmark localization. In First IEEE",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                597,
+                                459,
+                                610
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        597,
+                                        459,
+                                        610
+                                    ],
+                                    "score": 1.0,
+                                    "content": "International Workshop on Benchmarking Facial Image Analysis Technologies, 2011.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        }
+                    ],
+                    "index": 27
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        104,
+                        616,
+                        504,
+                        639
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                614,
+                                505,
+                                630
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        614,
+                                        505,
+                                        630
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Andrew Lavin. Fast algorithms for convolutional neural networks. arXiv preprint arXiv:1509.09308,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                626,
+                                143,
+                                640
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        626,
+                                        143,
+                                        640
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2015.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        }
+                    ],
+                    "index": 29.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        646,
+                        504,
+                        680
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                646,
+                                505,
+                                660
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        646,
+                                        505,
+                                        660
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Karel Lenc and Andrea Vedaldi. Understanding image representations by measuring their equiv-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                657,
+                                506,
+                                671
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        657,
+                                        506,
+                                        671
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ariance and equivalence. In Proceedings of the IEEE conference on computer vision and pattern",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                669,
+                                247,
+                                681
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        669,
+                                        247,
+                                        681
+                                    ],
+                                    "score": 1.0,
+                                    "content": "recognition, pp. 991–999, 2015.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        }
+                    ],
+                    "index": 32
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        687,
+                        505,
+                        731
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                687,
+                                506,
+                                700
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        687,
+                                        506,
+                                        700
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Kun Liu, Henrik Skibbe, Thorsten Schmidt, Thomas Blein, Klaus Palme, Thomas Brox, and Olaf",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                699,
+                                505,
+                                711
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        699,
+                                        505,
+                                        711
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Ronneberger. Rotation-Invariant HOG Descriptors Using Fourier Analysis in Polar and Spherical",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                709,
+                                506,
+                                722
+                            ],
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+                                    "bbox": [
+                                        115,
+                                        709,
+                                        506,
+                                        722
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Coordinates. International Journal of Computer Vision, 106(3):342–364, February 2014. ISSN",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                720,
+                                352,
+                                733
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+                            "spans": [
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+                                    "bbox": [
+                                        115,
+                                        720,
+                                        352,
+                                        733
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+                                    "score": 1.0,
+                                    "content": "0920-5691, 1573-1405. doi: 10.1007/s11263-013-0634-z.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        }
+                    ],
+                    "index": 35.5
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+            "page_idx": 9,
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+                792
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+                    "type": "title",
+                    "bbox": [
+                        107,
+                        244,
+                        176,
+                        257
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                245,
+                                176,
+                                258
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        245,
+                                        176,
+                                        258
+                                    ],
+                                    "score": 1.0,
+                                    "content": "REFERENCES",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        }
+                    ],
+                    "index": 4
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        263,
+                        504,
+                        285
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                262,
+                                505,
+                                276
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        262,
+                                        505,
+                                        276
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Joan Bruna, Arthur Szlam, and Yann LeCun. Learning stable group invariant representations with",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                274,
+                                372,
+                                286
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        274,
+                                        372,
+                                        286
+                                    ],
+                                    "score": 1.0,
+                                    "content": "convolutional networks. arXiv preprint arXiv:1301.3537, 2013.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        }
+                    ],
+                    "index": 5.5,
+                    "bbox_fs": [
+                        105,
+                        262,
+                        505,
+                        286
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        293,
+                        505,
+                        326
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                293,
+                                506,
+                                306
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        293,
+                                        506,
+                                        306
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Taco Cohen and Max Welling. Learning the Irreducible Representations of Commutative Lie",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                303,
+                                505,
+                                317
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        303,
+                                        505,
+                                        317
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Groups. In Proceedings of the 31st International Conference on Machine Learning (ICML-14),",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                313,
+                                144,
+                                327
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        313,
+                                        144,
+                                        327
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2014.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        }
+                    ],
+                    "index": 8,
+                    "bbox_fs": [
+                        106,
+                        293,
+                        506,
+                        327
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        334,
+                        503,
+                        357
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                334,
+                                505,
+                                347
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        334,
+                                        505,
+                                        347
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Taco Cohen and Max Welling. Group equivariant convolutional networks. In Proceedings of the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                344,
+                                403,
+                                357
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        344,
+                                        403,
+                                        357
+                                    ],
+                                    "score": 1.0,
+                                    "content": "33rd International Conference on Machine Learning (ICML-16), 2016.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        }
+                    ],
+                    "index": 10.5,
+                    "bbox_fs": [
+                        106,
+                        334,
+                        505,
+                        357
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        363,
+                        505,
+                        398
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                364,
+                                505,
+                                376
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        364,
+                                        505,
+                                        376
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Sander Dieleman, Kyle W Willett, and Joni Dambre. Rotation-invariant convolutional neural net-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                375,
+                                506,
+                                389
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        375,
+                                        506,
+                                        389
+                                    ],
+                                    "score": 1.0,
+                                    "content": "works for galaxy morphology prediction. Monthly notices of the royal astronomical society, 450",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                386,
+                                206,
+                                398
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        386,
+                                        206,
+                                        398
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(2):1441–1459, 2015.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        }
+                    ],
+                    "index": 13,
+                    "bbox_fs": [
+                        106,
+                        364,
+                        506,
+                        398
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        405,
+                        366,
+                        417
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                405,
+                                366,
+                                418
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        405,
+                                        366,
+                                        418
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Gerald B Folland. A course in abstract harmonic analysis. 1995.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        }
+                    ],
+                    "index": 15,
+                    "bbox_fs": [
+                        106,
+                        405,
+                        366,
+                        418
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        424,
+                        504,
+                        447
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                423,
+                                505,
+                                439
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        423,
+                                        505,
+                                        439
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Geremy Heitz and Daphne Koller. Learning spatial context: Using stuff to find things. In European",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                435,
+                                357,
+                                448
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        435,
+                                        357,
+                                        448
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Conference on Computer Vision, pp. 30–43. Springer, 2008.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        }
+                    ],
+                    "index": 16.5,
+                    "bbox_fs": [
+                        105,
+                        423,
+                        505,
+                        448
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        454,
+                        504,
+                        478
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                454,
+                                505,
+                                467
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        454,
+                                        505,
+                                        467
+                                    ],
+                                    "score": 1.0,
+                                    "content": "J. F. Henriques, P. Martins, R. Caseiro, and J. Batista. Fast training of pose detectors in the fourier",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                465,
+                                403,
+                                478
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        465,
+                                        403,
+                                        478
+                                    ],
+                                    "score": 1.0,
+                                    "content": "domain. In Advances in Neural Information Processing Systems, 2014.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        }
+                    ],
+                    "index": 18.5,
+                    "bbox_fs": [
+                        105,
+                        454,
+                        505,
+                        478
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        484,
+                        504,
+                        508
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                485,
+                                506,
+                                498
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        485,
+                                        506,
+                                        498
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Aapo Hyvärinen, Jarmo Hurri, and Patrick O Hoyer. Natural Image Statistics: A Probabilistic",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                496,
+                                505,
+                                509
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        496,
+                                        505,
+                                        509
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Approach to Early Computational Vision., volume 39. Springer Science & Business Media, 2009.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        }
+                    ],
+                    "index": 20.5,
+                    "bbox_fs": [
+                        106,
+                        485,
+                        506,
+                        509
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        514,
+                        505,
+                        538
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                515,
+                                505,
+                                528
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        515,
+                                        505,
+                                        528
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Max Jaderberg, Karen Simonyan, Andrew Zisserman, et al. Spatial transformer networks. In Ad-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                526,
+                                410,
+                                538
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        526,
+                                        410,
+                                        538
+                                    ],
+                                    "score": 1.0,
+                                    "content": "vances in Neural Information Processing Systems, pp. 2017–2025, 2015.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        }
+                    ],
+                    "index": 22.5,
+                    "bbox_fs": [
+                        106,
+                        515,
+                        505,
+                        538
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        545,
+                        504,
+                        568
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                544,
+                                505,
+                                557
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        544,
+                                        505,
+                                        557
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Angjoo Kanazawa, Abhishek Sharma, and David Jacobs. Locally scale-invariant convolutional",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                556,
+                                344,
+                                568
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        556,
+                                        344,
+                                        568
+                                    ],
+                                    "score": 1.0,
+                                    "content": "neural networks. arXiv preprint arXiv:1412.5104, 2014.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        }
+                    ],
+                    "index": 24.5,
+                    "bbox_fs": [
+                        106,
+                        544,
+                        505,
+                        568
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        575,
+                        505,
+                        609
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                575,
+                                505,
+                                587
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        575,
+                                        505,
+                                        587
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Martin Koestinger, Paul Wohlhart, Peter M. Roth, and Horst Bischof. Annotated facial landmarks",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                587,
+                                505,
+                                598
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        587,
+                                        505,
+                                        598
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in the wild: A large-scale, real-world database for facial landmark localization. In First IEEE",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                597,
+                                459,
+                                610
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        597,
+                                        459,
+                                        610
+                                    ],
+                                    "score": 1.0,
+                                    "content": "International Workshop on Benchmarking Facial Image Analysis Technologies, 2011.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        }
+                    ],
+                    "index": 27,
+                    "bbox_fs": [
+                        106,
+                        575,
+                        505,
+                        610
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        104,
+                        616,
+                        504,
+                        639
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                614,
+                                505,
+                                630
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        614,
+                                        505,
+                                        630
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Andrew Lavin. Fast algorithms for convolutional neural networks. arXiv preprint arXiv:1509.09308,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                626,
+                                143,
+                                640
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        626,
+                                        143,
+                                        640
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2015.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        }
+                    ],
+                    "index": 29.5,
+                    "bbox_fs": [
+                        105,
+                        614,
+                        505,
+                        640
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        646,
+                        504,
+                        680
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                646,
+                                505,
+                                660
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        646,
+                                        505,
+                                        660
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Karel Lenc and Andrea Vedaldi. Understanding image representations by measuring their equiv-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                657,
+                                506,
+                                671
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        657,
+                                        506,
+                                        671
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ariance and equivalence. In Proceedings of the IEEE conference on computer vision and pattern",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                669,
+                                247,
+                                681
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        669,
+                                        247,
+                                        681
+                                    ],
+                                    "score": 1.0,
+                                    "content": "recognition, pp. 991–999, 2015.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        }
+                    ],
+                    "index": 32,
+                    "bbox_fs": [
+                        105,
+                        646,
+                        506,
+                        681
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        687,
+                        505,
+                        731
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                687,
+                                506,
+                                700
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        687,
+                                        506,
+                                        700
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Kun Liu, Henrik Skibbe, Thorsten Schmidt, Thomas Blein, Klaus Palme, Thomas Brox, and Olaf",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                699,
+                                505,
+                                711
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        699,
+                                        505,
+                                        711
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Ronneberger. Rotation-Invariant HOG Descriptors Using Fourier Analysis in Polar and Spherical",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                709,
+                                506,
+                                722
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        709,
+                                        506,
+                                        722
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Coordinates. International Journal of Computer Vision, 106(3):342–364, February 2014. ISSN",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                720,
+                                352,
+                                733
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        720,
+                                        352,
+                                        733
+                                    ],
+                                    "score": 1.0,
+                                    "content": "0920-5691, 1573-1405. doi: 10.1007/s11263-013-0634-z.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        }
+                    ],
+                    "index": 35.5,
+                    "bbox_fs": [
+                        105,
+                        687,
+                        506,
+                        733
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        82,
+                        450,
+                        95
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                81,
+                                452,
+                                95
+                            ],
+                            "spans": [
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+                                    "bbox": [
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+                                    "score": 0.92,
+                                    "content": "q = { \\frac { p } { \\| p \\| } } \\left( k - { \\sqrt { k ^ { 2 } - d ^ { 2 } + r ^ { 2 } } } \\right) , k = { \\frac { f d } { \\| p \\| } } .",
+                                    "type": "interline_equation",
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+                                    "bbox": [
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+                                    "content": "If the argument of the square-root is negative, the ray does not intersect the sphere and so the point",
+                                    "type": "text"
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+                                    "score": 1.0,
+                                    "content": "sphere region. In practice, in such cases we simply leave the point unmodified.",
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+                                    "score": 0.91,
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+                                    "type": "text"
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+                                    "score": 0.95,
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+                                    "type": "interline_equation",
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+    "_backend": "pipeline",
+    "_version_name": "2.2.2"
+}
\ No newline at end of file
diff --git a/parse/train/BkmM8Dceg/BkmM8Dceg_model.json b/parse/train/BkmM8Dceg/BkmM8Dceg_model.json
new file mode 100644
index 0000000000000000000000000000000000000000..a606ab256afdb596af9dad397efe39e7ae177106
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diff --git a/parse/train/H1gzR2VKDH/H1gzR2VKDH_middle.json b/parse/train/H1gzR2VKDH/H1gzR2VKDH_middle.json
new file mode 100644
index 0000000000000000000000000000000000000000..28b2998ae22ced16a1e8ae878a299a37a9463f88
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+                                    "content": "et al., 1996; Yoshimi & Allen, 1994; Jagersand et al., 1997; Lampe & Riedmiller, 2013; Sadeghi",
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+                                    "content": "A number of recent works have explored reaching novel goals using only self-supervision (Finn",
+                                    "type": "text"
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+                                    "score": 1.0,
+                                    "content": "& Levine, 2016; Eysenbach et al., 2019; Kurutach et al., 2018; Wang et al., 2019; Jayaraman et al.,",
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+                                    "score": 1.0,
+                                    "content": "2019; Nair et al., 2018a). In particular, time-agnostic prediction (TAP) (Jayaraman et al., 2019) aims",
+                                    "type": "text"
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+                                    "score": 1.0,
+                                    "content": "& Levine, 2016) reach novel goals using model-free or model-based RL. We compare to all three of",
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+                                    "score": 1.0,
+                                    "content": "these methods in Section 5 and find that HVF significantly outperforms all of them.",
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+                                    "content": "3 PRELIMINARIES",
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+                                    "score": 1.0,
+                                    "content": "is the discount factor. In practice, acquiring cost functions that",
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+                                    "score": 1.0,
+                                    "content": "timize the objective via the cross entropy method (CEM) (Rubinstein & Kroese, 2004). In this work,",
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+                                    "content": "4 HIERARCHICAL VISUAL FORESIGHT",
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+                                    "score": 1.0,
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+                                    "score": 1.0,
+                                    "content": "be to find subgoals that minimize the total planning cost, we observe that this does not necessarily",
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+                                    "score": 1.0,
+                                    "content": "encourage splitting the task into shorter segments. Consider planning in a straight line: using any",
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+                                    "score": 1.0,
+                                    "content": "point on that line as a subgoal would equally minimize the total cost. Therefore, we instead optimize",
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+                                    "score": 1.0,
+                                    "content": "and measuring the predicted",
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+                            ],
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+                        {
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+                                    "score": 1.0,
+                                    "content": "cost achieved by that action sequence1. Once the subgoals are found, then the agent simply plans",
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+                        {
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+                                    "score": 1.0,
+                                    "content": "using visual MPC (Finn & Levine, 2016; Ebert et al., 2018b) from each",
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+                                    "score": 1.0,
+                                    "content": "until a cost",
+                                    "type": "text"
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+                            ],
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+                        {
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+                                    "score": 1.0,
+                                    "content": "threshold is reached or for a fixed, maximum number of timesteps, then from",
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+                                    "score": 1.0,
+                                    "content": "is the actual state reached when running MPC to get to",
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+                                    "score": 1.0,
+                                    "content": ". For a",
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+                            ],
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+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "full summary of the algorithm, see Algorithm 1. Next, we describe individual components in detail.",
+                                    "type": "text"
+                                }
+                            ],
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+                        }
+                    ],
+                    "index": 34
+                },
+                {
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+                                    "score": 1.0,
+                                    "content": "Generative model: To optimize subgoals, directly optimizing in image space is nearly impossible",
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+                            ],
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+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "due to the high dimensionality of images and the thin manifold on which they lie. Thus, we learn a",
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+                                }
+                            ],
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+                        }
+                    ],
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+                                    "score": 1.0,
+                                    "content": "1We compare max/mean cost in Section 5.4",
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+                                    "score": 1.0,
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+                                    "content": "full summary of the algorithm, see Algorithm 1. Next, we describe individual components in detail.",
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+                                            "html": "<table><tr><td></td><td>1: Receive current state St and goal state Sg</td></tr><tr><td>2:</td><td colspan=\"3\">Initialize q =N(0,I),M= 200,M*= 40,number of subgoals K while (o &gt;le-3)or (iterations&lt;5)do</td></tr><tr><td>3:</td><td>for m =1,2,...,M do</td><td></td><td></td></tr><tr><td>4:</td><td colspan=\"3\">m</td></tr><tr><td>5:</td><td>2m~q</td><td></td><td># Sample latent subgoal lists</td></tr><tr><td>6: 7:</td><td colspan=\"3\">for k = 1,2,.., K do</td></tr><tr><td>8:</td><td>s=9（2m[k],s）</td><td></td><td># Map latent to image subgoal</td></tr><tr><td>9:</td><td></td><td>ym</td><td># Optimal actions and planning cost</td></tr><tr><td>10:</td><td>end for</td><td></td><td></td></tr><tr><td>11:</td><td></td><td>m</td><td></td></tr><tr><td>12:</td><td></td><td>m</td><td># Max planning cost across segments</td></tr><tr><td>13:</td><td>end for</td><td></td><td></td></tr><tr><td>14:</td><td>Zsort = Sort(K : [Cost1,.,CostM],V : [z1,..,zM])</td><td></td><td># Rank by Costm</td></tr><tr><td>15:</td><td>Refit q to {Zsort[1],.,Zsort[M*]} with low cost</td><td></td><td></td></tr><tr><td>16:</td><td>end while</td><td></td><td></td></tr><tr><td>17:</td><td>for k = 1,2,...,K do</td><td></td><td></td></tr><tr><td>18:</td><td>Set final subgoal sk = gΦ(Zsorted[1]k)</td><td></td><td></td></tr><tr><td>19:</td><td>Execute Ak,-=MPC(fe,Sk-1,Sk)</td><td></td><td></td></tr><tr><td>20:</td><td>end for</td><td></td><td></td></tr><tr><td></td><td></td><td></td><td></td></tr><tr><td></td><td>21:Execute Ak,- = MPC(fθ,SK,Sg)</td><td></td><td></td></tr></table>",
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+                                    "score": 1.0,
+                                    "content": "to all scenes. To handle this setting, we condition the generative model on the current image, which",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                377,
+                                505,
+                                388
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        377,
+                                        505,
+                                        388
+                                    ],
+                                    "score": 1.0,
+                                    "content": "contains information about the current scene and the objects within view. Hence, in our experiments,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                387,
+                                504,
+                                398
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        387,
+                                        504,
+                                        398
+                                    ],
+                                    "score": 1.0,
+                                    "content": "we use either a variational autoencoder (VAE) or a conditional variational autoencoder (CVAE), with",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                398,
+                                505,
+                                411
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        398,
+                                        231,
+                                        411
+                                    ],
+                                    "score": 1.0,
+                                    "content": "a diagonal Gaussian prior over",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        231,
+                                        400,
+                                        237,
+                                        408
+                                    ],
+                                    "score": 0.71,
+                                    "content": "z",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        238,
+                                        398,
+                                        256,
+                                        411
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", i.e.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        257,
+                                        398,
+                                        308,
+                                        410
+                                    ],
+                                    "score": 0.93,
+                                    "content": "z \\sim \\mathcal { N } ( \\mathbf { 0 } , \\mathbf { I } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        309,
+                                        398,
+                                        505,
+                                        411
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". In the case of the CVAE, the decoder also takes",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                408,
+                                506,
+                                423
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        408,
+                                        310,
+                                        423
+                                    ],
+                                    "score": 1.0,
+                                    "content": "as input an encoding of the conditioned image, i.e.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        310,
+                                        409,
+                                        365,
+                                        421
+                                    ],
+                                    "score": 0.93,
+                                    "content": "s \\sim g _ { \\phi } ( z , s _ { 0 } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        366,
+                                        408,
+                                        506,
+                                        423
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". In practice, we use the inital state",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                419,
+                                506,
+                                433
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        422,
+                                        117,
+                                        431
+                                    ],
+                                    "score": 0.82,
+                                    "content": "s _ { 0 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        117,
+                                        419,
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+                                        433
+                                    ],
+                                    "score": 1.0,
+                                    "content": "as the conditioned image. We train the generative model on randomly collected interaction data.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                430,
+                                376,
+                                443
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        430,
+                                        376,
+                                        443
+                                    ],
+                                    "score": 1.0,
+                                    "content": "The architecture and training details can be found in Appendix A.3",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        }
+                    ],
+                    "index": 8.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
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+                        514
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
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+                                460
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "score": 1.0,
+                                    "content": "Dynamics model: The forward dynamics model",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        316,
+                                        448,
+                                        327,
+                                        459
+                                    ],
+                                    "score": 0.84,
+                                    "content": "f _ { \\theta }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "score": 1.0,
+                                    "content": "can be any forward dynamics model that",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                105,
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+                                506,
+                                473
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
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+                                    ],
+                                    "score": 1.0,
+                                    "content": "estimates",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        148,
+                                        459,
+                                        334,
+                                        471
+                                    ],
+                                    "score": 0.91,
+                                    "content": "p ( s _ { t + 1 } , s _ { t + 2 } , . . . , s _ { t + h } | s _ { t } , a _ { t } , a _ { t + 1 } , . . . , a _ { t + h - 1 } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        334,
+                                        458,
+                                        506,
+                                        473
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". In our case states are images, so we",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                470,
+                                505,
+                                482
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        470,
+                                        505,
+                                        482
+                                    ],
+                                    "score": 1.0,
+                                    "content": "use an action conditioned video prediction model, stochastic variational video prediction (SV2P)",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                481,
+                                505,
+                                492
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        481,
+                                        230,
+                                        492
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(Babaeizadeh et al., 2017) for",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        230,
+                                        481,
+                                        240,
+                                        492
+                                    ],
+                                    "score": 0.86,
+                                    "content": "f _ { \\theta }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        240,
+                                        481,
+                                        505,
+                                        492
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". We train the dynamics model on randomly collected interaction",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                491,
+                                505,
+                                504
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        491,
+                                        505,
+                                        504
+                                    ],
+                                    "score": 1.0,
+                                    "content": "data. Architecture and training parameters are identical to those used in (Babaeizadeh et al., 2017);",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                502,
+                                260,
+                                514
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        502,
+                                        260,
+                                        514
+                                    ],
+                                    "score": 1.0,
+                                    "content": "details can be found in Appendix A.4.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        }
+                    ],
+                    "index": 16.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        519,
+                        505,
+                        673
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                519,
+                                505,
+                                532
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        519,
+                                        505,
+                                        532
+                                    ],
+                                    "score": 1.0,
+                                    "content": "MPC & planning with subgoals: When optimizing subgoals, we need some way to measure the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                106,
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+                                543
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        530,
+                                        506,
+                                        543
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ease of planning to and from the subgoals. We explicitly compute this expected planning cost",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                540,
+                                506,
+                                554
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        540,
+                                        186,
+                                        554
+                                    ],
+                                    "score": 1.0,
+                                    "content": "between two states",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        187,
+                                        543,
+                                        222,
+                                        553
+                                    ],
+                                    "score": 0.86,
+                                    "content": "s _ { k } , s _ { k + 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        222,
+                                        540,
+                                        374,
+                                        554
+                                    ],
+                                    "score": 1.0,
+                                    "content": "by running model predictive control",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        375,
+                                        541,
+                                        492,
+                                        553
+                                    ],
+                                    "score": 0.9,
+                                    "content": "A , C = \\bar { \\mathrm { M P C } } ( \\bar { f _ { \\theta } , s _ { k } , s _ { k + 1 } } ) ^ { 2 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        492,
+                                        540,
+                                        506,
+                                        554
+                                    ],
+                                    "score": 1.0,
+                                    "content": "as",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                552,
+                                506,
+                                564
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        552,
+                                        506,
+                                        564
+                                    ],
+                                    "score": 1.0,
+                                    "content": "done in previous work (Finn & Levine, 2016; Nair et al., 2018b; Ebert et al., 2018b). This uses the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                563,
+                                506,
+                                576
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        563,
+                                        135,
+                                        576
+                                    ],
+                                    "score": 1.0,
+                                    "content": "model",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        135,
+                                        564,
+                                        145,
+                                        575
+                                    ],
+                                    "score": 0.87,
+                                    "content": "f _ { \\theta }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        146,
+                                        563,
+                                        323,
+                                        576
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to compute the optimal trajectory between",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        324,
+                                        565,
+                                        335,
+                                        574
+                                    ],
+                                    "score": 0.85,
+                                    "content": "s _ { k }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        335,
+                                        563,
+                                        354,
+                                        576
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        354,
+                                        565,
+                                        375,
+                                        575
+                                    ],
+                                    "score": 0.89,
+                                    "content": "s _ { k + 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        375,
+                                        563,
+                                        506,
+                                        576
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", and returns the optimal action",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                573,
+                                505,
+                                588
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        575,
+                                        115,
+                                        585
+                                    ],
+                                    "score": 0.67,
+                                    "content": "A",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        116,
+                                        573,
+                                        198,
+                                        588
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and associated cost",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        198,
+                                        575,
+                                        207,
+                                        584
+                                    ],
+                                    "score": 0.75,
+                                    "content": "C",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        208,
+                                        573,
+                                        505,
+                                        588
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Note this does not step any actions in the real environment, but simply",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                585,
+                                506,
+                                598
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        585,
+                                        506,
+                                        598
+                                    ],
+                                    "score": 1.0,
+                                    "content": "produces an estimated planning cost. Details on this procedure can be found in Appendices A.1 and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                595,
+                                504,
+                                609
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        595,
+                                        393,
+                                        609
+                                    ],
+                                    "score": 1.0,
+                                    "content": "A.2. Once the subgoals have been computed, the same procedure is run",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        393,
+                                        596,
+                                        471,
+                                        608
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\mathrm { M P C } ( f _ { \\theta } , s _ { k - 1 } , s _ { k } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        471,
+                                        595,
+                                        493,
+                                        609
+                                    ],
+                                    "score": 1.0,
+                                    "content": "until",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        493,
+                                        598,
+                                        504,
+                                        608
+                                    ],
+                                    "score": 0.83,
+                                    "content": "s _ { k }",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                608,
+                                504,
+                                619
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        608,
+                                        504,
+                                        619
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is reached (measured by a cost threshold) or for a fixed, maximum number of timesteps, then from",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                617,
+                                505,
+                                632
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        618,
+                                        269,
+                                        630
+                                    ],
+                                    "score": 0.86,
+                                    "content": "\\begin{array} { r } { \\mathbf { M P C } ( f _ { \\theta } , s _ { k } ^ { * } , s _ { k + 1 } ) , . . . , \\mathbf { M P C } ( f _ { \\theta } , s _ { K } ^ { * } , s _ { g } ) } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        270,
+                                        617,
+                                        382,
+                                        632
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(Alg. 1 Lines 17:21), where",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        383,
+                                        619,
+                                        393,
+                                        630
+                                    ],
+                                    "score": 0.89,
+                                    "content": "s _ { k } ^ { * }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        394,
+                                        617,
+                                        505,
+                                        632
+                                    ],
+                                    "score": 1.0,
+                                    "content": "represents the state actually",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                629,
+                                505,
+                                642
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        629,
+                                        228,
+                                        642
+                                    ],
+                                    "score": 1.0,
+                                    "content": "reached after trying to plan to",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        228,
+                                        631,
+                                        239,
+                                        640
+                                    ],
+                                    "score": 0.83,
+                                    "content": "s _ { k }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        239,
+                                        629,
+                                        505,
+                                        642
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". In this case, the best action at each step is actually applied in the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                639,
+                                504,
+                                652
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        639,
+                                        504,
+                                        652
+                                    ],
+                                    "score": 1.0,
+                                    "content": "environment until the task is completed, or the horizon runs out. Note we only compute subgoals",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                650,
+                                505,
+                                664
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        650,
+                                        230,
+                                        664
+                                    ],
+                                    "score": 1.0,
+                                    "content": "once in the beginning calling",
+                                    "type": "text"
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+                                    "content": ". In the case of the CVAE, the decoder also takes",
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+                                    "content": ". In practice, we use the inital state",
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+                                    "content": "(Babaeizadeh et al., 2017) for",
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+                                    "score": 1.0,
+                                    "content": ". We train the dynamics model on randomly collected interaction",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                491,
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+                                504
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        491,
+                                        505,
+                                        504
+                                    ],
+                                    "score": 1.0,
+                                    "content": "data. Architecture and training parameters are identical to those used in (Babaeizadeh et al., 2017);",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                502,
+                                260,
+                                514
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        502,
+                                        260,
+                                        514
+                                    ],
+                                    "score": 1.0,
+                                    "content": "details can be found in Appendix A.4.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        }
+                    ],
+                    "index": 16.5,
+                    "bbox_fs": [
+                        105,
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+                        514
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
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+                        673
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        519,
+                                        505,
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+                                    ],
+                                    "score": 1.0,
+                                    "content": "MPC & planning with subgoals: When optimizing subgoals, we need some way to measure the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                106,
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
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+                                    ],
+                                    "score": 1.0,
+                                    "content": "ease of planning to and from the subgoals. We explicitly compute this expected planning cost",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                105,
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+                                554
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
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+                                        554
+                                    ],
+                                    "score": 1.0,
+                                    "content": "between two states",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        187,
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+                                        222,
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+                                    ],
+                                    "score": 0.86,
+                                    "content": "s _ { k } , s _ { k + 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        222,
+                                        540,
+                                        374,
+                                        554
+                                    ],
+                                    "score": 1.0,
+                                    "content": "by running model predictive control",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        375,
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+                                        553
+                                    ],
+                                    "score": 0.9,
+                                    "content": "A , C = \\bar { \\mathrm { M P C } } ( \\bar { f _ { \\theta } , s _ { k } , s _ { k + 1 } } ) ^ { 2 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "score": 1.0,
+                                    "content": "as",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                105,
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+                                564
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
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+                                    ],
+                                    "score": 1.0,
+                                    "content": "done in previous work (Finn & Levine, 2016; Nair et al., 2018b; Ebert et al., 2018b). This uses the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                105,
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+                                576
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
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+                                        135,
+                                        576
+                                    ],
+                                    "score": 1.0,
+                                    "content": "model",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        135,
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+                                        575
+                                    ],
+                                    "score": 0.87,
+                                    "content": "f _ { \\theta }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        146,
+                                        563,
+                                        323,
+                                        576
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to compute the optimal trajectory between",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        324,
+                                        565,
+                                        335,
+                                        574
+                                    ],
+                                    "score": 0.85,
+                                    "content": "s _ { k }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        335,
+                                        563,
+                                        354,
+                                        576
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        354,
+                                        565,
+                                        375,
+                                        575
+                                    ],
+                                    "score": 0.89,
+                                    "content": "s _ { k + 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        375,
+                                        563,
+                                        506,
+                                        576
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", and returns the optimal action",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                573,
+                                505,
+                                588
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        575,
+                                        115,
+                                        585
+                                    ],
+                                    "score": 0.67,
+                                    "content": "A",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        116,
+                                        573,
+                                        198,
+                                        588
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and associated cost",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        198,
+                                        575,
+                                        207,
+                                        584
+                                    ],
+                                    "score": 0.75,
+                                    "content": "C",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        208,
+                                        573,
+                                        505,
+                                        588
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Note this does not step any actions in the real environment, but simply",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                585,
+                                506,
+                                598
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        585,
+                                        506,
+                                        598
+                                    ],
+                                    "score": 1.0,
+                                    "content": "produces an estimated planning cost. Details on this procedure can be found in Appendices A.1 and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                595,
+                                504,
+                                609
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        595,
+                                        393,
+                                        609
+                                    ],
+                                    "score": 1.0,
+                                    "content": "A.2. Once the subgoals have been computed, the same procedure is run",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        393,
+                                        596,
+                                        471,
+                                        608
+                                    ],
+                                    "score": 0.91,
+                                    "content": "\\mathrm { M P C } ( f _ { \\theta } , s _ { k - 1 } , s _ { k } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        471,
+                                        595,
+                                        493,
+                                        609
+                                    ],
+                                    "score": 1.0,
+                                    "content": "until",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
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+                                        598,
+                                        504,
+                                        608
+                                    ],
+                                    "score": 0.83,
+                                    "content": "s _ { k }",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                608,
+                                504,
+                                619
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        608,
+                                        504,
+                                        619
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is reached (measured by a cost threshold) or for a fixed, maximum number of timesteps, then from",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                617,
+                                505,
+                                632
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        618,
+                                        269,
+                                        630
+                                    ],
+                                    "score": 0.86,
+                                    "content": "\\begin{array} { r } { \\mathbf { M P C } ( f _ { \\theta } , s _ { k } ^ { * } , s _ { k + 1 } ) , . . . , \\mathbf { M P C } ( f _ { \\theta } , s _ { K } ^ { * } , s _ { g } ) } \\end{array}",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        270,
+                                        617,
+                                        382,
+                                        632
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(Alg. 1 Lines 17:21), where",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        383,
+                                        619,
+                                        393,
+                                        630
+                                    ],
+                                    "score": 0.89,
+                                    "content": "s _ { k } ^ { * }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        394,
+                                        617,
+                                        505,
+                                        632
+                                    ],
+                                    "score": 1.0,
+                                    "content": "represents the state actually",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                629,
+                                505,
+                                642
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        629,
+                                        228,
+                                        642
+                                    ],
+                                    "score": 1.0,
+                                    "content": "reached after trying to plan to",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        228,
+                                        631,
+                                        239,
+                                        640
+                                    ],
+                                    "score": 0.83,
+                                    "content": "s _ { k }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        239,
+                                        629,
+                                        505,
+                                        642
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". In this case, the best action at each step is actually applied in the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                639,
+                                504,
+                                652
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        639,
+                                        504,
+                                        652
+                                    ],
+                                    "score": 1.0,
+                                    "content": "environment until the task is completed, or the horizon runs out. Note we only compute subgoals",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                650,
+                                505,
+                                664
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        650,
+                                        230,
+                                        664
+                                    ],
+                                    "score": 1.0,
+                                    "content": "once in the beginning calling",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        231,
+                                        651,
+                                        323,
+                                        663
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\mathrm { H V F } ( f _ { \\theta } , g _ { \\phi } ( z ) , s _ { 0 } , s _ { g } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        324,
+                                        650,
+                                        505,
+                                        664
+                                    ],
+                                    "score": 1.0,
+                                    "content": ", the plan with those subgoals. In principle",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                661,
+                                466,
+                                675
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        661,
+                                        466,
+                                        675
+                                    ],
+                                    "score": 1.0,
+                                    "content": "HVF can be called at every step, but for computational efficiency we only call HVF once.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        }
+                    ],
+                    "index": 26.5,
+                    "bbox_fs": [
+                        104,
+                        519,
+                        506,
+                        675
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        678,
+                        505,
+                        712
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                678,
+                                505,
+                                692
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        678,
+                                        505,
+                                        692
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Subgoal optimization: Since we need to search in the space of subgoals to optimize Equation 1, we",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                690,
+                                505,
+                                703
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        690,
+                                        505,
+                                        703
+                                    ],
+                                    "score": 1.0,
+                                    "content": "perform subgoal optimization using the cross entropy method (CEM) (Rubinstein & Kroese, 2004)",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                701,
+                                506,
+                                714
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        701,
+                                        282,
+                                        714
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in the latent space of our generative model",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        282,
+                                        701,
+                                        306,
+                                        713
+                                    ],
+                                    "score": 0.92,
+                                    "content": "g _ { \\phi } ( z )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        701,
+                                        506,
+                                        714
+                                    ],
+                                    "score": 1.0,
+                                    "content": ". Note this subgoal optimization CEM is distinct",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                209,
+                                506,
+                                223
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        209,
+                                        506,
+                                        223
+                                    ],
+                                    "score": 1.0,
+                                    "content": "from the CEM used for computing the planning cost, which we use as a subroutine within this outer",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                221,
+                                505,
+                                234
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        221,
+                                        505,
+                                        234
+                                    ],
+                                    "score": 1.0,
+                                    "content": "level of CEM. At a high-level, the subgoal optimization samples a list of subgoals, evaluates their",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                230,
+                                505,
+                                245
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        230,
+                                        505,
+                                        245
+                                    ],
+                                    "score": 1.0,
+                                    "content": "effectiveness towards reaching the goal, and then iteratively refines the subgoals through resampling",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                241,
+                                505,
+                                256
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        241,
+                                        275,
+                                        256
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and reevaluation. We begin by drawing",
+                                    "type": "text",
+                                    "cross_page": true
+                                },
+                                {
+                                    "bbox": [
+                                        275,
+                                        243,
+                                        288,
+                                        253
+                                    ],
+                                    "score": 0.75,
+                                    "content": "M",
+                                    "type": "inline_equation",
+                                    "cross_page": true
+                                },
+                                {
+                                    "bbox": [
+                                        288,
+                                        241,
+                                        485,
+                                        256
+                                    ],
+                                    "score": 1.0,
+                                    "content": "samples from a diagonal Gaussian distribution",
+                                    "type": "text",
+                                    "cross_page": true
+                                },
+                                {
+                                    "bbox": [
+                                        485,
+                                        244,
+                                        505,
+                                        254
+                                    ],
+                                    "score": 0.86,
+                                    "content": "q =",
+                                    "type": "inline_equation",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                107,
+                                254,
+                                505,
+                                266
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        254,
+                                        139,
+                                        266
+                                    ],
+                                    "score": 0.93,
+                                    "content": "\\mathcal { N } ( \\mathbf { 0 } , \\mathbf { I } )",
+                                    "type": "inline_equation",
+                                    "cross_page": true
+                                },
+                                {
+                                    "bbox": [
+                                        140,
+                                        254,
+                                        257,
+                                        266
+                                    ],
+                                    "score": 1.0,
+                                    "content": "where the dimensionality of",
+                                    "type": "text",
+                                    "cross_page": true
+                                },
+                                {
+                                    "bbox": [
+                                        258,
+                                        255,
+                                        264,
+                                        266
+                                    ],
+                                    "score": 0.79,
+                                    "content": "q",
+                                    "type": "inline_equation",
+                                    "cross_page": true
+                                },
+                                {
+                                    "bbox": [
+                                        264,
+                                        254,
+                                        275,
+                                        266
+                                    ],
+                                    "score": 1.0,
+                                    "content": "is",
+                                    "type": "text",
+                                    "cross_page": true
+                                },
+                                {
+                                    "bbox": [
+                                        275,
+                                        254,
+                                        302,
+                                        264
+                                    ],
+                                    "score": 0.89,
+                                    "content": "K * L",
+                                    "type": "inline_equation",
+                                    "cross_page": true
+                                },
+                                {
+                                    "bbox": [
+                                        303,
+                                        254,
+                                        334,
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+                                    ],
+                                    "score": 1.0,
+                                    "content": ", where",
+                                    "type": "text",
+                                    "cross_page": true
+                                },
+                                {
+                                    "bbox": [
+                                        334,
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+                                        344,
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+                                    ],
+                                    "score": 0.82,
+                                    "content": "K",
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+                                            "score": 1.0,
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+                                    "score": 1.0,
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+                                    "score": 1.0,
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+                                    "score": 1.0,
+                                    "content": "et al., 2012). We compare against three prior methods: (a) visual foresight (Finn & Levine, 2016;",
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+                                    "score": 1.0,
+                                    "content": "nipulation of diverse objects. The simulation environments use the MuJoCo physics engine (Todorov",
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+                                    "score": 1.0,
+                                    "content": "et al., 2012). We compare against three prior methods: (a) visual foresight (Finn & Levine, 2016;",
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+                                    "content": "Ebert et al., 2018b), which uses no subgoals, (b) RIG (Nair et al., 2018a) which trains a model-free",
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+                                    "score": 1.0,
+                                    "content": "subgoals generated by time-agnostic prediction (TAP) (Jayaraman et al., 2019), a state-of-the-art",
+                                    "type": "text"
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+                                    "content": "the most likely frame between the current and goal state.",
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+                                    "score": 1.0,
+                                    "content": "for the agent (the green block) to move to a",
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+                                    "score": 1.0,
+                                    "content": "Results: In Figure 2, we observe that using HVF subgoals consistently improves success rate over",
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+                                    "score": 1.0,
+                                    "content": "that make the long-horizon task more manageable. Additionally, we compare to the “Ground Truth",
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+                                    "content": "Bottleneck” that uses manually-designed subgoals, where the subgoal is exactly at the gaps in the",
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+                        },
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+                                    "score": 1.0,
+                                    "content": "walls (or the midpoint between states in the “easy” case). We find that while using the oracle",
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+                            ],
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+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "subgoals tends to yield the highest performance, the oracle subgoals do not perform perfectly, sug-",
+                                    "type": "text"
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+                            "index": 12
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+                                    "score": 1.0,
+                                    "content": "gesting that a non-trivial amount of performance gains are to be had from improving the consistency",
+                                    "type": "text"
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+                            ],
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+                        },
+                        {
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "of the video prediction model and cost function for short-horizon problems, as opposed to the sub-",
+                                    "type": "text"
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+                            "index": 14
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+                        {
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+                                    "score": 1.0,
+                                    "content": "goals. We also show that HVF outperforms time agnostic prediction (TAP) (Jayaraman et al., 2019)",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "in Appendix C.3.",
+                                    "type": "text"
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+                        }
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+                },
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+                    "type": "text",
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+                                    "score": 1.0,
+                                    "content": "We next qualitatively examine the subgoals discovered by HVF in Figure 3, and find empirically that",
+                                    "type": "text"
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+                            ],
+                            "index": 17
+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "they seem to correspond to semantically meaningful states. In this task there are clear bottlenecks -",
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+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
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+                                    "bbox": [
+                                        105,
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+                                    "score": 1.0,
+                                    "content": "specifically reaching the gaps in the walls and find that HVF outputs close to these states as subgoals.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "For example, when the agent starts in the leftmost section, and has to pass through two narrow gaps",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "in walls, we observe the first subgoal goal corresponds to the agent around the bottleneck for the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "first gap and the second subgoal is near the second gap.",
+                                    "type": "text"
+                                }
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+                        }
+                    ],
+                    "index": 19.5
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+                {
+                    "type": "title",
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+                                    "score": 1.0,
+                                    "content": "5.2 SIMULATED DESK MANIPULATION",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        }
+                    ],
+                    "index": 23
+                },
+                {
+                    "type": "text",
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+                                    "score": 1.0,
+                                    "content": "We now study the performance improvement",
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+                                    "score": 1.0,
+                                    "content": "and subgoal quality of HVF in a challeng-",
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+                                    "score": 1.0,
+                                    "content": "ing simulated robotic manipulation domain.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
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+                                    "score": 1.0,
+                                    "content": "Specifically, a simulated Franka Emika Panda",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "robot arm is mounted in front of a desk (as used",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "in (Lynch et al., 2019)). The desk consists of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
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+                                    "score": 1.0,
+                                    "content": "3 blocks, a sliding door, three buttons, and a",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
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+                        {
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+                                    "score": 1.0,
+                                    "content": "drawer. We explore four tasks in this space:",
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+                                }
+                            ],
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+                        {
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+                                    "score": 1.0,
+                                    "content": "door closing, 2 block pushing, door closing",
+                                    "type": "text"
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+                                {
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+                                    "score": 0.71,
+                                    "content": "^ +",
+                                    "type": "inline_equation"
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+                        {
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "block pushing, and door closing",
+                                    "type": "text"
+                                },
+                                {
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+                                    "score": 0.83,
+                                    "content": "^ { + 2 }",
+                                    "type": "inline_equation"
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+                                {
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+                                    "score": 1.0,
+                                    "content": "block push-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
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+                            "spans": [
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "ing. Example start and goal images for each",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "task are visualized in Figure 5, and task de-",
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+                                }
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+                        {
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+                                    "score": 1.0,
+                                    "content": "tails are in Appendix B.2. The arm is controlled",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
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+                                    "score": 1.0,
+                                    "content": "with 3D Cartesian velocity control of the end-",
+                                    "type": "text"
+                                }
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+                                    "content": "visual foresight (Finn & Levine, 2016) without subgoals, indicating that it is able to find subgoals",
+                                    "type": "text"
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+                                    "score": 1.0,
+                                    "content": "that make the long-horizon task more manageable. Additionally, we compare to the “Ground Truth",
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+                                    "score": 1.0,
+                                    "content": "Bottleneck” that uses manually-designed subgoals, where the subgoal is exactly at the gaps in the",
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+                                    "score": 1.0,
+                                    "content": "walls (or the midpoint between states in the “easy” case). We find that while using the oracle",
+                                    "type": "text"
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+                                    "content": "subgoals tends to yield the highest performance, the oracle subgoals do not perform perfectly, sug-",
+                                    "type": "text"
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+                                    "score": 1.0,
+                                    "content": "gesting that a non-trivial amount of performance gains are to be had from improving the consistency",
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+                                    "score": 1.0,
+                                    "content": "of the video prediction model and cost function for short-horizon problems, as opposed to the sub-",
+                                    "type": "text"
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+                                    "score": 1.0,
+                                    "content": "goals. We also show that HVF outperforms time agnostic prediction (TAP) (Jayaraman et al., 2019)",
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+                                    "score": 1.0,
+                                    "content": "in Appendix C.3.",
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+                                    "score": 1.0,
+                                    "content": "We next qualitatively examine the subgoals discovered by HVF in Figure 3, and find empirically that",
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+                                    "content": "they seem to correspond to semantically meaningful states. In this task there are clear bottlenecks -",
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+                                    "score": 1.0,
+                                    "content": "specifically reaching the gaps in the walls and find that HVF outputs close to these states as subgoals.",
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+                        {
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+                                    "score": 1.0,
+                                    "content": "For example, when the agent starts in the leftmost section, and has to pass through two narrow gaps",
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+                        {
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+                                    "score": 1.0,
+                                    "content": "in walls, we observe the first subgoal goal corresponds to the agent around the bottleneck for the",
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+                                    "score": 1.0,
+                                    "content": "first gap and the second subgoal is near the second gap.",
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+                                    "score": 1.0,
+                                    "content": "5.2 SIMULATED DESK MANIPULATION",
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+                    ],
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+                                    "score": 1.0,
+                                    "content": "Specifically, a simulated Franka Emika Panda",
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+                        {
+                            "bbox": [
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+                                    "score": 1.0,
+                                    "content": "robot arm is mounted in front of a desk (as used",
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+                                    "score": 1.0,
+                                    "content": "in (Lynch et al., 2019)). The desk consists of",
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+                                    "content": "3 blocks, a sliding door, three buttons, and a",
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+                                    "score": 1.0,
+                                    "content": "drawer. We explore four tasks in this space:",
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+                                    "score": 1.0,
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+                                    "cross_page": true
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+                                    "content": "tion details are in the Appendix B.3. Results:",
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+                                    "content": "lenges of sparse costs, so one might suspect that HVF would be less valuable in these settings. On",
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+                                    "content": "the contrary, we find that HVF still significantly outperforms no subgoals, and the improvement",
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+                                    "content": "6 CONCLUSION AND LIMITATIONS",
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+                                    "content": "We presented an self-supervised approach for hierarchical planning with vision-based tasks, hier-",
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+                                    "score": 1.0,
+                                    "content": "archical visual foresight (HVF), which decomposes a visual goal into a sequence of subgoals. By",
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+                                    "content": "explicitly optimizing for subgoals that minimize planning cost, HVF is able to discover semanti-",
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+                                    "score": 1.0,
+                                    "content": "cally meaningful goals in visual space, and when using these goal for planning, perform a variety",
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+                        {
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+                                    "score": 1.0,
+                                    "content": "of challenging, long-horizon vision-based tasks. Further, HVF learns these tasks in an entirely self-",
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+                                    "content": "While HVF significantly extends the capabilities of prior methods, a number of limitations remain.",
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+                                    "score": 1.0,
+                                    "content": ", one iteration of visual MPC has com-",
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+                                    "type": "inline_equation"
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+                                    "content": "subgoal se-",
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+                                    "score": 1.0,
+                                    "content": "quences. Then normal visual foresight or TAP would have cost",
+                                    "type": "text"
+                                },
+                                {
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+                                    "score": 0.91,
+                                    "content": "T \\times C",
+                                    "type": "inline_equation"
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+                                {
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+                                    "score": 1.0,
+                                    "content": ", while HVF would have",
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+                                    "type": "text"
+                                },
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+                                    "bbox": [
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+                                    "score": 0.92,
+                                    "content": "( T \\times C ) + ( K \\times N \\times C )",
+                                    "type": "inline_equation"
+                                },
+                                {
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+                                    "score": 1.0,
+                                    "content": ". However note - the computation of",
+                                    "type": "text"
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+                                    "content": "( K \\times N \\times C )",
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+                                    "content": "can be heavily",
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+                                    "score": 1.0,
+                                    "content": "parallelized because it is done completely offline (without environment interaction). We also expect",
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+                                    "content": "that this can be mitigated by reformulating the subgoal prediction problem as policy inference, and",
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+                                    "content": "training a subgoal generation policy in the loop of training, an interesting direction for future work.",
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+                                    "score": 1.0,
+                                    "content": "neck in furthering the performance of HVF. Specifically, learning dynamics models and cost func-",
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+                                    "score": 1.0,
+                                    "content": "tions which can more effectively capture the state of all the objects in the scene would significantly",
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+                                    "score": 1.0,
+                                    "content": "improve the performance of HVF.",
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+                                    "content": "Lastly, development of better generative models that can capture the scene and generate possible",
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+                            ],
+                            "index": 37
+                        },
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+                                    "content": "McGrew, Josh Tobin, Pieter Abbeel, and Wojciech Zaremba. Hindsight experience replay. CoRR,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
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+                                115,
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+                                590
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+                                        115,
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+                            "index": 40
+                        },
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+                                        115,
+                                        600,
+                                        398,
+                                        613
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+                                    "content": "Stochastic variational video prediction. CoRR, abs/1710.11252, 2017.",
+                                    "type": "text"
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+                            ],
+                            "index": 41
+                        },
+                        {
+                            "bbox": [
+                                105,
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+                                        624
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+                                    "score": 1.0,
+                                    "content": "Pierre-Luc Bacon, Jean Harb, and Doina Precup. The option-critic architecture. CoRR,",
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+                            ],
+                            "index": 42
+                        },
+                        {
+                            "bbox": [
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+                                        115,
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+                                    "content": "( T \\times C ) + ( K \\times N \\times C )",
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+                                    "score": 1.0,
+                                    "content": "We would like to thank Sudeep Dasari, Vikash Kumar, Sherry Moore, Michael Ahn, and Tuna",
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+                                    "content": "Tokosz for help with infrastructure, as well as Sergey Levine, Abhishek Gupta, Dumitru Erhan,",
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+                                    "score": 1.0,
+                                    "content": "Brian Ichter, and Vincent Vanhouke for valuable discussions. This work was supported in part by an",
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+                                    "content": "NSF GRFP award. Chelsea Finn is a CIFAR Fellow in the Learning in Machines & Brains program.",
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+                                    "content": "McGrew, Josh Tobin, Pieter Abbeel, and Wojciech Zaremba. Hindsight experience replay. CoRR,",
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+                                }
+                            ],
+                            "index": 38
+                        },
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+                                115,
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+                                    "content": "Pierre-Luc Bacon, Jean Harb, and Doina Precup. The option-critic architecture. CoRR,",
+                                    "type": "text"
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+                            ],
+                            "index": 42,
+                            "is_list_start_line": true
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+                                    ],
+                                    "score": 1.0,
+                                    "content": "B. Boots, A. Byravan, and D. Fox. Learning predictive models of a depth camera amp; manipulator",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 48,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                687,
+                                505,
+                                701
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        687,
+                                        505,
+                                        701
+                                    ],
+                                    "score": 1.0,
+                                    "content": "from raw execution traces. In 2014 IEEE International Conference on Robotics and Automation",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 49
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                699,
+                                403,
+                                711
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        699,
+                                        403,
+                                        711
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(ICRA), pp. 4021–4028, May 2014. doi: 10.1109/ICRA.2014.6907443.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 50,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                708,
+                                505,
+                                723
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        708,
+                                        505,
+                                        723
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Arunkumar Byravan and Dieter Fox. Se3-nets: Learning rigid body motion using deep neural",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 51,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                720,
+                                281,
+                                733
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        720,
+                                        281,
+                                        733
+                                    ],
+                                    "score": 1.0,
+                                    "content": "networks. CoRR, abs/1606.02378, 2016.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 52,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                82,
+                                505,
+                                96
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        82,
+                                        505,
+                                        96
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Howie Choset, Kevin M. Lynch, Seth Hutchinson, George Kantor, Wolfram Burgard, Lydia Kavraki,",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 0,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                94,
+                                505,
+                                108
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        94,
+                                        505,
+                                        108
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and Sebastian Thrun. Principles of Robot Motion: Theory, Algorithms, and Implementations. MIT",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                105,
+                                168,
+                                117
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        105,
+                                        168,
+                                        117
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Press, 2005.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 2,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                115,
+                                505,
+                                129
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        115,
+                                        505,
+                                        129
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Frederik Ebert, Chelsea Finn, Alex X. Lee, and Sergey Levine. Self-supervised visual planning with",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 3,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                126,
+                                351,
+                                141
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        126,
+                                        351,
+                                        141
+                                    ],
+                                    "score": 1.0,
+                                    "content": "temporal skip connections. CoRR, abs/1710.05268, 2017.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 4,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                137,
+                                507,
+                                154
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        137,
+                                        507,
+                                        154
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Frederik Ebert, Sudeep Dasari, Alex X. Lee, Sergey Levine, and Chelsea Finn. Robustness via",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 5,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                150,
+                                506,
+                                164
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        150,
+                                        506,
+                                        164
+                                    ],
+                                    "score": 1.0,
+                                    "content": "retrying: Closed-loop robotic manipulation with self-supervised learning. CoRR, abs/1810.03043,",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                161,
+                                147,
+                                173
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        161,
+                                        147,
+                                        173
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2018a.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 7,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                172,
+                                506,
+                                186
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        172,
+                                        506,
+                                        186
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Frederik Ebert, Chelsea Finn, Sudeep Dasari, Annie Xie, Alex X. Lee, and Sergey Levine. Visual",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 8,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                181,
+                                506,
+                                198
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        181,
+                                        506,
+                                        198
+                                    ],
+                                    "score": 1.0,
+                                    "content": "foresight: Model-based deep reinforcement learning for vision-based robotic control. CoRR,",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                194,
+                                216,
+                                206
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        194,
+                                        216,
+                                        206
+                                    ],
+                                    "score": 1.0,
+                                    "content": "abs/1812.00568, 2018b.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 10,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                204,
+                                507,
+                                220
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        204,
+                                        507,
+                                        220
+                                    ],
+                                    "score": 1.0,
+                                    "content": "B. Espiau, F. Chaumette, and P. Rives. A new approach to visual servoing in robotics. IEEE",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 11,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                216,
+                                469,
+                                230
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        216,
+                                        469,
+                                        230
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Transactions on Robotics and Automation, 8(3):313–326, June 1992. ISSN 1042-296X.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 12,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                228,
+                                504,
+                                242
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        228,
+                                        504,
+                                        242
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Benjamin Eysenbach, Abhishek Gupta, Julian Ibarz, and Sergey Levine. Diversity is all you need:",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 13,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                240,
+                                409,
+                                251
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        240,
+                                        409,
+                                        251
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Learning skills without a reward function. CoRR, abs/1802.06070, 2018.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 14,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                248,
+                                505,
+                                266
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        248,
+                                        505,
+                                        266
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Benjamin Eysenbach, Ruslan Salakhutdinov, and Sergey Levine. Search on the replay buffer: Bridg-",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 15,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                261,
+                                406,
+                                275
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        261,
+                                        406,
+                                        275
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ing planning and reinforcement learning. CoRR, abs/1906.05253, 2019.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 16,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                271,
+                                506,
+                                288
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        271,
+                                        506,
+                                        288
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Chelsea Finn and Sergey Levine. Deep visual foresight for planning robot motion. CoRR,",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 17,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                282,
+                                211,
+                                297
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        282,
+                                        211,
+                                        297
+                                    ],
+                                    "score": 1.0,
+                                    "content": "abs/1610.00696, 2016.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 18,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                295,
+                                506,
+                                309
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        295,
+                                        506,
+                                        309
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Roy Fox, Richard Shin, Sanjay Krishnan, Ken Goldberg, Dawn Song, and Ion Stoica. Parametrized",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 19,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                305,
+                                505,
+                                322
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        305,
+                                        505,
+                                        322
+                                    ],
+                                    "score": 1.0,
+                                    "content": "hierarchical procedures for neural programming. In International Conference on Learning Rep-",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                318,
+                                195,
+                                330
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        318,
+                                        195,
+                                        330
+                                    ],
+                                    "score": 1.0,
+                                    "content": "resentations, 2018.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 21,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                329,
+                                504,
+                                342
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        329,
+                                        504,
+                                        342
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Ali Ghadirzadeh, Atsuto Maki, Danica Kragic, and Marten Bj ˚ orkman. Deep predictive policy train- ¨",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 22,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                339,
+                                376,
+                                353
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        339,
+                                        376,
+                                        353
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ing using reinforcement learning. CoRR, abs/1703.00727, 2017.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 23,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                351,
+                                506,
+                                365
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        351,
+                                        506,
+                                        365
+                                    ],
+                                    "score": 1.0,
+                                    "content": "De-An Huang, Suraj Nair, Danfei Xu, Yuke Zhu, Animesh Garg, Li Fei-Fei, Silvio Savarese, and",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 24,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                362,
+                                505,
+                                376
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        362,
+                                        505,
+                                        376
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Juan Carlos Niebles. Neural task graphs: Generalizing to unseen tasks from a single video demon-",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                373,
+                                276,
+                                386
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        373,
+                                        276,
+                                        386
+                                    ],
+                                    "score": 1.0,
+                                    "content": "stration. CoRR, abs/1807.03480, 2018.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 26,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                385,
+                                505,
+                                398
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        385,
+                                        505,
+                                        398
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Brian Ichter and Marco Pavone. Robot motion planning in learned latent spaces. CoRR,",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 27,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                396,
+                                210,
+                                408
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        396,
+                                        210,
+                                        408
+                                    ],
+                                    "score": 1.0,
+                                    "content": "abs/1807.10366, 2018.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 28,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                405,
+                                507,
+                                422
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        405,
+                                        507,
+                                        422
+                                    ],
+                                    "score": 1.0,
+                                    "content": "M. Jagersand, O. Fuentes, and R. Nelson. Experimental evaluation of uncalibrated visual servoing",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 29,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                418,
+                                505,
+                                432
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        418,
+                                        505,
+                                        432
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for precision manipulation. In Proceedings of International Conference on Robotics and Automa-",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                429,
+                                316,
+                                442
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        429,
+                                        316,
+                                        442
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tion, volume 4, pp. 2874–2880 vol.4, April 1997.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 31,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                440,
+                                506,
+                                454
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        440,
+                                        506,
+                                        454
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Stephen James, Andrew J. Davison, and Edward Johns. Transferring end-to-end visuomotor control",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 32,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                452,
+                                448,
+                                466
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        452,
+                                        448,
+                                        466
+                                    ],
+                                    "score": 1.0,
+                                    "content": "from simulation to real world for a multi-stage task. CoRR, abs/1707.02267, 2017.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 33,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                463,
+                                505,
+                                477
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        463,
+                                        505,
+                                        477
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Dinesh Jayaraman, Frederik Ebert, Alexei Efros, and Sergey Levine. Time-agnostic prediction:",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 34,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                472,
+                                506,
+                                490
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        472,
+                                        506,
+                                        490
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Predicting predictable video frames. In International Conference on Learning Representations,",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                486,
+                                142,
+                                498
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        486,
+                                        142,
+                                        498
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2019.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 36,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                496,
+                                438,
+                                512
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        496,
+                                        438,
+                                        512
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Leslie Pack Kaelbling. Learning to achieve goals. In IJCAI, pp. 1094–1098, 1993.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 37,
+                            "is_list_start_line": true,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                508,
+                                505,
+                                522
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        508,
+                                        505,
+                                        522
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Leslie Pack Kaelbling and Tomas Lozano-Perez. Hierarchical task and motion planning in the now.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 38,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                113,
+                                518,
+                                505,
+                                534
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        113,
+                                        518,
+                                        505,
+                                        534
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In IEEE Conference on Robotics and Automation (ICRA), 2011. Finalist, Best Manipulation Paper",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                531,
+                                147,
+                                543
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        531,
+                                        147,
+                                        543
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Award.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 40,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                540,
+                                507,
+                                557
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        540,
+                                        507,
+                                        557
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Dmitry Kalashnikov, Alex Irpan, Peter Pastor, Julian Ibarz, Alexander Herzog, Eric Jang, Deirdre",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 41,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                551,
+                                506,
+                                568
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        551,
+                                        506,
+                                        568
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Quillen, Ethan Holly, Mrinal Kalakrishnan, Vincent Vanhoucke, and Sergey Levine. Qt-opt:",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 42
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                563,
+                                505,
+                                577
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        563,
+                                        505,
+                                        577
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Scalable deep reinforcement learning for vision-based robotic manipulation. arxiv:Preprint, 2018.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 43
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                575,
+                                505,
+                                589
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        575,
+                                        505,
+                                        589
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Nal Kalchbrenner, Aaron van den Oord, Karen Simonyan, Ivo Danihelka, Oriol Vinyals, Alex ¨",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 44,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                586,
+                                464,
+                                598
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        586,
+                                        464,
+                                        598
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Graves, and Koray Kavukcuoglu. Video pixel networks. CoRR, abs/1610.00527, 2016.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 45,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                597,
+                                505,
+                                611
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        597,
+                                        505,
+                                        611
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Sanjay Krishnan, Roy Fox, Ion Stoica, and Ken Goldberg. DDCO: discovery of deep continuous",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 46,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                609,
+                                430,
+                                622
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        609,
+                                        430,
+                                        622
+                                    ],
+                                    "score": 1.0,
+                                    "content": "options forrobot learning from demonstrations. CoRR, abs/1710.05421, 2017.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 47,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                620,
+                                505,
+                                634
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        620,
+                                        505,
+                                        634
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Thanard Kurutach, Aviv Tamar, Ge Yang, Stuart J. Russell, and Pieter Abbeel. Learning plannable",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 48,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                631,
+                                386,
+                                644
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        631,
+                                        386,
+                                        644
+                                    ],
+                                    "score": 1.0,
+                                    "content": "representations with causal infogan. CoRR, abs/1807.09341, 2018.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 49,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                641,
+                                506,
+                                657
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        641,
+                                        506,
+                                        657
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Thomas Lampe and Martin Riedmiller. Acquiring visual servoing reaching and grasping skills using",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 50,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                654,
+                                505,
+                                668
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        654,
+                                        505,
+                                        668
+                                    ],
+                                    "score": 1.0,
+                                    "content": "neural reinforcement learning. In International Joint Conference on Neural Networks (IJCNN",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 51
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                665,
+                                171,
+                                678
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        665,
+                                        171,
+                                        678
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2013), 2013.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 52,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                675,
+                                506,
+                                691
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        675,
+                                        506,
+                                        691
+                                    ],
+                                    "score": 1.0,
+                                    "content": "S. Lange, M. Riedmiller, and A. Voigtlander. Autonomous reinforcement learning on raw visual ¨",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 53,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                686,
+                                506,
+                                701
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        686,
+                                        506,
+                                        701
+                                    ],
+                                    "score": 1.0,
+                                    "content": "input data in a real world application. In The 2012 International Joint Conference on Neural",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 54
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                698,
+                                242,
+                                712
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        698,
+                                        242,
+                                        712
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Networks (IJCNN), June 2012.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 55,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                709,
+                                505,
+                                723
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        709,
+                                        505,
+                                        723
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Steven M. LaValle. Planning Algorithms. Cambridge University Press, 2006. doi: 10.1017/",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 56,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                720,
+                                207,
+                                734
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        720,
+                                        207,
+                                        734
+                                    ],
+                                    "score": 1.0,
+                                    "content": "CBO9780511546877.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 57,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                82,
+                                504,
+                                96
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        82,
+                                        504,
+                                        96
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Alex X. Lee, Richard Zhang, Frederik Ebert, Pieter Abbeel, Chelsea Finn, and Sergey Levine.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 0,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                93,
+                                399,
+                                107
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        93,
+                                        399,
+                                        107
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Stochastic adversarial video prediction. CoRR, abs/1804.01523, 2018.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 1,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                104,
+                                505,
+                                119
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        104,
+                                        505,
+                                        119
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Sergey Levine, Chelsea Finn, Trevor Darrell, and Pieter Abbeel. End-to-end training of deep visuo-",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 2,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                115,
+                                303,
+                                128
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        115,
+                                        303,
+                                        128
+                                    ],
+                                    "score": 1.0,
+                                    "content": "motor policies. CoRR, abs/1504.00702, 2015.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 3,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                126,
+                                505,
+                                142
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        126,
+                                        505,
+                                        142
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Andrew Levy, Robert Platt, and Kate Saenko. Hierarchical reinforcement learning with hindsight.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 4,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                138,
+                                376,
+                                152
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        138,
+                                        376,
+                                        152
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In International Conference on Learning Representations, 2019.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 5,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                149,
+                                506,
+                                165
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        149,
+                                        506,
+                                        165
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Corey Lynch, Mohi Khansari, Ted Xiao, Vikash Kumar, Jonathan Tompson, Sergey Levine, and",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 6,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                161,
+                                439,
+                                174
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        161,
+                                        439,
+                                        174
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Pierre Sermanet. Learning latent plans from play. CoRR, abs/1903.01973, 2019.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 7,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                173,
+                                505,
+                                186
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        173,
+                                        505,
+                                        186
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Jan Matas, Stephen James, and Andrew J. Davison. Sim-to-real reinforcement learning for de-",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 8,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                183,
+                                364,
+                                197
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        183,
+                                        364,
+                                        197
+                                    ],
+                                    "score": 1.0,
+                                    "content": "formable object manipulation. CoRR, abs/1806.07851, 2018.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 9,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                192,
+                                505,
+                                209
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        192,
+                                        505,
+                                        209
+                                    ],
+                                    "score": 1.0,
+                                    "content": "K. Mohta, V. Kumar, and K. Daniilidis. Vision-based control of a quadrotor for perching on lines.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 10,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                206,
+                                473,
+                                219
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        206,
+                                        473,
+                                        219
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In 2014 IEEE International Conference on Robotics and Automation (ICRA), May 2014.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 11,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                217,
+                                504,
+                                232
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        217,
+                                        504,
+                                        232
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Ofir Nachum, Shixiang Gu, Honglak Lee, and Sergey Levine. Data-efficient hierarchical reinforce-",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 12,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                228,
+                                299,
+                                241
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        228,
+                                        299,
+                                        241
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ment learning. CoRR, abs/1805.08296, 2018.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 13,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                239,
+                                506,
+                                254
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        239,
+                                        506,
+                                        254
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Ashvin Nair, Vitchyr Pong, Murtaza Dalal, Shikhar Bahl, Steven Lin, and Sergey Levine. Visual",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 14,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                250,
+                                424,
+                                264
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        250,
+                                        424,
+                                        264
+                                    ],
+                                    "score": 1.0,
+                                    "content": "reinforcement learning with imagined goals. CoRR, abs/1807.04742, 2018a.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 15,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                261,
+                                506,
+                                277
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        261,
+                                        506,
+                                        277
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Suraj Nair, Mohammad Babaeizadeh, Chelsea Finn, Sergey Levine, and Vikash Kumar. Time rever-",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 16,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                273,
+                                340,
+                                286
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        273,
+                                        340,
+                                        286
+                                    ],
+                                    "score": 1.0,
+                                    "content": "sal as self-supervision. CoRR, abs/1810.01128, 2018b.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 17,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                281,
+                                506,
+                                301
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        281,
+                                        506,
+                                        301
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Alexander Neitz, Giambattista Parascandolo, Stefan Bauer, and Bernhard Scholkopf. Adaptive skip ¨",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 18,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                296,
+                                504,
+                                309
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        296,
+                                        504,
+                                        309
+                                    ],
+                                    "score": 1.0,
+                                    "content": "intervals: Temporal abstraction for recurrent dynamical models. In Advances in Neural Informa-",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                113,
+                                306,
+                                256,
+                                321
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        113,
+                                        306,
+                                        256,
+                                        321
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tion Processing Systems 31. 2018.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 20,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                316,
+                                506,
+                                333
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        316,
+                                        506,
+                                        333
+                                    ],
+                                    "score": 1.0,
+                                    "content": "OpenAI, Marcin Andrychowicz, Bowen Baker, Maciek Chociej, Rafal Jozefowicz, Bob McGrew, ´",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 21,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                113,
+                                327,
+                                506,
+                                344
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        113,
+                                        327,
+                                        506,
+                                        344
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Jakub W. Pachocki, Jakub Pachocki, Arthur Petron, Matthias Plappert, Glenn Powell, Alex Ray,",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                113,
+                                338,
+                                506,
+                                355
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        113,
+                                        338,
+                                        506,
+                                        355
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Jonas Schneider, Szymon Sidor, Josh Tobin, Peter Welinder, Lilian Weng, and Wojciech Zaremba.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                113,
+                                350,
+                                409,
+                                365
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        113,
+                                        350,
+                                        409,
+                                        365
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Learning dexterous in-hand manipulation. CoRR, abs/1808.00177, 2018.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 24,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                362,
+                                506,
+                                376
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        362,
+                                        506,
+                                        376
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Chris Paxton, Yotam Barnoy, Kapil D. Katyal, Raman Arora, and Gregory D. Hager. Visual robot",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 25,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                373,
+                                297,
+                                387
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        373,
+                                        297,
+                                        387
+                                    ],
+                                    "score": 1.0,
+                                    "content": "task planning. CoRR, abs/1804.00062, 2018.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 26,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                385,
+                                506,
+                                399
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        385,
+                                        506,
+                                        399
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Lerrel Pinto and Abhinav Gupta. Supersizing self-supervision: Learning to grasp from 50k tries and",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 27,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                395,
+                                307,
+                                409
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        395,
+                                        307,
+                                        409
+                                    ],
+                                    "score": 1.0,
+                                    "content": "700 robot hours. CoRR, abs/1509.06825, 2015.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 28,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                407,
+                                505,
+                                421
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        407,
+                                        505,
+                                        421
+                                    ],
+                                    "score": 1.0,
+                                    "content": "R Rubinstein and D Kroese. The Cross-Entropy Method: A Unified Approach to Combinatorial",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 29,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                418,
+                                409,
+                                432
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        418,
+                                        409,
+                                        432
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Optimization, Monte-Carlo Simulation and Machine Learning. 01 2004.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 30,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                430,
+                                505,
+                                444
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        430,
+                                        505,
+                                        444
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Fereshteh Sadeghi. Divis: Domain invariant visual servoing for collision-free goal reaching. CoRR,",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 31,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                442,
+                                209,
+                                453
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        442,
+                                        209,
+                                        453
+                                    ],
+                                    "score": 1.0,
+                                    "content": "abs/1902.05947, 2019.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 32,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                452,
+                                506,
+                                466
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        452,
+                                        506,
+                                        466
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Fereshteh Sadeghi, Alexander Toshev, Eric Jang, and Sergey Levine. Sim2real viewpoint invariant",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 33,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                461,
+                                506,
+                                478
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        461,
+                                        506,
+                                        478
+                                    ],
+                                    "score": 1.0,
+                                    "content": "visual servoing by recurrent control. In The IEEE Conference on Computer Vision and Pattern",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                474,
+                                250,
+                                488
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        474,
+                                        250,
+                                        488
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Recognition (CVPR), June 2018.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 35,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                484,
+                                505,
+                                501
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        484,
+                                        505,
+                                        501
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Tom Schaul, Daniel Horgan, Karol Gregor, and David Silver. Universal value function approxima-",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 36,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                496,
+                                369,
+                                511
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        496,
+                                        369,
+                                        511
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tors. In International Conference on Machine Learning, 2015.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 37,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                506,
+                                506,
+                                523
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        506,
+                                        506,
+                                        523
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Connor Schenck and Dieter Fox. Visual closed-loop control for pouring liquids. CoRR,",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 38,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                518,
+                                210,
+                                532
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        518,
+                                        210,
+                                        532
+                                    ],
+                                    "score": 1.0,
+                                    "content": "abs/1610.02610, 2016.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 39,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                531,
+                                506,
+                                544
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        531,
+                                        506,
+                                        544
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Avi Singh, Larry Yang, Kristian Hartikainen, Chelsea Finn, and Sergey Levine. End-to-end robotic",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 40,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                113,
+                                541,
+                                447,
+                                555
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        113,
+                                        541,
+                                        447,
+                                        555
+                                    ],
+                                    "score": 1.0,
+                                    "content": "reinforcement learning without reward engineering. CoRR, abs/1904.07854, 2019.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 41,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                552,
+                                506,
+                                568
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        552,
+                                        506,
+                                        568
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Aravind Srinivas, Allan Jabri, Pieter Abbeel, Sergey Levine, and Chelsea Finn. Universal planning",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 42,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                564,
+                                282,
+                                577
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        564,
+                                        282,
+                                        577
+                                    ],
+                                    "score": 1.0,
+                                    "content": "networks. CoRR, abs/1804.00645, 2018.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 43,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                576,
+                                506,
+                                589
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        576,
+                                        506,
+                                        589
+                                    ],
+                                    "score": 1.0,
+                                    "content": "S. Srivastava, E. Fang, L. Riano, R. Chitnis, S. Russell, and P. Abbeel. Combined task and motion",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 44,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                586,
+                                506,
+                                601
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        586,
+                                        506,
+                                        601
+                                    ],
+                                    "score": 1.0,
+                                    "content": "planning through an extensible planner-independent interface layer. In 2014 IEEE International",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 45
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                597,
+                                360,
+                                611
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        597,
+                                        360,
+                                        611
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Conference on Robotics and Automation (ICRA), May 2014.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 46,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                609,
+                                506,
+                                622
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        609,
+                                        506,
+                                        622
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Richard Sutton, Doina Precup, and Satinder Singh. Between mdps and semi-mdps: A framework",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 47,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                619,
+                                495,
+                                635
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        619,
+                                        495,
+                                        635
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for temporal abstraction in reinforcement learning. Artificial Intelligence, 112:181–211, 1999.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 48
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                630,
+                                506,
+                                646
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        630,
+                                        506,
+                                        646
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Emanuel Todorov, Tom Erez, and Yuval Tassa. Mujoco: A physics engine for model-based control.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 49,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                113,
+                                642,
+                                380,
+                                656
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        113,
+                                        642,
+                                        380,
+                                        656
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In IROS, pp. 5026–5033. IEEE, 2012. ISBN 978-1-4673-1737-5.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 50,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                654,
+                                506,
+                                667
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        654,
+                                        506,
+                                        667
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Marc Toussaint, Kelsey R Allen, Kevin A Smith, and Josh B Tenenbaum. Differentiable physics and",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 51,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                664,
+                                506,
+                                680
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        664,
+                                        506,
+                                        680
+                                    ],
+                                    "score": 1.0,
+                                    "content": "stable modes for tool-use and manipulation planning – extended abstract, 2019. Sister Conference",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 52
+                        },
+                        {
+                            "bbox": [
+                                113,
+                                674,
+                                358,
+                                691
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        113,
+                                        674,
+                                        358,
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+                                    "bbox": [
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+                                        505,
+                                        96
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+                                    "cross_page": true
+                                }
+                            ],
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+                                    "cross_page": true
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+                                    "bbox": [
+                                        105,
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+                                        505,
+                                        117
+                                    ],
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+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 2,
+                            "is_list_start_line": true
+                        },
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+                                115,
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+                                505,
+                                128
+                            ],
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+                                    "bbox": [
+                                        115,
+                                        115,
+                                        505,
+                                        128
+                                    ],
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+                                    "content": "bed to control: A locally linear latent dynamics model for control from raw images. CoRR,",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                116,
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+                                209,
+                                138
+                            ],
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+                                {
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+                                        138
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+                                    "bbox": [
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+                                        505,
+                                        149
+                                    ],
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+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
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+                            "is_list_start_line": true
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+                                480,
+                                160
+                            ],
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+                                    "bbox": [
+                                        115,
+                                        149,
+                                        480,
+                                        160
+                                    ],
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+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 6,
+                            "is_list_end_line": true
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+                                    "bbox": [
+                                        105,
+                                        159,
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+                                        172
+                                    ],
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+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 7,
+                            "is_list_start_line": true
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+                                493,
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+                                        170,
+                                        493,
+                                        183
+                                    ],
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+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
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+                                        105,
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+                                    ],
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+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
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+                            "is_list_start_line": true
+                        },
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+                            ],
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+                                {
+                                    "bbox": [
+                                        115,
+                                        191,
+                                        505,
+                                        205
+                                    ],
+                                    "score": 1.0,
+                                    "content": "task programming: Learning to generalize across hierarchical tasks. CoRR, abs/1710.01813,",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                202,
+                                142,
+                                215
+                            ],
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+                                {
+                                    "bbox": [
+                                        115,
+                                        202,
+                                        142,
+                                        215
+                                    ],
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+                                    "cross_page": true
+                                }
+                            ],
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+                            "is_list_end_line": true
+                        },
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+                                227
+                            ],
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+                                        213,
+                                        506,
+                                        227
+                                    ],
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+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 12,
+                            "is_list_start_line": true
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+                                239
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+                                    "cross_page": true
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+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
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+                                        246,
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+                                    "cross_page": true
+                                }
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+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 17
+                        },
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+                                        115,
+                                        280,
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+                                    ],
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+                                    "cross_page": true
+                                }
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+                            "is_list_end_line": true
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+                            "bbox": [
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+                                        114,
+                                        126,
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+                        },
+                        {
+                            "bbox": [
+                                104,
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+                                        507,
+                                        154
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+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                115,
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+                                        150,
+                                        506,
+                                        164
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+                            ],
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+                        },
+                        {
+                            "bbox": [
+                                116,
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+                                173
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+                                    "bbox": [
+                                        116,
+                                        161,
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+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                172,
+                                506,
+                                186
+                            ],
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+                                    "bbox": [
+                                        106,
+                                        172,
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+                                        186
+                                    ],
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+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                181,
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+                                198
+                            ],
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+                                {
+                                    "bbox": [
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+                                        181,
+                                        506,
+                                        198
+                                    ],
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+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                194,
+                                216,
+                                206
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        194,
+                                        216,
+                                        206
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+                                }
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+                        },
+                        {
+                            "bbox": [
+                                104,
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+                                220
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+                                    "bbox": [
+                                        104,
+                                        204,
+                                        507,
+                                        220
+                                    ],
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+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                216,
+                                469,
+                                230
+                            ],
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+                                    "bbox": [
+                                        116,
+                                        216,
+                                        469,
+                                        230
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+                                }
+                            ],
+                            "index": 12
+                        },
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+                            "bbox": [
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+                                    "bbox": [
+                                        106,
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+                                        504,
+                                        242
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+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                240,
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+                                251
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+                                    "bbox": [
+                                        115,
+                                        240,
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+                                        251
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+                                    "content": "Learning skills without a reward function. CoRR, abs/1802.06070, 2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
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+                                    ],
+                                    "score": 1.0,
+                                    "content": "Benjamin Eysenbach, Ruslan Salakhutdinov, and Sergey Levine. Search on the replay buffer: Bridg-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                261,
+                                406,
+                                275
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        261,
+                                        406,
+                                        275
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ing planning and reinforcement learning. CoRR, abs/1906.05253, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                271,
+                                506,
+                                288
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        271,
+                                        506,
+                                        288
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Chelsea Finn and Sergey Levine. Deep visual foresight for planning robot motion. CoRR,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                282,
+                                211,
+                                297
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        282,
+                                        211,
+                                        297
+                                    ],
+                                    "score": 1.0,
+                                    "content": "abs/1610.00696, 2016.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                295,
+                                506,
+                                309
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        295,
+                                        506,
+                                        309
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Roy Fox, Richard Shin, Sanjay Krishnan, Ken Goldberg, Dawn Song, and Ion Stoica. Parametrized",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                305,
+                                505,
+                                322
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        305,
+                                        505,
+                                        322
+                                    ],
+                                    "score": 1.0,
+                                    "content": "hierarchical procedures for neural programming. In International Conference on Learning Rep-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                318,
+                                195,
+                                330
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        318,
+                                        195,
+                                        330
+                                    ],
+                                    "score": 1.0,
+                                    "content": "resentations, 2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                329,
+                                504,
+                                342
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        329,
+                                        504,
+                                        342
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Ali Ghadirzadeh, Atsuto Maki, Danica Kragic, and Marten Bj ˚ orkman. Deep predictive policy train- ¨",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                339,
+                                376,
+                                353
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        339,
+                                        376,
+                                        353
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ing using reinforcement learning. CoRR, abs/1703.00727, 2017.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                351,
+                                506,
+                                365
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        351,
+                                        506,
+                                        365
+                                    ],
+                                    "score": 1.0,
+                                    "content": "De-An Huang, Suraj Nair, Danfei Xu, Yuke Zhu, Animesh Garg, Li Fei-Fei, Silvio Savarese, and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                362,
+                                505,
+                                376
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        362,
+                                        505,
+                                        376
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Juan Carlos Niebles. Neural task graphs: Generalizing to unseen tasks from a single video demon-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                373,
+                                276,
+                                386
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        373,
+                                        276,
+                                        386
+                                    ],
+                                    "score": 1.0,
+                                    "content": "stration. CoRR, abs/1807.03480, 2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                385,
+                                505,
+                                398
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        385,
+                                        505,
+                                        398
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Brian Ichter and Marco Pavone. Robot motion planning in learned latent spaces. CoRR,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                396,
+                                210,
+                                408
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        396,
+                                        210,
+                                        408
+                                    ],
+                                    "score": 1.0,
+                                    "content": "abs/1807.10366, 2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                405,
+                                507,
+                                422
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        405,
+                                        507,
+                                        422
+                                    ],
+                                    "score": 1.0,
+                                    "content": "M. Jagersand, O. Fuentes, and R. Nelson. Experimental evaluation of uncalibrated visual servoing",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                418,
+                                505,
+                                432
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        418,
+                                        505,
+                                        432
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for precision manipulation. In Proceedings of International Conference on Robotics and Automa-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                429,
+                                316,
+                                442
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        429,
+                                        316,
+                                        442
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tion, volume 4, pp. 2874–2880 vol.4, April 1997.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                440,
+                                506,
+                                454
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        440,
+                                        506,
+                                        454
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Stephen James, Andrew J. Davison, and Edward Johns. Transferring end-to-end visuomotor control",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                452,
+                                448,
+                                466
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        452,
+                                        448,
+                                        466
+                                    ],
+                                    "score": 1.0,
+                                    "content": "from simulation to real world for a multi-stage task. CoRR, abs/1707.02267, 2017.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                463,
+                                505,
+                                477
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        463,
+                                        505,
+                                        477
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Dinesh Jayaraman, Frederik Ebert, Alexei Efros, and Sergey Levine. Time-agnostic prediction:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                472,
+                                506,
+                                490
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        472,
+                                        506,
+                                        490
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Predicting predictable video frames. In International Conference on Learning Representations,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                486,
+                                142,
+                                498
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        486,
+                                        142,
+                                        498
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                496,
+                                438,
+                                512
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        496,
+                                        438,
+                                        512
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Leslie Pack Kaelbling. Learning to achieve goals. In IJCAI, pp. 1094–1098, 1993.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                508,
+                                505,
+                                522
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        508,
+                                        505,
+                                        522
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Leslie Pack Kaelbling and Tomas Lozano-Perez. Hierarchical task and motion planning in the now.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                113,
+                                518,
+                                505,
+                                534
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        113,
+                                        518,
+                                        505,
+                                        534
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In IEEE Conference on Robotics and Automation (ICRA), 2011. Finalist, Best Manipulation Paper",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                531,
+                                147,
+                                543
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        531,
+                                        147,
+                                        543
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Award.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                540,
+                                507,
+                                557
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        540,
+                                        507,
+                                        557
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Dmitry Kalashnikov, Alex Irpan, Peter Pastor, Julian Ibarz, Alexander Herzog, Eric Jang, Deirdre",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                551,
+                                506,
+                                568
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        551,
+                                        506,
+                                        568
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Quillen, Ethan Holly, Mrinal Kalakrishnan, Vincent Vanhoucke, and Sergey Levine. Qt-opt:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                563,
+                                505,
+                                577
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        563,
+                                        505,
+                                        577
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Scalable deep reinforcement learning for vision-based robotic manipulation. arxiv:Preprint, 2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                575,
+                                505,
+                                589
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        575,
+                                        505,
+                                        589
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Nal Kalchbrenner, Aaron van den Oord, Karen Simonyan, Ivo Danihelka, Oriol Vinyals, Alex ¨",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                586,
+                                464,
+                                598
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        586,
+                                        464,
+                                        598
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Graves, and Koray Kavukcuoglu. Video pixel networks. CoRR, abs/1610.00527, 2016.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 45
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                597,
+                                505,
+                                611
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        597,
+                                        505,
+                                        611
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Sanjay Krishnan, Roy Fox, Ion Stoica, and Ken Goldberg. DDCO: discovery of deep continuous",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 46
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                609,
+                                430,
+                                622
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        609,
+                                        430,
+                                        622
+                                    ],
+                                    "score": 1.0,
+                                    "content": "options forrobot learning from demonstrations. CoRR, abs/1710.05421, 2017.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 47
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                620,
+                                505,
+                                634
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        620,
+                                        505,
+                                        634
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Thanard Kurutach, Aviv Tamar, Ge Yang, Stuart J. Russell, and Pieter Abbeel. Learning plannable",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 48
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                631,
+                                386,
+                                644
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        631,
+                                        386,
+                                        644
+                                    ],
+                                    "score": 1.0,
+                                    "content": "representations with causal infogan. CoRR, abs/1807.09341, 2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 49
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                641,
+                                506,
+                                657
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        641,
+                                        506,
+                                        657
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Thomas Lampe and Martin Riedmiller. Acquiring visual servoing reaching and grasping skills using",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 50
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                654,
+                                505,
+                                668
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        654,
+                                        505,
+                                        668
+                                    ],
+                                    "score": 1.0,
+                                    "content": "neural reinforcement learning. In International Joint Conference on Neural Networks (IJCNN",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 51
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                665,
+                                171,
+                                678
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        665,
+                                        171,
+                                        678
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2013), 2013.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 52
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                675,
+                                506,
+                                691
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        675,
+                                        506,
+                                        691
+                                    ],
+                                    "score": 1.0,
+                                    "content": "S. Lange, M. Riedmiller, and A. Voigtlander. Autonomous reinforcement learning on raw visual ¨",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 53
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                686,
+                                506,
+                                701
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        686,
+                                        506,
+                                        701
+                                    ],
+                                    "score": 1.0,
+                                    "content": "input data in a real world application. In The 2012 International Joint Conference on Neural",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 54
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                698,
+                                242,
+                                712
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        698,
+                                        242,
+                                        712
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Networks (IJCNN), June 2012.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 55
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                709,
+                                505,
+                                723
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        709,
+                                        505,
+                                        723
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Steven M. LaValle. Planning Algorithms. Cambridge University Press, 2006. doi: 10.1017/",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 56
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                720,
+                                207,
+                                734
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        720,
+                                        207,
+                                        734
+                                    ],
+                                    "score": 1.0,
+                                    "content": "CBO9780511546877.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 57
+                        }
+                    ],
+                    "index": 28.5
+                }
+            ],
+            "page_idx": 9,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        107,
+                        27,
+                        294,
+                        37
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                26,
+                                294,
+                                38
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        26,
+                                        294,
+                                        38
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Published as a conference paper at ICLR 2020",
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+                                106,
+                                82,
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+                                96
+                            ],
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+                                    "bbox": [
+                                        106,
+                                        82,
+                                        504,
+                                        96
+                                    ],
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+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                93,
+                                399,
+                                107
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        93,
+                                        399,
+                                        107
+                                    ],
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+                                    "content": "Stochastic adversarial video prediction. CoRR, abs/1804.01523, 2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                104,
+                                505,
+                                119
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        104,
+                                        505,
+                                        119
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Sergey Levine, Chelsea Finn, Trevor Darrell, and Pieter Abbeel. End-to-end training of deep visuo-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                115,
+                                303,
+                                128
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        115,
+                                        303,
+                                        128
+                                    ],
+                                    "score": 1.0,
+                                    "content": "motor policies. CoRR, abs/1504.00702, 2015.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                126,
+                                505,
+                                142
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        126,
+                                        505,
+                                        142
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Andrew Levy, Robert Platt, and Kate Saenko. Hierarchical reinforcement learning with hindsight.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                138,
+                                376,
+                                152
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        138,
+                                        376,
+                                        152
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In International Conference on Learning Representations, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                149,
+                                506,
+                                165
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        149,
+                                        506,
+                                        165
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Corey Lynch, Mohi Khansari, Ted Xiao, Vikash Kumar, Jonathan Tompson, Sergey Levine, and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                161,
+                                439,
+                                174
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        161,
+                                        439,
+                                        174
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Pierre Sermanet. Learning latent plans from play. CoRR, abs/1903.01973, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                173,
+                                505,
+                                186
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        173,
+                                        505,
+                                        186
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Jan Matas, Stephen James, and Andrew J. Davison. Sim-to-real reinforcement learning for de-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                183,
+                                364,
+                                197
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        183,
+                                        364,
+                                        197
+                                    ],
+                                    "score": 1.0,
+                                    "content": "formable object manipulation. CoRR, abs/1806.07851, 2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                192,
+                                505,
+                                209
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        192,
+                                        505,
+                                        209
+                                    ],
+                                    "score": 1.0,
+                                    "content": "K. Mohta, V. Kumar, and K. Daniilidis. Vision-based control of a quadrotor for perching on lines.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                206,
+                                473,
+                                219
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        206,
+                                        473,
+                                        219
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In 2014 IEEE International Conference on Robotics and Automation (ICRA), May 2014.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                217,
+                                504,
+                                232
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        217,
+                                        504,
+                                        232
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Ofir Nachum, Shixiang Gu, Honglak Lee, and Sergey Levine. Data-efficient hierarchical reinforce-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                228,
+                                299,
+                                241
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        228,
+                                        299,
+                                        241
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ment learning. CoRR, abs/1805.08296, 2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                239,
+                                506,
+                                254
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        239,
+                                        506,
+                                        254
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Ashvin Nair, Vitchyr Pong, Murtaza Dalal, Shikhar Bahl, Steven Lin, and Sergey Levine. Visual",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                250,
+                                424,
+                                264
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        250,
+                                        424,
+                                        264
+                                    ],
+                                    "score": 1.0,
+                                    "content": "reinforcement learning with imagined goals. CoRR, abs/1807.04742, 2018a.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                261,
+                                506,
+                                277
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        261,
+                                        506,
+                                        277
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Suraj Nair, Mohammad Babaeizadeh, Chelsea Finn, Sergey Levine, and Vikash Kumar. Time rever-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                273,
+                                340,
+                                286
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        273,
+                                        340,
+                                        286
+                                    ],
+                                    "score": 1.0,
+                                    "content": "sal as self-supervision. CoRR, abs/1810.01128, 2018b.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                281,
+                                506,
+                                301
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        281,
+                                        506,
+                                        301
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Alexander Neitz, Giambattista Parascandolo, Stefan Bauer, and Bernhard Scholkopf. Adaptive skip ¨",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                296,
+                                504,
+                                309
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        296,
+                                        504,
+                                        309
+                                    ],
+                                    "score": 1.0,
+                                    "content": "intervals: Temporal abstraction for recurrent dynamical models. In Advances in Neural Informa-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                113,
+                                306,
+                                256,
+                                321
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        113,
+                                        306,
+                                        256,
+                                        321
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tion Processing Systems 31. 2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                316,
+                                506,
+                                333
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        316,
+                                        506,
+                                        333
+                                    ],
+                                    "score": 1.0,
+                                    "content": "OpenAI, Marcin Andrychowicz, Bowen Baker, Maciek Chociej, Rafal Jozefowicz, Bob McGrew, ´",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                113,
+                                327,
+                                506,
+                                344
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        113,
+                                        327,
+                                        506,
+                                        344
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Jakub W. Pachocki, Jakub Pachocki, Arthur Petron, Matthias Plappert, Glenn Powell, Alex Ray,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                113,
+                                338,
+                                506,
+                                355
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        113,
+                                        338,
+                                        506,
+                                        355
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Jonas Schneider, Szymon Sidor, Josh Tobin, Peter Welinder, Lilian Weng, and Wojciech Zaremba.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                113,
+                                350,
+                                409,
+                                365
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        113,
+                                        350,
+                                        409,
+                                        365
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Learning dexterous in-hand manipulation. CoRR, abs/1808.00177, 2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                362,
+                                506,
+                                376
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        362,
+                                        506,
+                                        376
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Chris Paxton, Yotam Barnoy, Kapil D. Katyal, Raman Arora, and Gregory D. Hager. Visual robot",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                373,
+                                297,
+                                387
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        373,
+                                        297,
+                                        387
+                                    ],
+                                    "score": 1.0,
+                                    "content": "task planning. CoRR, abs/1804.00062, 2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                385,
+                                506,
+                                399
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        385,
+                                        506,
+                                        399
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Lerrel Pinto and Abhinav Gupta. Supersizing self-supervision: Learning to grasp from 50k tries and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                395,
+                                307,
+                                409
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        395,
+                                        307,
+                                        409
+                                    ],
+                                    "score": 1.0,
+                                    "content": "700 robot hours. CoRR, abs/1509.06825, 2015.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                407,
+                                505,
+                                421
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        407,
+                                        505,
+                                        421
+                                    ],
+                                    "score": 1.0,
+                                    "content": "R Rubinstein and D Kroese. The Cross-Entropy Method: A Unified Approach to Combinatorial",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                418,
+                                409,
+                                432
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        418,
+                                        409,
+                                        432
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Optimization, Monte-Carlo Simulation and Machine Learning. 01 2004.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                430,
+                                505,
+                                444
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        430,
+                                        505,
+                                        444
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Fereshteh Sadeghi. Divis: Domain invariant visual servoing for collision-free goal reaching. CoRR,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                442,
+                                209,
+                                453
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        442,
+                                        209,
+                                        453
+                                    ],
+                                    "score": 1.0,
+                                    "content": "abs/1902.05947, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                452,
+                                506,
+                                466
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        452,
+                                        506,
+                                        466
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Fereshteh Sadeghi, Alexander Toshev, Eric Jang, and Sergey Levine. Sim2real viewpoint invariant",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                461,
+                                506,
+                                478
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        461,
+                                        506,
+                                        478
+                                    ],
+                                    "score": 1.0,
+                                    "content": "visual servoing by recurrent control. In The IEEE Conference on Computer Vision and Pattern",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                474,
+                                250,
+                                488
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        474,
+                                        250,
+                                        488
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Recognition (CVPR), June 2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                484,
+                                505,
+                                501
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        484,
+                                        505,
+                                        501
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Tom Schaul, Daniel Horgan, Karol Gregor, and David Silver. Universal value function approxima-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                496,
+                                369,
+                                511
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        496,
+                                        369,
+                                        511
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tors. In International Conference on Machine Learning, 2015.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                506,
+                                506,
+                                523
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        506,
+                                        506,
+                                        523
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Connor Schenck and Dieter Fox. Visual closed-loop control for pouring liquids. CoRR,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                518,
+                                210,
+                                532
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        518,
+                                        210,
+                                        532
+                                    ],
+                                    "score": 1.0,
+                                    "content": "abs/1610.02610, 2016.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                531,
+                                506,
+                                544
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        531,
+                                        506,
+                                        544
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Avi Singh, Larry Yang, Kristian Hartikainen, Chelsea Finn, and Sergey Levine. End-to-end robotic",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                113,
+                                541,
+                                447,
+                                555
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        113,
+                                        541,
+                                        447,
+                                        555
+                                    ],
+                                    "score": 1.0,
+                                    "content": "reinforcement learning without reward engineering. CoRR, abs/1904.07854, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                552,
+                                506,
+                                568
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        552,
+                                        506,
+                                        568
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Aravind Srinivas, Allan Jabri, Pieter Abbeel, Sergey Levine, and Chelsea Finn. Universal planning",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                564,
+                                282,
+                                577
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        564,
+                                        282,
+                                        577
+                                    ],
+                                    "score": 1.0,
+                                    "content": "networks. CoRR, abs/1804.00645, 2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                576,
+                                506,
+                                589
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        576,
+                                        506,
+                                        589
+                                    ],
+                                    "score": 1.0,
+                                    "content": "S. Srivastava, E. Fang, L. Riano, R. Chitnis, S. Russell, and P. Abbeel. Combined task and motion",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                586,
+                                506,
+                                601
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        586,
+                                        506,
+                                        601
+                                    ],
+                                    "score": 1.0,
+                                    "content": "planning through an extensible planner-independent interface layer. In 2014 IEEE International",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 45
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                597,
+                                360,
+                                611
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        597,
+                                        360,
+                                        611
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Conference on Robotics and Automation (ICRA), May 2014.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 46
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                609,
+                                506,
+                                622
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        609,
+                                        506,
+                                        622
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Richard Sutton, Doina Precup, and Satinder Singh. Between mdps and semi-mdps: A framework",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 47
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                619,
+                                495,
+                                635
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        619,
+                                        495,
+                                        635
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for temporal abstraction in reinforcement learning. Artificial Intelligence, 112:181–211, 1999.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 48
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                630,
+                                506,
+                                646
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        630,
+                                        506,
+                                        646
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Emanuel Todorov, Tom Erez, and Yuval Tassa. Mujoco: A physics engine for model-based control.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 49
+                        },
+                        {
+                            "bbox": [
+                                113,
+                                642,
+                                380,
+                                656
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        113,
+                                        642,
+                                        380,
+                                        656
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In IROS, pp. 5026–5033. IEEE, 2012. ISBN 978-1-4673-1737-5.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 50
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                654,
+                                506,
+                                667
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        654,
+                                        506,
+                                        667
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Marc Toussaint, Kelsey R Allen, Kevin A Smith, and Josh B Tenenbaum. Differentiable physics and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 51
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                664,
+                                506,
+                                680
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        664,
+                                        506,
+                                        680
+                                    ],
+                                    "score": 1.0,
+                                    "content": "stable modes for tool-use and manipulation planning – extended abstract, 2019. Sister Conference",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 52
+                        },
+                        {
+                            "bbox": [
+                                113,
+                                674,
+                                358,
+                                691
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        113,
+                                        674,
+                                        358,
+                                        691
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Best Paper Track – Extended abstract of the R:SS’18 paper.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 53
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                687,
+                                506,
+                                701
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        687,
+                                        506,
+                                        701
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Ashish Vaswani, Samy Bengio, Eugene Brevdo, Francois Chollet, Aidan N. Gomez, Stephan",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 54
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                699,
+                                506,
+                                712
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        699,
+                                        506,
+                                        712
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Gouws, Llion Jones, Łukasz Kaiser, Nal Kalchbrenner, Niki Parmar, Ryan Sepassi, Noam",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 55
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                709,
+                                506,
+                                723
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        709,
+                                        465,
+                                        723
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Shazeer, and Jakob Uszkoreit. Tensor2tensor for neural machine translation.",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
+                                        474,
+                                        709,
+                                        506,
+                                        723
+                                    ],
+                                    "score": 1.0,
+                                    "content": "CoRR,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 56
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                720,
+                                210,
+                                734
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        720,
+                                        210,
+                                        734
+                                    ],
+                                    "score": 1.0,
+                                    "content": "abs/1803.07416, 2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 57
+                        }
+                    ],
+                    "index": 28.5
+                }
+            ],
+            "page_idx": 10,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        108,
+                        27,
+                        294,
+                        37
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
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+                                38
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
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+                                        38
+                                    ],
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+                                    "type": "text"
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+                        }
+                    ]
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+                {
+                    "type": "discarded",
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+                        300,
+                        751,
+                        310,
+                        760
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                299,
+                                750,
+                                312,
+                                765
+                            ],
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+                                {
+                                    "bbox": [
+                                        299,
+                                        750,
+                                        312,
+                                        765
+                                    ],
+                                    "score": 1.0,
+                                    "content": "",
+                                    "type": "text",
+                                    "height": 15,
+                                    "width": 13
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "list",
+                    "bbox": [
+                        105,
+                        84,
+                        506,
+                        731
+                    ],
+                    "lines": [],
+                    "index": 28.5,
+                    "bbox_fs": [
+                        104,
+                        82,
+                        506,
+                        734
+                    ],
+                    "lines_deleted": true
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        82,
+                        506,
+                        291
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                82,
+                                505,
+                                96
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        82,
+                                        505,
+                                        96
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Angelina Wang, Thanard Kurutach, Kara Liu, Pieter Abbeel, and Aviv Tamar. Learning robotic",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                94,
+                                438,
+                                106
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        94,
+                                        438,
+                                        106
+                                    ],
+                                    "score": 1.0,
+                                    "content": "manipulation through visual planning and acting. CoRR, abs/1905.04411, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                104,
+                                505,
+                                117
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        104,
+                                        505,
+                                        117
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Manuel Watter, Jost Tobias Springenberg, Joschka Boedecker, and Martin A. Riedmiller. Em-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                115,
+                                505,
+                                128
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        115,
+                                        505,
+                                        128
+                                    ],
+                                    "score": 1.0,
+                                    "content": "bed to control: A locally linear latent dynamics model for control from raw images. CoRR,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                127,
+                                209,
+                                138
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        127,
+                                        209,
+                                        138
+                                    ],
+                                    "score": 1.0,
+                                    "content": "abs/1506.07365, 2015.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                138,
+                                505,
+                                149
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        138,
+                                        505,
+                                        149
+                                    ],
+                                    "score": 1.0,
+                                    "content": "W. J. Wilson, C. C. Williams Hulls, and G. S. Bell. Relative end-effector control using cartesian",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                149,
+                                480,
+                                160
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        149,
+                                        480,
+                                        160
+                                    ],
+                                    "score": 1.0,
+                                    "content": "position based visual servoing. IEEE Transactions on Robotics and Automation, Oct 1996.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                159,
+                                505,
+                                172
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        159,
+                                        505,
+                                        172
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Annie Xie, Frederik Ebert, Sergey Levine, and Chelsea Finn. Improvisation through physical un-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                170,
+                                493,
+                                183
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        170,
+                                        493,
+                                        183
+                                    ],
+                                    "score": 1.0,
+                                    "content": "derstanding: Using novel objects as tools with visual foresight. CoRR, abs/1904.05538, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                181,
+                                506,
+                                195
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        181,
+                                        506,
+                                        195
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Danfei Xu, Suraj Nair, Yuke Zhu, Julian Gao, Animesh Garg, Li Fei-Fei, and Silvio Savarese. Neural",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                191,
+                                505,
+                                205
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        191,
+                                        505,
+                                        205
+                                    ],
+                                    "score": 1.0,
+                                    "content": "task programming: Learning to generalize across hierarchical tasks. CoRR, abs/1710.01813,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                202,
+                                142,
+                                215
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        202,
+                                        142,
+                                        215
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2017.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                213,
+                                506,
+                                227
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        213,
+                                        506,
+                                        227
+                                    ],
+                                    "score": 1.0,
+                                    "content": "B. H. Yoshimi and P. K. Allen. Active, uncalibrated visual servoing. In Proceedings of the 1994",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                225,
+                                486,
+                                239
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        225,
+                                        486,
+                                        239
+                                    ],
+                                    "score": 1.0,
+                                    "content": "IEEE International Conference on Robotics and Automation, pp. 156–161 vol.1, May 1994.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                235,
+                                505,
+                                249
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        235,
+                                        505,
+                                        249
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Tianhe Yu, Gleb Shevchuk, Dorsa Sadigh, and Chelsea Finn. Unsupervised visuomotor control",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                246,
+                                407,
+                                259
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        246,
+                                        407,
+                                        259
+                                    ],
+                                    "score": 1.0,
+                                    "content": "through distributional planning networks. CoRR, abs/1902.05542, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                258,
+                                505,
+                                271
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        258,
+                                        505,
+                                        271
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Andy Zeng, Shuran Song, Stefan Welker, Johnny Lee, Alberto Rodriguez, and Thomas A.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                268,
+                                505,
+                                283
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        268,
+                                        505,
+                                        283
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Funkhouser. Learning synergies between pushing and grasping with self-supervised deep re-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                280,
+                                329,
+                                292
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        280,
+                                        329,
+                                        292
+                                    ],
+                                    "score": 1.0,
+                                    "content": "inforcement learning. CoRR, abs/1803.09956, 2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        }
+                    ],
+                    "index": 9
+                }
+            ],
+            "page_idx": 11,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        108,
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+                        293,
+                        37
+                    ],
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+                            ],
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+                            ]
+                        }
+                    ]
+                },
+                {
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+                        300,
+                        751,
+                        311,
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+                    ],
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+                        {
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+                                    "content": ". Additionally, the cost of a sequence of 5 actions is the cost of the",
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+                                    "score": 1.0,
+                                    "content": "in these experiments.",
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+                                    "type": "text"
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+                                    "content": "prediction (SV2P) (Babaeizadeh et al., 2017). See architecture below:",
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+                                            "content": "(taken from (Babaeizadeh et al., 2017) with permission). The architecture has two",
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+                                            "content": "main sub-networks, one convolutional network which approximates the distribution of latent values give all the",
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+                                    "content": "B EXPERIMENT DETAILS",
+                                    "type": "text"
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+                                    "content": "interaction. That is, for each action we sample uniformly in the delta",
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+                                    "score": 1.0,
+                                    "content": ". Additionally, the cost of a sequence of 5 actions is the cost of the",
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+                                    "cross_page": true
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+                                {
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+                                    "score": 1.0,
+                                    "content": ": The agent must both slide the",
+                                    "type": "text",
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+                                    "score": 1.0,
+                                    "content": "door closed from a random position, as well as push a block off of the table. This requires both",
+                                    "type": "text",
+                                    "cross_page": true
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+                            ],
+                            "index": 5
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+                        {
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+                            "spans": [
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+                                    "bbox": [
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+                                        506,
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+                                    "score": 1.0,
+                                    "content": "grasping and sliding the door from the previous task, as well as positioning the end effector behind",
+                                    "type": "text",
+                                    "cross_page": true
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+                            ],
+                            "index": 6
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+                                    "cross_page": true
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+                                    "type": "inline_equation",
+                                    "cross_page": true
+                                }
+                            ],
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+                                    "score": 1.0,
+                                    "content": "Block: A combination of the 2 Block and Door",
+                                    "type": "text",
+                                    "cross_page": true
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+                                    "score": 0.72,
+                                    "content": "^ +",
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+                                    "cross_page": true
+                                },
+                                {
+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "Block task. The agent must close the door and",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 8
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+                        {
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "slide both blocks off the table within 100 timesteps.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
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+                    ],
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+                            ],
+                            "index": 4
+                        },
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+                                    "type": "text"
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+                                    "type": "inline_equation"
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+                                    "type": "text"
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+                                    "score": 1.0,
+                                    "content": "Block task. The agent must close the door and",
+                                    "type": "text"
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+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
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+                                    ],
+                                    "score": 1.0,
+                                    "content": "slide both blocks off the table within 100 timesteps.",
+                                    "type": "text"
+                                }
+                            ],
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+                    ],
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+                {
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+                                    "content": "Data Collection: For the simulated desk manipulation environment data is again collected through",
+                                    "type": "text"
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+                            ],
+                            "index": 10
+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "random policy interaction. That is, for each action we sample uniformly in the delta",
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+                                },
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+                                    "content": "action",
+                                    "type": "text"
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+                                    "score": 1.0,
+                                    "content": "space of the robot end effector. We collect 10000 episodes, each with random initialization of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
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+                                    "content": "the desk door/drawer and blocks. Each episode contains 100 transitions. The images are of size",
+                                    "type": "text"
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+                                    "content": "6 4 \\mathrm { x } 6 4 \\mathrm { x } 3",
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+                                    "content": "C ( s _ { i } , s _ { j } )",
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+                                    "score": 0.87,
+                                    "content": "\\ell _ { 2 }",
+                                    "type": "inline_equation"
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+                                    "content": "pixel dis-",
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+                                    "score": 1.0,
+                                    "content": "tance between the images, that is",
+                                    "type": "text"
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+                                {
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+                                    "score": 0.91,
+                                    "content": "| | s _ { i } - s _ { j } | | _ { 2 } ^ { 2 }",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 16
+                        }
+                    ],
+                    "index": 15.5
+                },
+                {
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+                                }
+                            ],
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+                        {
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+                                    "score": 0.89,
+                                    "content": "H = 1 5",
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+                                    "score": 1.0,
+                                    "content": ", which actually consists of 5 actions, each repeated 3 times. Addi-",
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+                                    "type": "inline_equation"
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+                                {
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+                                    "type": "text"
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+                                    "score": 0.83,
+                                    "content": "C",
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+                                    "score": 1.0,
+                                    "content": "of the last frame only. Note",
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+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "this is distinct from the maze environment. Lastly, we use",
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+                                    "score": 0.89,
+                                    "content": "T = 5 0",
+                                    "type": "inline_equation"
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+                                {
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+                                    "score": 1.0,
+                                    "content": "or 100 and",
+                                    "type": "text"
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+                                {
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+                                    "score": 0.9,
+                                    "content": "T ^ { * } = 2 0",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "in these",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "experiments, depending on the task.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        }
+                    ],
+                    "index": 19
+                },
+                {
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+                                    "content": "This supports the idea that simply using longer",
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+                                    "score": 1.0,
+                                    "content": "to doing long-horizon tasks. Further, we find",
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diff --git a/parse/train/H1gzR2VKDH/H1gzR2VKDH_model.json b/parse/train/H1gzR2VKDH/H1gzR2VKDH_model.json
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index 0000000000000000000000000000000000000000..fe1df854dd35dff6ef181b302ec81fdea84e5a4c
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diff --git a/parse/train/O9bnihsFfXU/O9bnihsFfXU_middle.json b/parse/train/O9bnihsFfXU/O9bnihsFfXU_middle.json
new file mode 100644
index 0000000000000000000000000000000000000000..89d1207962fe9b382f491b1fc92c6741d4c5c100
--- /dev/null
+++ b/parse/train/O9bnihsFfXU/O9bnihsFfXU_middle.json
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+                                    "score": 1.0,
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+                                    "score": 1.0,
+                                    "content": "collected, referred to as offline RL (Lange et al., 2012; Agarwal et al., 2020; Levine et al., 2020),",
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+                                    "score": 1.0,
+                                    "content": "methods, including Q-learning (Mnih et al., 2015; Hessel et al., 2018) and actor-critic (Haarnoja",
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+                                    "content": "et al., 2018), as well as neural fitted-Q iteration (Riedmiller, 2005; Ernst et al., 2005). To isolate the",
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+                                    "content": "issue, we study the effective rank of the features in the penultimate layer of the value network (Sec-",
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+                                    "score": 1.0,
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+                                    "content": "deep neural networks, are trained with gradient descent using iterated regression",
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+                                    "score": 1.0,
+                                    "content": "acterize this loss of expressivity via a drop in the rank of the learned value net-",
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+                                    "content": "work features, and show that this typically corresponds to a performance drop.",
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+                                    "content": "We demonstrate this phenomenon on Atari and Gym benchmarks, in both offline",
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+                                    "score": 1.0,
+                                    "content": "and online RL settings. We formally analyze this phenomenon and show that it",
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+                                    "score": 1.0,
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+                                    "content": "controlling rank collapse can improve performance.",
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+                                    "content": "1 INTRODUCTION",
+                                    "type": "text"
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+                                    "score": 1.0,
+                                    "content": "2017), these algorithms are highly unreliable due to poorly understood optimization issues. Al-",
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+                                    "score": 1.0,
+                                    "content": "though a number of hypotheses have been proposed to explain these issues (Achiam et al., 2019;",
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+                                    "content": "Bengio et al., 2020; Fu et al., 2019; Igl et al., 2020; Liu et al., 2018; Kumar et al., 2020a), a com-",
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+                                    "score": 1.0,
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+                                    "score": 1.0,
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+                                    "content": "Gunasekar et al., 2017; Arora et al.,",
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+                                    "score": 1.0,
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+                                    "score": 1.0,
+                                    "content": "ing. This over-aliasing causes an otherwise expressive value network to implicitly behave as an",
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+                                    "type": "text"
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+                                    "score": 1.0,
+                                    "content": "causes the problem to emerge more frequently. In the extreme case when no additional data is",
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+                                    "score": 1.0,
+                                    "content": "collected, referred to as offline RL (Lange et al., 2012; Agarwal et al., 2020; Levine et al., 2020),",
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+                                    "score": 1.0,
+                                    "content": "We demonstrate the existence of implicit under-parameterization in common value-based deep RL",
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+                                    "score": 1.0,
+                                    "content": "methods, including Q-learning (Mnih et al., 2015; Hessel et al., 2018) and actor-critic (Haarnoja",
+                                    "type": "text"
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+                            "index": 40
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+                                    "score": 1.0,
+                                    "content": "et al., 2018), as well as neural fitted-Q iteration (Riedmiller, 2005; Ernst et al., 2005). To isolate the",
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+                                    "score": 1.0,
+                                    "content": "issue, we study the effective rank of the features in the penultimate layer of the value network (Sec-",
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+                                    "score": 1.0,
+                                    "content": "tion 3). We observe that after an initial learning period, the rank of the learned features drops steeply.",
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+                                    "score": 1.0,
+                                    "content": "As the rank decreases, the ability of the features to fit subsequent target values and the optimal value",
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+                                    "score": 1.0,
+                                    "content": ", which can be written in vector",
+                                    "type": "text"
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+                        {
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+                                    "score": 0.9,
+                                    "content": "\\mathbf { Q } ^ { \\pi } = \\mathbf { R } + \\gamma P ^ { \\pi } \\mathbf { Q } ^ { \\pi }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": ". The optimal Q-function,",
+                                    "type": "text"
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+                                {
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+                                    "score": 0.9,
+                                    "content": "Q ^ { * } ( \\mathbf { s } , \\mathbf { a } )",
+                                    "type": "inline_equation"
+                                },
+                                {
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+                                    "score": 1.0,
+                                    "content": ", is the fixed point of the Bellman",
+                                    "type": "text"
+                                }
+                            ],
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+                        {
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+                                    "score": 0.83,
+                                    "content": "\\begin{array} { r } { \\mathcal { T } : \\mathcal { T } Q ( \\mathbf { s } , \\mathbf { a } ) : = R ( \\mathbf { s } , \\mathbf { a } ) + \\gamma \\mathbb { E } _ { \\mathbf { s } ^ { \\prime } \\sim P ( \\cdot | \\mathbf { s } , \\mathbf { a } ) } \\left[ \\operatorname* { m a x } _ { \\mathbf { a } ^ { \\prime } } Q ( \\mathbf { s } ^ { \\prime } , \\mathbf { a } ^ { \\prime } ) \\right] . } \\end{array}",
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+                                    "type": "text"
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+                            ],
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+                        }
+                    ],
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+                },
+                {
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+                                    "score": 1.0,
+                                    "content": "Practical Q-learning methods (e.g., Mnih et al., 2015; Hessel et al., 2018; Haarnoja et al., 2018)",
+                                    "type": "text"
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+                            "index": 32
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+                        {
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+                                    "score": 1.0,
+                                    "content": "via gradient descent. This objective, known as mean-squared temporal difference (TD) error, is",
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+                        {
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+                                    "content": "\\begin{array} { r } { L ( \\theta ) = \\sum _ { \\mathbf { s } , \\mathbf { a } } \\left( R ( \\mathbf { s } , \\mathbf { a } ) + \\gamma \\bar { Q } _ { \\theta } ( \\mathbf { s } ^ { \\prime } , \\mathbf { a } ^ { \\prime } ) - Q ( \\mathbf { s } , \\mathbf { a } ) \\right) ^ { 2 } } \\end{array}",
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+                                },
+                                {
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+                                    "score": 1.0,
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+                                {
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+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "is a delayed copy of the",
+                                    "type": "text"
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+                            ],
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+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "Q-function, typically referred to as the target network. These methods train Q-networks via gradient",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
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+                            "spans": [
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+                                    "score": 1.0,
+                                    "content": "descent and slowly update the target network via Polyak averaging on its parameters. We refer the",
+                                    "type": "text"
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+                            ],
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+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "output of the penultimate layer of the deep Q-network as the learned feature matrix",
+                                    "type": "text"
+                                },
+                                {
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+                                    "score": 0.79,
+                                    "content": "\\Phi",
+                                    "type": "inline_equation"
+                                },
+                                {
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+                                    "score": 1.0,
+                                    "content": ", such that",
+                                    "type": "text"
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+                            ],
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+                        }
+                    ],
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+                },
+                {
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+                                    "score": 0.93,
+                                    "content": "Q ( \\mathbf { s } , \\mathbf { a } ) = \\mathbf { w } ^ { T } \\Phi ( \\mathbf { s } , \\mathbf { a } )",
+                                    "type": "inline_equation"
+                                },
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+                                    "content": "\\mathbf { w } \\in \\mathbb { R } ^ { d }",
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+                                    "content": "\\mathbf { \\bar { \\Phi } } \\in \\mathbb { R } ^ { | \\cal { S } | | \\cal { A } | \\times d }",
+                                    "type": "inline_equation"
+                                }
+                            ],
+                            "index": 39
+                        }
+                    ],
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+                },
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+                    "lines": [
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+                                    "score": 1.0,
+                                    "content": "For simplicity of analysis, we abstract deep Q-learning",
+                                    "type": "text"
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+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "methods into a generic fitted Q-iteration (FQI) frame-",
+                                    "type": "text"
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+                        },
+                        {
+                            "bbox": [
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+                                    "score": 1.0,
+                                    "content": "work (Ernst et al., 2005). We refer to FQI with neural",
+                                    "type": "text"
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+                            ],
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+                        },
+                        {
+                            "bbox": [
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+                                    "score": 1.0,
+                                    "content": "nets as neural FQI (Riedmiller, 2005). In the",
+                                    "type": "text"
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+                                {
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+                                    "score": 0.81,
+                                    "content": "k",
+                                    "type": "inline_equation"
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+                                {
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+                                    "score": 1.0,
+                                    "content": "-th fitting",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        },
+                        {
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+                                    ],
+                                    "score": 1.0,
+                                    "content": "iteration, FQI trains the Q-function,",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "score": 0.88,
+                                    "content": "\\mathbf { Q } _ { k }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": ", to match the tar-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        },
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
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+                                    "bbox": [
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+                                        687,
+                                        150,
+                                        700
+                                    ],
+                                    "score": 1.0,
+                                    "content": "get values,",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
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+                                        699
+                                    ],
+                                    "score": 0.92,
+                                    "content": "\\mathbf { y } _ { k } = \\mathbf { R } + \\gamma P ^ { \\pi } \\mathbf { Q } _ { k - 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
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+                                        336,
+                                        700
+                                    ],
+                                    "score": 1.0,
+                                    "content": "generated using previous",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 45
+                        },
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
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+                                    ],
+                                    "score": 1.0,
+                                    "content": "Q-function,",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
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+                                        711
+                                    ],
+                                    "score": 0.88,
+                                    "content": "\\mathbf { Q } _ { k - 1 }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "score": 1.0,
+                                    "content": "(Algorithm 1). Practical methods can",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 46
+                        },
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
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+                                    "bbox": [
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+                                    ],
+                                    "score": 1.0,
+                                    "content": "be instantiated as variants of FQI, with different target",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 47
+                        },
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "score": 1.0,
+                                    "content": "update styles, different optimizers, etc.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 48
+                        }
+                    ],
+                    "index": 44
+                },
+                {
+                    "type": "title",
+                    "bbox": [
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+                    ],
+                    "lines": [
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+                                    ],
+                                    "score": 1.0,
+                                    "content": "Algorithm 1 Fitted Q-Iteration (FQI)",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 49
+                        }
+                    ],
+                    "index": 49
+                },
+                {
+                    "type": "text",
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+                    ],
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+                                    "content": "1: Initialize Q-network",
+                                    "type": "text"
+                                },
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+                                    "content": "\\mathbf { Q } _ { \\theta }",
+                                    "type": "inline_equation"
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+                                    "content": ", buffer",
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+                                    "score": 0.77,
+                                    "content": "\\mu",
+                                    "type": "inline_equation"
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+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 50
+                        },
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+                                    "content": "2: for fitting iteration",
+                                    "type": "text"
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+                                    "content": "k",
+                                    "type": "inline_equation"
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+                                    "score": 1.0,
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+                                    "type": "inline_equation"
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+                                    "score": 1.0,
+                                    "content": "(Algorithm 1). Practical methods can",
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+                                    "score": 1.0,
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+                                    "type": "text"
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+                                    "score": 1.0,
+                                    "content": ", that occurs implicitly as a by-product of learning deep neural network",
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+                                    "score": 1.0,
+                                    "content": "While rank decrease also occurs in supervised learning, it is usually beneficial for obtaining gener-",
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+                                    "score": 1.0,
+                                    "content": "alizable solutions (Gunasekar et al., 2017; Arora et al., 2019). However, we will show that in deep",
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+                                    "content": "Q-learning, an interaction between bootstrapping and gradient descent can lead to more aggressive",
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+                                    "score": 1.0,
+                                    "content": "rank reduction (or rank collapse), which can hurt performance.",
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+                                    "score": 1.0,
+                                    "content": "Experimental setup. To study implicit under-parameterization empirically, we compute srank",
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+                                    "score": 1.0,
+                                    "content": "on a minibatch of state-action pairs sampled i.i.d. from the training data (i.e., the dataset in the offline",
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+                                    "score": 1.0,
+                                    "content": "setting, and the replay buffer in the online setting). We investigate offline and online RL settings on",
+                                    "type": "text"
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+                            ],
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+                                    "score": 1.0,
+                                    "content": "values. When the network maps different states to orthogonal feature vectors, then",
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+                                    "score": 1.0,
+                                    "content": "takes on a small value.",
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+                                    "content": "Definition 1. Implicit under-parameterization refers to a reduction in the effective rank of the fea-",
+                                    "type": "text"
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+                                    "score": 1.0,
+                                    "content": ", that occurs implicitly as a by-product of learning deep neural network",
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+                                    "score": 1.0,
+                                    "content": "-functions.",
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+                    ],
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+                                    "score": 1.0,
+                                    "content": "While rank decrease also occurs in supervised learning, it is usually beneficial for obtaining gener-",
+                                    "type": "text"
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+                        {
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+                                    "score": 1.0,
+                                    "content": "alizable solutions (Gunasekar et al., 2017; Arora et al., 2019). However, we will show that in deep",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "Q-learning, an interaction between bootstrapping and gradient descent can lead to more aggressive",
+                                    "type": "text"
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+                            ],
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+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "rank reduction (or rank collapse), which can hurt performance.",
+                                    "type": "text"
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+                                    "score": 1.0,
+                                    "content": "Experimental setup. To study implicit under-parameterization empirically, we compute srank",
+                                    "type": "text"
+                                },
+                                {
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+                        {
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "on a minibatch of state-action pairs sampled i.i.d. from the training data (i.e., the dataset in the offline",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
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+                                        106,
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+                                    "score": 1.0,
+                                    "content": "setting, and the replay buffer in the online setting). We investigate offline and online RL settings on",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "benchmarks including Atari games (Bellemare et al., 2013) and Gym environments (Brockman et al.,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
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+                                    "bbox": [
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+                                    ],
+                                    "score": 1.0,
+                                    "content": "2016). We also utilize gridworlds described by Fu et al. (2019) to compare the learned Q-function",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
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+                            ],
+                            "spans": [
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+                                    ],
+                                    "score": 1.0,
+                                    "content": "against the oracle solution computed using tabular value iteration. We evaluate DQN (Mnih et al.,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "2015) on gridworld and Atari and SAC (Haarnoja et al., 2018) on Gym domains.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        }
+                    ],
+                    "index": 28,
+                    "bbox_fs": [
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+                    "lines": [
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+                                    "bbox": [
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+                                    ],
+                                    "score": 1.0,
+                                    "content": "Data-efficient offline RL. In offline RL, our goal is to learn effective policies by performing Q-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "learning on a fixed dataset of transitions. We investigate the presence of rank collapse when deep",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "Q-learning is used with broad state coverage offline datasets from Agarwal et al. (2020). In the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "top row of Figure 2, we show that after an initial learning period,",
+                                    "type": "text"
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+                                    "score": 0.57,
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+                                    "type": "inline_equation"
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+                                    "content": "dataset, which often affects the performance of Q-learning methods, we also study CQL (Kumar",
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+                                    "score": 1.0,
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+                                    "score": 1.0,
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+                                            "score": 1.0,
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+                                            "score": 1.0,
+                                            "content": "and SAC on Gym domains in the online RL setting, with varying numbers of gradient steps per environment",
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+                                    "score": 1.0,
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+                                    "score": 1.0,
+                                    "content": "results in higher levels of rank collapse as well as",
+                                    "type": "text"
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+                                    "score": 1.0,
+                                    "content": "performance degradation. In the top row of Figure 3, we show that larger values of",
+                                    "type": "text"
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+                                    "score": 1.0,
+                                    "content": "lead to a",
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+                                    "score": 1.0,
+                                    "content": "more aggressive drop in srank",
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+                                    "score": 0.52,
+                                    "content": "\\delta \\left( \\Phi \\right)",
+                                    "type": "inline_equation"
+                                },
+                                {
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+                                    "score": 1.0,
+                                    "content": "(red vs. blue/orange lines), and that rank continues to decrease",
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+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
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+                            "spans": [
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "with more training. Furthermore, the bottom row illustrates that larger values of",
+                                    "type": "text"
+                                },
+                                {
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+                                    "score": 1.0,
+                                    "content": "result in worse",
+                                    "type": "text"
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+                            ],
+                            "index": 23
+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "performance, corroborating Fu et al. (2019); Fedus et al. (2020b). We find similar results with the",
+                                    "type": "text"
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+                            "index": 24
+                        },
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+                                    "score": 1.0,
+                                    "content": "Rainbow algorithm (Hessel et al., 2018) (Appendix A.2). As in the offline setting, directly regressing",
+                                    "type": "text"
+                                }
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+                                    "score": 1.0,
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+                                    "score": 0.89,
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+                                    "type": "inline_equation"
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+                                {
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+                                    "score": 1.0,
+                                    "content": "via supervised learning does not cause rank collapse (black line in Figure 3).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
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+                    ],
+                    "index": 21.5
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+                                    "content": "3.1 UNDERSTANDING IMPLICIT UNDER-PARAMETERIZATION AND ITS IMPLICATIONS",
+                                    "type": "text"
+                                }
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+                    ],
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+                        {
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+                                    "score": 1.0,
+                                    "content": "decreases, so does the network’s ability to fit the",
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+                                    "score": 1.0,
+                                    "content": "subsequent target values, and eventually results in inability to fit",
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+                                    "score": 1.0,
+                                    "content": ". In the gridworld domain, we",
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+                                    "score": 1.0,
+                                    "content": "measure this loss of expressivity by measuring the error in fitting oracle-computed",
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+                                    "score": 1.0,
+                                    "content": "values via a",
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+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
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+                                    "score": 1.0,
+                                    "content": "linear transformation of",
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+                                    "score": 1.0,
+                                    "content": ". When rank collapse occurs, the error in fitting",
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+                                    "score": 1.0,
+                                    "content": "steadily increases dur-",
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+                                    "score": 1.0,
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+                                    "score": 1.0,
+                                    "content": "at all by the end of training (Fig-",
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+                                    "score": 1.0,
+                                    "content": "ure 4a) – this entails a drop in performance. In Atari domains, we do not have access to",
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+                                    "score": 1.0,
+                                    "content": ", and so",
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+                            "index": 35
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+                                    "score": 1.0,
+                                    "content": "we instead measure TD error, that is, the error in fitting the target value estimates,",
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+                                    "content": "\\mathbf { R } + \\gamma P ^ { \\pi } \\mathbf { Q } _ { k }",
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+                                    "content": ". In",
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+                            "index": 36
+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "SEAQUEST, as rank decreases, the TD error increases (Figure 4b) and the value function is unable to",
+                                    "type": "text"
+                                }
+                            ],
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+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "fit the target values, culminating in a performance plateau (Figure 3). This observation is consistent",
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+                            ],
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+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "across other environments; we present further supporting evidence in Appendix A.4.",
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+                            ],
+                            "index": 39
+                        }
+                    ],
+                    "index": 33.5
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+                                    "content": "Does bootstrapping cause implicit under-parameterization? We perform a number of controlled",
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+                                    "score": 1.0,
+                                    "content": "and bootstrapping. We first remove confounding issues of poor network initialization (Fedus et al.,",
+                                    "type": "text"
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+                            ],
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+                                    "score": 1.0,
+                                    "content": "2020a) and non-stationarity (Igl et al., 2020) by showing that rank collapse occurs even when the",
+                                    "type": "text"
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+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "Q-network is re-initialized from scratch at the start of each fitting iteration (Figure 4c). To show that",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        }
+                    ],
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+                }
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+                                    "score": 1.0,
+                                    "content": "to utilize the replay data more effectively.",
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+                        {
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+                                    "score": 1.0,
+                                    "content": "However, we find that using larger values of",
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+                                    "score": 1.0,
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+                                    "score": 1.0,
+                                    "content": "performance degradation. In the top row of Figure 3, we show that larger values of",
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+                                    "score": 1.0,
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+                                    "score": 0.52,
+                                    "content": "\\delta \\left( \\Phi \\right)",
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+                                    "score": 1.0,
+                                    "content": "(red vs. blue/orange lines), and that rank continues to decrease",
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+                            "index": 22
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+                        {
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+                                    "score": 1.0,
+                                    "content": "with more training. Furthermore, the bottom row illustrates that larger values of",
+                                    "type": "text"
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+                                {
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+                                    "score": 1.0,
+                                    "content": "result in worse",
+                                    "type": "text"
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+                            "index": 23
+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "performance, corroborating Fu et al. (2019); Fedus et al. (2020b). We find similar results with the",
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+                            "index": 24
+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "Rainbow algorithm (Hessel et al., 2018) (Appendix A.2). As in the offline setting, directly regressing",
+                                    "type": "text"
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+                            "index": 25
+                        },
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+                                    "content": "Q ^ { * }",
+                                    "type": "inline_equation"
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+                                    "score": 1.0,
+                                    "content": "via supervised learning does not cause rank collapse (black line in Figure 3).",
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+                    ],
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+                                    "content": "3.1 UNDERSTANDING IMPLICIT UNDER-PARAMETERIZATION AND ITS IMPLICATIONS",
+                                    "type": "text"
+                                }
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+                    ],
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+                                    "score": 1.0,
+                                    "content": "ence of rank collapse in data-efficient RL, we now discuss how it can adversely affect performance.",
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+                        {
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+                                    "score": 1.0,
+                                    "content": "As the effective rank of the network features",
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+                                    "type": "inline_equation"
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+                                    "score": 1.0,
+                                    "content": "decreases, so does the network’s ability to fit the",
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+                                    "score": 1.0,
+                                    "content": "subsequent target values, and eventually results in inability to fit",
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+                                    "content": ". In the gridworld domain, we",
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+                                    "score": 1.0,
+                                    "content": "ing training, and the consequent network is not able to predict",
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+                                    "score": 1.0,
+                                    "content": "at all by the end of training (Fig-",
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+                                    "score": 1.0,
+                                    "content": "ure 4a) – this entails a drop in performance. In Atari domains, we do not have access to",
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+                                    "score": 1.0,
+                                    "content": "we instead measure TD error, that is, the error in fitting the target value estimates,",
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+                                    "score": 1.0,
+                                    "content": "SEAQUEST, as rank decreases, the TD error increases (Figure 4b) and the value function is unable to",
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+                                    "score": 1.0,
+                                    "content": "fit the target values, culminating in a performance plateau (Figure 3). This observation is consistent",
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+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "across other environments; we present further supporting evidence in Appendix A.4.",
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+                    ],
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+                                    "score": 1.0,
+                                    "content": "and bootstrapping. We first remove confounding issues of poor network initialization (Fedus et al.,",
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+                        {
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+                                    "score": 1.0,
+                                    "content": "2020a) and non-stationarity (Igl et al., 2020) by showing that rank collapse occurs even when the",
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+                                    "score": 1.0,
+                                    "content": "Q-network is re-initialized from scratch at the start of each fitting iteration (Figure 4c). To show that",
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+                                    "score": 1.0,
+                                    "content": "the problem is not isolated to the control setting, we show evidence of rank collapse in the policy",
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+                                    "score": 1.0,
+                                    "content": "evaluation setting as well. We trained a value network using fitted",
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+                                    "content": "-evaluation for a fixed policy",
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+                                    "score": 1.0,
+                                    "content": "(i.e., using the Bellman operator",
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+                                    "cross_page": true
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+                                    "score": 1.0,
+                                    "content": "instead of",
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+                                    "cross_page": true
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+                                    "score": 1.0,
+                                    "content": "), and found that rank drop still occurs (FQE in",
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+                        {
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+                                    "score": 1.0,
+                                    "content": "Figure 4d). Finally, we show that by removing bootstrapped updates and instead regressing directly",
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+                                    "content": "Figure 4d). These results, along with similar findings on other Atari environments (Appendix A.3),",
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+                                            "content": "for SEAQUEST in Figure 3 (middle). TD error increases with rank degradation. (c) Q-network",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 5
+                                },
+                                {
+                                    "bbox": [
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+                                    "spans": [
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+                                            "bbox": [
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+                                            "score": 1.0,
+                                            "content": "re-initialization in each fitting iteration on gridworld. (d) Trend of srank",
+                                            "type": "text"
+                                        },
+                                        {
+                                            "bbox": [
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+                                            "score": 0.66,
+                                            "content": "\\delta \\left( \\Phi \\right)",
+                                            "type": "inline_equation"
+                                        },
+                                        {
+                                            "bbox": [
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+                                            "score": 1.0,
+                                            "content": "for policy evaluation based on",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 6
+                                },
+                                {
+                                    "bbox": [
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+                                            "bbox": [
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+                                            "score": 1.0,
+                                            "content": "bootstrapped updates (FQE) vs Monte-Carlo returns (no bootstrapping). Note that rank-collapse still persists",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 7
+                                },
+                                {
+                                    "bbox": [
+                                        105,
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+                                    "spans": [
+                                        {
+                                            "bbox": [
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+                                            "score": 1.0,
+                                            "content": "with reinitialization and FQE, but goes away in the absence of bootstrapping.",
+                                            "type": "text"
+                                        }
+                                    ],
+                                    "index": 8
+                                }
+                            ],
+                            "index": 5.5
+                        }
+                    ],
+                    "index": 3.25
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+                {
+                    "type": "text",
+                    "bbox": [
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+                    "lines": [
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+                                    "score": 1.0,
+                                    "content": "the problem is not isolated to the control setting, we show evidence of rank collapse in the policy",
+                                    "type": "text"
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+                                    "score": 1.0,
+                                    "content": "evaluation setting as well. We trained a value network using fitted",
+                                    "type": "text"
+                                },
+                                {
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+                                    "score": 0.27,
+                                    "content": "\\mathbf { Q }",
+                                    "type": "inline_equation"
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+                                {
+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "-evaluation for a fixed policy",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
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+                                    "type": "inline_equation"
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+                                {
+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "(i.e., using the Bellman operator",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "score": 0.87,
+                                    "content": "\\mathcal { T } ^ { \\pi }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "instead of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "score": 0.74,
+                                    "content": "\\tau _ { \\cdot }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "score": 1.0,
+                                    "content": "), and found that rank drop still occurs (FQE in",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "Figure 4d). Finally, we show that by removing bootstrapped updates and instead regressing directly",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
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+                                302
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
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+                                        505,
+                                        302
+                                    ],
+                                    "score": 1.0,
+                                    "content": "to Monte-Carlo (MC) estimates of the value, the effective rank does not collapse (MC Returns in",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        301,
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+                                        313
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+                                    "score": 1.0,
+                                    "content": "Figure 4d). These results, along with similar findings on other Atari environments (Appendix A.3),",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                106,
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+                                465,
+                                324
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "score": 1.0,
+                                    "content": "our analysis indicates that bootstrapping is at the core of implicit under-parameterization.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        }
+                    ],
+                    "index": 12
+                },
+                {
+                    "type": "title",
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+                    ],
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+                                    "score": 1.0,
+                                    "content": "4 THEORETICAL ANALYSIS OF IMPLICIT UNDER-PARAMETERIZATION",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        }
+                    ],
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+                },
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+                    "type": "text",
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+                    ],
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+                                    "score": 1.0,
+                                    "content": "In this section, we formally analyze implicit under-parameterization and prove that training neural",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "networks with bootstrapping reduces the effective rank of the Q-network, corroborating the empiri-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "cal observations in the previous section. We focus on policy evaluation (Figure 4d and Figure A.9),",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "where we aim to learn a Q-function that satisfies",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
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+                                    "score": 0.93,
+                                    "content": "{ \\bf Q } = { \\bf R } + \\gamma P ^ { \\pi } { \\bf Q }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "for a fixed",
+                                    "type": "text"
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+                                    "score": 0.75,
+                                    "content": "\\pi",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": ", for ease of analysis.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
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+                            ],
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "We also presume a fixed dataset of transitions,",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
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+                                    "score": 0.81,
+                                    "content": "\\mathcal { D }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
+                                        303,
+                                        392,
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+                                        403
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+                                    "score": 1.0,
+                                    "content": ", to learn the Q-function.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        }
+                    ],
+                    "index": 19
+                },
+                {
+                    "type": "title",
+                    "bbox": [
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+                    ],
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+                            "bbox": [
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+                                    "score": 1.0,
+                                    "content": "4.1 ANALYSIS VIA KERNEL REGRESSION",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        }
+                    ],
+                    "index": 22
+                },
+                {
+                    "type": "text",
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+                    ],
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "We first study bootstrapping with neural networks through a mathematical abstraction that treats the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
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+                            "spans": [
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "Q-network as a kernel machine, following the neural tangent kernel (NTK) formalism (Jacot et al.,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
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+                                    "bbox": [
+                                        106,
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+                                    "score": 1.0,
+                                    "content": "2018). Building on prior analysis of self-distillation (Mobahi et al., 2020), we assume that each",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
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+                                    "bbox": [
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+                                    ],
+                                    "score": 1.0,
+                                    "content": "iteration of bootstrapping, the Q-function optimizes the squared TD error to target labels",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "score": 0.87,
+                                    "content": "\\mathbf { y } _ { k }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "score": 1.0,
+                                    "content": "with a",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
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+                            "spans": [
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+                                    "bbox": [
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+                                    ],
+                                    "score": 1.0,
+                                    "content": "kernel regularizer. This regularizer captures the inductive bias from gradient-based optimization of",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
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+                            "spans": [
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "TD error and resembles the regularization imposed by gradient descent under NTK (Mobahi et al.,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
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+                                    "bbox": [
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+                                    ],
+                                    "score": 1.0,
+                                    "content": "2020). The error is computed on",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
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+                                    "score": 0.92,
+                                    "content": "( \\mathbf { s } _ { i } , \\mathbf { a } _ { i } ) \\in \\mathcal { D }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "whereas the regularization imposed by a universal",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
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+                            "spans": [
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+                                    "score": 1.0,
+                                    "content": "kernel",
+                                    "type": "text"
+                                },
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+                                    "score": 0.73,
+                                    "content": "u",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
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+                                        230,
+                                        512
+                                    ],
+                                    "score": 1.0,
+                                    "content": "with a coefficient of",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
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+                                        501,
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+                                        511
+                                    ],
+                                    "score": 0.91,
+                                    "content": "c \\geq 0",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "score": 1.0,
+                                    "content": "is applied to the Q-values at all state-action pairs as shown",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
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+                                    ],
+                                    "score": 1.0,
+                                    "content": "in Equation 1. We consider a setting",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "score": 0.89,
+                                    "content": "c > 0",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "score": 1.0,
+                                    "content": "for all rounds of bootstrapping, which corresponds to",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "score": 1.0,
+                                    "content": "the solution obtained by performing gradient descent on TD error for a small number of iterations",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "score": 1.0,
+                                    "content": "with early stopping in each round (Suggala et al., 2018) and thus, resembles how the updates in",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "score": 1.0,
+                                    "content": "Algorithm 1 are typically implemented in practice.",
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+                                            "content": "bootstrapped updates (FQE) vs Monte-Carlo returns (no bootstrapping). Note that rank-collapse still persists",
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+                                    "content": "4 THEORETICAL ANALYSIS OF IMPLICIT UNDER-PARAMETERIZATION",
+                                    "type": "text"
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+                                    "score": 1.0,
+                                    "content": "networks with bootstrapping reduces the effective rank of the Q-network, corroborating the empiri-",
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+                                    "score": 1.0,
+                                    "content": "cal observations in the previous section. We focus on policy evaluation (Figure 4d and Figure A.9),",
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+                                    "score": 1.0,
+                                    "content": "where we aim to learn a Q-function that satisfies",
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+                                    "content": "{ \\bf Q } = { \\bf R } + \\gamma P ^ { \\pi } { \\bf Q }",
+                                    "type": "inline_equation"
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+                                    "content": "We also presume a fixed dataset of transitions,",
+                                    "type": "text"
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+                                    "content": "\\mathcal { D }",
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+                                    "content": ", to learn the Q-function.",
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+                                    "content": "4.1 ANALYSIS VIA KERNEL REGRESSION",
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+                                    "content": "We first study bootstrapping with neural networks through a mathematical abstraction that treats the",
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+                                    "content": "Q-network as a kernel machine, following the neural tangent kernel (NTK) formalism (Jacot et al.,",
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+                                    "score": 1.0,
+                                    "content": "2018). Building on prior analysis of self-distillation (Mobahi et al., 2020), we assume that each",
+                                    "type": "text"
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+                        },
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+                                    "content": "iteration of bootstrapping, the Q-function optimizes the squared TD error to target labels",
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+                                    "content": "kernel regularizer. This regularizer captures the inductive bias from gradient-based optimization of",
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+                                    "score": 1.0,
+                                    "content": "2020). The error is computed on",
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+                                    "content": "( \\mathbf { s } _ { i } , \\mathbf { a } _ { i } ) \\in \\mathcal { D }",
+                                    "type": "inline_equation"
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+                                    "score": 1.0,
+                                    "content": "whereas the regularization imposed by a universal",
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+                                    "score": 1.0,
+                                    "content": "is applied to the Q-values at all state-action pairs as shown",
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+                                    "score": 1.0,
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+                                    "score": 1.0,
+                                    "content": "with early stopping in each round (Suggala et al., 2018) and thus, resembles how the updates in",
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+                                    "content": "Algorithm 1 are typically implemented in practice.",
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+                                    "content": "( \\mathbf { s } , \\mathbf { a } )",
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+                                    "content": "(Mobahi et al., 2020, Proposition 1). A detailed proof is",
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+                                    "content": "in Appendix C. When combined with the fitted Q-iteration recursion, setting labels",
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+                                    "content": "{ \\bf y } _ { k } = { \\bf R } + { \\bf \\Delta }",
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+                                    "content": ", we recover a recurrence that relates subsequent value function iterates",
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+                                    "content": "\\mathbf { Q } _ { k + 1 } = \\mathbf { G } ( c \\mathbf { I } + \\mathbf { G } ) ^ { - 1 } \\mathbf { y } _ { k } = \\underbrace { \\mathbf { G } ( c \\mathbf { I } + \\mathbf { G } ) ^ { - 1 } } _ { \\mathbf { A } } [ \\mathbf { R } + \\gamma P ^ { \\pi } \\mathbf { Q } _ { k } ] = \\mathbf { A } \\left( \\sum _ { i = 1 } ^ { k } \\gamma ^ { k - i } \\left( P ^ { \\pi } \\mathbf { A } \\right) ^ { k - i } \\right) \\mathbf { R } : = \\mathbf { A } \\mathbf { M } _ { k } \\mathbf { R } .",
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+                                    "content": "is equal to its singular values. We will discuss how this assumption can be relaxed in Appendix A.7.",
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+                                    "score": 1.0,
+                                    "content": "exhibits a generally decreasing trend.",
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+                                    "content": "While Section 4.1 demonstrates rank collapse will occur in a kernel-regression model of Q-learning,",
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+                                    "content": "represented as a deep linear neural network (Arora et al., 2019), which is a widely-studied setting",
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+                                    "content": "for analyzing implicit regularization of gradient descent in supervised learning (Gunasekar et al.,",
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+                                    "score": 1.0,
+                                    "content": "2017; 2018; Arora et al., 2018; 2019). Our analysis will show that rank collapse can emerge as",
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+                                    "content": "the generated target values begin to approach the previous value estimate, in particular, when in the",
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+                                    "score": 1.0,
+                                    "content": "vicinity of the optimal Q-function.",
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+                                    "content": "Proof strategy. Our proof consists of two steps: (1) We show that the effective rank of the feature",
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+                        },
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+                                    "content": "Proposition 4.1 explains (1) and Proposition 4.2, Theorem 4.2 and Appendix D.2 discuss (2).",
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+                                    "score": 1.0,
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+                                    "score": 1.0,
+                                    "content": "since the rank of features",
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+                                    "content": "\\Phi = \\mathbf { W } _ { \\phi } ( k , t ) [ S , \\mathcal { A } ]",
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+                                    "score": 1.0,
+                                    "content": "provided the state-action inputs have high rank.",
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+                                    "content": ". To simplify analysis, we also assume that",
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+                                    "content": "all except the last-layer weights follow a “balancedness” property (Equation D.4), which suggests",
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+                        {
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+                                    "score": 1.0,
+                                    "content": "values (but with different permutations). However, note that we do not assume balancedness for",
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+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "the last layer which trivially leads to rank-1 features, making our analysis strictly more general than",
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+                                    "score": 1.0,
+                                    "content": "conventionally studied deep linear networks. In this model, we can characterize the evolution of the",
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+                                    "score": 1.0,
+                                    "content": ", using techniques analogous to Arora et al. (2019):",
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+                                    "content": "Summary of our analysis. Our analysis of bootstrapping and gradient descent from the view of",
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+                                    "score": 1.0,
+                                    "content": "happen in every iteration (and rank may increase between two consecutive iterations occasionally),",
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+                                    "score": 1.0,
+                                    "content": "exhibits a generally decreasing trend.",
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+                    ],
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+                                    "score": 1.0,
+                                    "content": "While Section 4.1 demonstrates rank collapse will occur in a kernel-regression model of Q-learning,",
+                                    "type": "text"
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+                        {
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+                                    "content": "it does not illustrate when the rank collapse occurs. To better specify a point in training when",
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+                                    "score": 1.0,
+                                    "content": "rank collapse emerges, we present a complementary derivation for the case when the Q-function is",
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+                                    "score": 1.0,
+                                    "content": "represented as a deep linear neural network (Arora et al., 2019), which is a widely-studied setting",
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+                        {
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+                                    "score": 1.0,
+                                    "content": "for analyzing implicit regularization of gradient descent in supervised learning (Gunasekar et al.,",
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+                        {
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+                                    "score": 1.0,
+                                    "content": "2017; 2018; Arora et al., 2018; 2019). Our analysis will show that rank collapse can emerge as",
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+                            "index": 23
+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "the generated target values begin to approach the previous value estimate, in particular, when in the",
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+                        {
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+                                    "score": 1.0,
+                                    "content": "vicinity of the optimal Q-function.",
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+                                    "score": 1.0,
+                                    "content": "Proof strategy. Our proof consists of two steps: (1) We show that the effective rank of the feature",
+                                    "type": "text"
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+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "matrix decreases within one fitting iteration (for a given target value) due to the low-rank affinity, (2)",
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+                        },
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+                                    "score": 1.0,
+                                    "content": "We show that this effective rank drop is “compounded” as we train using a bootstrapped objective.",
+                                    "type": "text"
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+                            "index": 28
+                        },
+                        {
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+                                    "content": "Proposition 4.1 explains (1) and Proposition 4.2, Theorem 4.2 and Appendix D.2 discuss (2).",
+                                    "type": "text"
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+                                    "content": "Additional notation and assumptions. We represent the Q-function as a deep linear network",
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+                                    "content": "of bootstrapping, we make a simplification and express this solution as the minimum of Equation 5.",
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+                                    "content": "Since srank",
+                                    "type": "text"
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+                                    "type": "inline_equation"
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+                                {
+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "is always regularized, our analysis assumes that",
+                                    "type": "text"
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+                                    "score": 0.92,
+                                    "content": "\\lambda _ { k } > 0",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "(see Appendix D.1).",
+                                    "type": "text"
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+                            ],
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+                        }
+                    ],
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+                },
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+                    "type": "text",
+                    "bbox": [
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+                        {
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+                                    "content": "Rank drop within a fitting iteration “compounds” due to bootstrapping. In the RL setting, the",
+                                    "type": "text"
+                                }
+                            ],
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+                        },
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+                                    "content": "y _ { k } ( \\mathbf { s } , \\mathbf { a } ) = r ( \\mathbf { s } , \\mathbf { a } ) + \\gamma P ^ { \\pi } Q _ { k - 1 } ( \\mathbf { s } , \\mathbf { a } )",
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+                                    "content": ". First note that when",
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+                                    "content": "P ^ { \\pi } = \\mathbf { I }",
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+                                    "score": 1.0,
+                                    "content": ", i.e., when the bootstrapping update resembles self-regression, we first note that just",
+                                    "type": "text"
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+                            ],
+                            "index": 26
+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "“copying over weights” from iteration",
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+                                    "content": "k - 1",
+                                    "type": "inline_equation"
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+                                {
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+                                    "content": "to iteration",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
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+                                    "score": 0.82,
+                                    "content": "k",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "is a feasible point for solving Equation 5,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
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+                                384
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "which attains zero TD error with no increase in",
+                                    "type": "text"
+                                },
+                                {
+                                    "bbox": [
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+                                    "score": 0.48,
+                                    "content": "\\mathrm { s r a n k } _ { \\delta }",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": ". A better solution to Equation 5 can thus be",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
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+                            "spans": [
+                                {
+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "obtained by incurring non-zero TD error at the benefit of a decreased srank, indicating that in this",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
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+                            "spans": [
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+                                    "score": 1.0,
+                                    "content": "setting,",
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+                                    "score": 0.73,
+                                    "content": "\\operatorname { s r a n k } _ { \\delta } ( \\mathbf { W } _ { \\phi } )",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "drops in each fitting iteration, leading to a compounding rank drop effect.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        }
+                    ],
+                    "index": 27
+                },
+                {
+                    "type": "text",
+                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "We next extend this analysis to the full bootstrapping setting. Unlike the self-training setting,",
+                                    "type": "text"
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+                                {
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+                                    "content": "is not directly expressible as a function of the previous",
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+                                    "content": "\\mathbf { W } _ { \\phi } ( k , T )",
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+                                {
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+                                    "score": 1.0,
+                                    "content": "due to additional reward",
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+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
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+                            "spans": [
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "and dynamics transformations. Assuming closure of the function class (Assumption D.1) under the",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "Bellman update (Munos & Szepesvari ´ , 2008; Chen & Jiang, 2019), we reason about the compound-",
+                                    "type": "text"
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+                            ],
+                            "index": 34
+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "ing effect of rank drop across iterations in Proposition 4.2 (proof in Appendix D.2). Specifically,",
+                                    "type": "text"
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+                            ],
+                            "index": 35
+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "can increase in each fitting iteration due to",
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+                                    "score": 0.52,
+                                    "content": "\\mathbf { R }",
+                                    "type": "inline_equation"
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+                                {
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+                                    "content": "and",
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+                                    "content": "P ^ { \\pi }",
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+                                    "score": 1.0,
+                                    "content": "transformations, but will decrease due",
+                                    "type": "text"
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+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
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+                            "spans": [
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "to low rank preference of gradient descent. This change in rank then compounds as shown below.",
+                                    "type": "text"
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+                            ],
+                            "index": 37
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+                    ],
+                    "index": 34
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+                                    "score": 1.0,
+                                    "content": "Proposition 4.2. Assume that the",
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+                                    "content": "{ \\bf W } _ { N } ( 0 )",
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+                                    "score": 1.0,
+                                    "content": ". Let the",
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+                            ],
+                            "index": 38
+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "-function class be closed under the backup, i.e.,",
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+                                    "score": 0.88,
+                                    "content": "\\exists \\mathbf { W } _ { N } ^ { P } , \\mathbf { W } _ { \\phi } ^ { P }",
+                                    "type": "inline_equation"
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+                                {
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+                                    "score": 1.0,
+                                    "content": ", s.t.",
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+                                    "bbox": [
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+                                    "score": 0.69,
+                                    "content": "\\left( { \\bf R } + \\gamma P ^ { \\pi } { \\bf Q } _ { k - 1 } \\right) ^ { T } =",
+                                    "type": "inline_equation"
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+                            ],
+                            "index": 39
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+                                    "score": 0.9,
+                                    "content": "\\mathbf { W } _ { N } ^ { P } ( k ) \\mathbf { W } _ { \\phi } ^ { P } ( k ) [ S ; \\mathcal { A } ] ^ { T }",
+                                    "type": "inline_equation"
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+                                    "score": 1.0,
+                                    "content": ", and assume that the change in srank due to dynamics and reward",
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+                        },
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+                                    "score": 1.0,
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+                                    "score": 0.76,
+                                    "content": "k _ { \\delta } ( \\mathbf { W } _ { \\phi } ^ { P } ( k ) ) \\leq s r a n k _ { \\delta } ( \\mathbf { W } _ { \\phi } ( k - 1 ) ) + c _ { k }",
+                                    "type": "inline_equation"
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+                                    "score": 1.0,
+                                    "content": ". Then,",
+                                    "type": "text"
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+                            "index": 41
+                        },
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+                                    "score": 0.58,
+                                    "content": "s r a n k _ { \\delta } ( \\mathbf { W } _ { \\phi } ( k ) ) \\leq s r a n k _ { \\delta } ( \\mathbf { W } _ { \\phi } ( 0 ) ) + \\sum _ { j = 1 } ^ { k } c _ { j } - \\sum _ { j = 1 } ^ { k } \\frac { | | \\mathbf { Q } _ { j } - \\mathbf { y } _ { j } | | } { \\lambda _ { j } } .",
+                                    "type": "inline_equation",
+                                    "image_path": "8fd2eb57162b35dedaff8f94e5437d1494423ebef9315273650321408d49362b.jpg"
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+                                    "score": 1.0,
+                                    "content": "Proposition 4.2 provides a bound on the value of srank after",
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+                                    "content": "rounds of bootstrapping. srank de-",
+                                    "type": "text"
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+                                    "score": 1.0,
+                                    "content": "creases in each iteration due to non-zero TD errors, but potentially increases due to reward and",
+                                    "type": "text"
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+                        },
+                        {
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+                                    "content": "bootstrapping transformations. To instantiate a concrete case where rank clearly collapses, we in-",
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+                                    "score": 1.0,
+                                    "content": "as the value function gets closer to the Bellman fixed point, which is a favourable",
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+                                    "score": 1.0,
+                                    "content": "initialization for the Q-function in Theorem 4.2. In this case, the learning dynamics begins to re-",
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+                                    "content": "semble the self-training regime, as the target values approach the previous value iterate",
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+                                    "score": 1.0,
+                                    "content": "in Proposition 4.2) converges to 0.",
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+                                    "score": 0.9,
+                                    "content": "y _ { k } ( \\mathbf { s } , \\mathbf { a } ) = Q _ { k - 1 } ( \\mathbf { s } , \\mathbf { a } ) + \\varepsilon ( \\mathbf { s } , \\mathbf { a } )",
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+                                    "score": 0.79,
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+                                    "content": "also occurs empirically, illustrated in the figure on the right (also see Fig-",
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+                                    "content": "of bootstrapping, we make a simplification and express this solution as the minimum of Equation 5.",
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+                                    "content": "is always regularized, our analysis assumes that",
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+                                    "content": "(see Appendix D.1).",
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+                                    "content": "Rank drop within a fitting iteration “compounds” due to bootstrapping. In the RL setting, the",
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+                                    "content": "y _ { k } ( \\mathbf { s } , \\mathbf { a } ) = r ( \\mathbf { s } , \\mathbf { a } ) + \\gamma P ^ { \\pi } Q _ { k - 1 } ( \\mathbf { s } , \\mathbf { a } )",
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+                                    "content": ". First note that when",
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+                                    "content": ", i.e., when the bootstrapping update resembles self-regression, we first note that just",
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+                                    "score": 1.0,
+                                    "content": "is a feasible point for solving Equation 5,",
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+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "which attains zero TD error with no increase in",
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+                                    "score": 1.0,
+                                    "content": ". A better solution to Equation 5 can thus be",
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+                                }
+                            ],
+                            "index": 28
+                        },
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+                                    "content": "obtained by incurring non-zero TD error at the benefit of a decreased srank, indicating that in this",
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+                                    "content": "drops in each fitting iteration, leading to a compounding rank drop effect.",
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+                                    "content": "We next extend this analysis to the full bootstrapping setting. Unlike the self-training setting,",
+                                    "type": "text"
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+                                    "content": "y _ { k } ( \\mathbf { s } , \\mathbf { a } )",
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+                                    "content": "is not directly expressible as a function of the previous",
+                                    "type": "text"
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+                                    "content": "\\mathbf { W } _ { \\phi } ( k , T )",
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+                                    "score": 1.0,
+                                    "content": "due to additional reward",
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+                            "index": 32
+                        },
+                        {
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+                            "spans": [
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "and dynamics transformations. Assuming closure of the function class (Assumption D.1) under the",
+                                    "type": "text"
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+                            ],
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+                        },
+                        {
+                            "bbox": [
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "Bellman update (Munos & Szepesvari ´ , 2008; Chen & Jiang, 2019), we reason about the compound-",
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+                                    "score": 1.0,
+                                    "content": "ing effect of rank drop across iterations in Proposition 4.2 (proof in Appendix D.2). Specifically,",
+                                    "type": "text"
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+                                    "score": 1.0,
+                                    "content": "can increase in each fitting iteration due to",
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+                                    "score": 1.0,
+                                    "content": "transformations, but will decrease due",
+                                    "type": "text"
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+                            ],
+                            "index": 36
+                        },
+                        {
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+                            "spans": [
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+                                    "score": 1.0,
+                                    "content": "to low rank preference of gradient descent. This change in rank then compounds as shown below.",
+                                    "type": "text"
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+                    ],
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+                                    "content": "{ \\bf W } _ { N } ( 0 )",
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+                                    "score": 1.0,
+                                    "content": ". Let the",
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+                            "index": 38
+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "-function class be closed under the backup, i.e.,",
+                                    "type": "text"
+                                },
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+                                    "score": 0.88,
+                                    "content": "\\exists \\mathbf { W } _ { N } ^ { P } , \\mathbf { W } _ { \\phi } ^ { P }",
+                                    "type": "inline_equation"
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+                                {
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+                                    "score": 1.0,
+                                    "content": ", s.t.",
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+                                    "score": 0.69,
+                                    "content": "\\left( { \\bf R } + \\gamma P ^ { \\pi } { \\bf Q } _ { k - 1 } \\right) ^ { T } =",
+                                    "type": "inline_equation"
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+                            ],
+                            "index": 39
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+                        {
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+                                    "score": 0.9,
+                                    "content": "\\mathbf { W } _ { N } ^ { P } ( k ) \\mathbf { W } _ { \\phi } ^ { P } ( k ) [ S ; \\mathcal { A } ] ^ { T }",
+                                    "type": "inline_equation"
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+                                    "score": 1.0,
+                                    "content": ", and assume that the change in srank due to dynamics and reward",
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+                            "index": 40
+                        },
+                        {
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+                                    "score": 0.76,
+                                    "content": "k _ { \\delta } ( \\mathbf { W } _ { \\phi } ^ { P } ( k ) ) \\leq s r a n k _ { \\delta } ( \\mathbf { W } _ { \\phi } ( k - 1 ) ) + c _ { k }",
+                                    "type": "inline_equation"
+                                },
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+                                    "score": 1.0,
+                                    "content": ". Then,",
+                                    "type": "text"
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+                            ],
+                            "index": 41
+                        },
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+                                    "content": "s r a n k _ { \\delta } ( \\mathbf { W } _ { \\phi } ( k ) ) \\leq s r a n k _ { \\delta } ( \\mathbf { W } _ { \\phi } ( 0 ) ) + \\sum _ { j = 1 } ^ { k } c _ { j } - \\sum _ { j = 1 } ^ { k } \\frac { | | \\mathbf { Q } _ { j } - \\mathbf { y } _ { j } | | } { \\lambda _ { j } } .",
+                                    "type": "inline_equation",
+                                    "image_path": "8fd2eb57162b35dedaff8f94e5437d1494423ebef9315273650321408d49362b.jpg"
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+                                    "content": "Proposition 4.2 provides a bound on the value of srank after",
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+                        },
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+                                    "score": 1.0,
+                                    "content": "creases in each iteration due to non-zero TD errors, but potentially increases due to reward and",
+                                    "type": "text"
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+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "bootstrapping transformations. To instantiate a concrete case where rank clearly collapses, we in-",
+                                    "type": "text"
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+                            ],
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+                        },
+                        {
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+                                    "content": "vestigate",
+                                    "type": "text"
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+                                {
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+                                    "score": 0.85,
+                                    "content": "c _ { k }",
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+                                },
+                                {
+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "as the value function gets closer to the Bellman fixed point, which is a favourable",
+                                    "type": "text"
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+                            ],
+                            "index": 46
+                        },
+                        {
+                            "bbox": [
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "initialization for the Q-function in Theorem 4.2. In this case, the learning dynamics begins to re-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 47
+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "semble the self-training regime, as the target values approach the previous value iterate",
+                                    "type": "text"
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+                                    "score": 0.93,
+                                    "content": "\\mathbf { y } _ { k } \\approx \\mathbf { Q } _ { k - 1 }",
+                                    "type": "inline_equation"
+                                },
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+                                    "score": 1.0,
+                                    "content": ",",
+                                    "type": "text"
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+                            "index": 48
+                        },
+                        {
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "and thus, as we show next, the potential increase in srank (",
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+                                    "score": 0.83,
+                                    "content": "\\dot { c } _ { k }",
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+                                {
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+                                    "score": 1.0,
+                                    "content": "in Proposition 4.2) converges to 0.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 49
+                        }
+                    ],
+                    "index": 46,
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+                                    "score": 1.0,
+                                    "content": "Theorem 4.2. Suppose target values",
+                                    "type": "text"
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+                                    "content": "\\mathbf { y } _ { k } = \\mathbf { R } + \\gamma P ^ { \\pi } \\mathbf { Q } _ { k - 1 }",
+                                    "type": "inline_equation"
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+                                {
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+                                    "content": "are close to the previous value esti-",
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+                                    "content": "\\mathbf { Q } _ { k - 1 }",
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+                                    "score": 1.0,
+                                    "content": ", i.e.",
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+                                    "content": "\\forall",
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+                                {
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+                                    "score": 1.0,
+                                    "content": "s, a,",
+                                    "type": "text"
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+                                {
+                                    "bbox": [
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+                                    "score": 0.9,
+                                    "content": "y _ { k } ( \\mathbf { s } , \\mathbf { a } ) = Q _ { k - 1 } ( \\mathbf { s } , \\mathbf { a } ) + \\varepsilon ( \\mathbf { s } , \\mathbf { a } )",
+                                    "type": "inline_equation"
+                                },
+                                {
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+                                    "score": 1.0,
+                                    "content": ", with",
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+                                {
+                                    "bbox": [
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+                                    "score": 0.89,
+                                    "content": "| \\varepsilon ( \\mathbf { s } , \\mathbf { a } ) | \\ll | Q _ { k - 1 } ( \\mathbf { s } , \\mathbf { a } ) |",
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+                                },
+                                {
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+                                    "score": 1.0,
+                                    "content": ". Then,",
+                                    "type": "text"
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+                            ],
+                            "index": 51
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+                                    "content": "vergence under restrictive assumptions (Yang et al., 2020; Cai et al., 2019; Zhang et al., 2020; Xu &",
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+                                    "score": 1.0,
+                                    "content": "2007) present variants of LSTD (Boyan, 1999), which model the Q-function as a kernel-machine",
+                                    "type": "text"
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+                                    "score": 1.0,
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+                                    "score": 1.0,
+                                    "content": "is essential for implicit under-parameterization. Igl et al. (2020); Fedus et al. (2020a) argue that",
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+                                    "score": 1.0,
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+                                    "score": 1.0,
+                                    "content": "that network re-initialization does little to prevent rank collapse (Figure 4c). Luo et al. (2020) pro-",
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+                                    "score": 1.0,
+                                    "content": "poses a regularization similar to ours, but in a different setting, finding that more expressive features",
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+                                {
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+                                    "score": 0.93,
+                                    "content": "| S | \\times | A |",
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+                                    "type": "inline_equation"
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+                                    "score": 1.0,
+                                    "content": "-matrix are preferable. We analyze a fundamentally different object: the learned features (and",
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+                                    "score": 1.0,
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+                                    "type": "text"
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+                            ],
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+                        {
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+                                    "score": 1.0,
+                                    "content": "by the number of actions (e.g., 24 for Atari).",
+                                    "type": "text"
+                                }
+                            ],
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+                    ],
+                    "index": 33.5
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+                {
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+                                    "content": "7 DISCUSSION",
+                                    "type": "text"
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+                                    "content": "version of this paper. We thank Hossein Mobahi for insightful discussions about self-distillation",
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+                                    "content": "and Hanie Sedghi for insightful discussions about implicit regularization and generalization in deep",
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+                                    "content": "networks. We additionally thank Michael Janner, Aaron Courville, Dale Schuurmans and Marc",
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+                                    "content": "Bellemare for helpful discussions. AK was partly funded by the DARPA Assured Autonomy pro-",
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+                                    "content": "gram, and DG was supported by a NSF graduate fellowship and compute support from Amazon.",
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+                        }
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+                                    "score": 1.0,
+                                    "content": "Martin Abadi, Paul Barham, Jianmin Chen, Zhifeng Chen, Andy Davis, Jeffrey Dean, Matthieu",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
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+                                    "content": "Devin, Sanjay Ghemawat, Geoffrey Irving, Michael Isard, Manjunath Kudlur, Josh Levenberg,",
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+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
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+                                115,
+                                240,
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+                                253
+                            ],
+                            "spans": [
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+                                    "bbox": [
+                                        115,
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+                                    "score": 1.0,
+                                    "content": "Rajat Monga, Sherry Moore, Derek G. Murray, Benoit Steiner, Paul Tucker, Vijay Vasudevan,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
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+                                        505,
+                                        264
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+                                    "score": 1.0,
+                                    "content": "Pete Warden, Martin Wicke, Yuan Yu, and Xiaoqiang Zheng. Tensorflow: A system for large-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                263,
+                                504,
+                                275
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        263,
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+                                        275
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+                                    "score": 1.0,
+                                    "content": "scale machine learning. In 12th USENIX Symposium on Operating Systems Design and Imple-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
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+                                    "score": 1.0,
+                                    "content": "mentation (OSDI 16), pp. 265–283, 2016. URL https://www.usenix.org/system/",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
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+                                361,
+                                297
+                            ],
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+                                    "content": "files/conference/osdi16/osdi16-abadi.pdf.",
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+                        },
+                        {
+                            "bbox": [
+                                115,
+                                315,
+                                277,
+                                327
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        315,
+                                        277,
+                                        327
+                                    ],
+                                    "score": 1.0,
+                                    "content": "learning. ArXiv, abs/1903.08894, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        }
+                    ],
+                    "index": 16.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        334,
+                        503,
+                        357
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                333,
+                                505,
+                                348
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        333,
+                                        505,
+                                        348
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Rishabh Agarwal, Dale Schuurmans, and Mohammad Norouzi. An optimistic perspective on offline",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                345,
+                                476,
+                                358
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        345,
+                                        476,
+                                        358
+                                    ],
+                                    "score": 1.0,
+                                    "content": "reinforcement learning. In International Conference on Machine Learning (ICML), 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        }
+                    ],
+                    "index": 18.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        364,
+                        503,
+                        388
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                364,
+                                505,
+                                377
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        364,
+                                        505,
+                                        377
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Sanjeev Arora, Nadav Cohen, and Elad Hazan. On the optimization of deep networks: Implicit",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                375,
+                                432,
+                                388
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        375,
+                                        432,
+                                        388
+                                    ],
+                                    "score": 1.0,
+                                    "content": "acceleration by overparameterization. arXiv preprint arXiv:1802.06509, 2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        }
+                    ],
+                    "index": 20.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        395,
+                        504,
+                        418
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                394,
+                                505,
+                                408
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        394,
+                                        505,
+                                        408
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Sanjeev Arora, Nadav Cohen, Wei Hu, and Yuping Luo. Implicit regularization in deep matrix",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                405,
+                                487,
+                                418
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        405,
+                                        487,
+                                        418
+                                    ],
+                                    "score": 1.0,
+                                    "content": "factorization. In Advances in Neural Information Processing Systems, pp. 7413–7424, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        }
+                    ],
+                    "index": 22.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        425,
+                        504,
+                        459
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                425,
+                                505,
+                                438
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        425,
+                                        505,
+                                        438
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Marc G. Bellemare, Yavar Naddaf, Joel Veness, and Michael Bowling. The arcade learning envi-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                436,
+                                504,
+                                448
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        436,
+                                        504,
+                                        448
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ronment: An evaluation platform for general agents. J. Artif. Int. Res., 47(1):253–279, May 2013.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                447,
+                                189,
+                                458
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        447,
+                                        189,
+                                        458
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ISSN 1076-9757.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        }
+                    ],
+                    "index": 25
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        466,
+                        504,
+                        500
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                467,
+                                505,
+                                479
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        467,
+                                        505,
+                                        479
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Marc G Bellemare, Will Dabney, and Remi Munos. A distributional perspective on reinforcement ´",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                478,
+                                505,
+                                490
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        478,
+                                        505,
+                                        490
+                                    ],
+                                    "score": 1.0,
+                                    "content": "learning. In Proceedings of the 34th International Conference on Machine Learning-Volume 70,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                489,
+                                245,
+                                501
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        489,
+                                        245,
+                                        501
+                                    ],
+                                    "score": 1.0,
+                                    "content": "pp. 449–458. JMLR. org, 2017.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        }
+                    ],
+                    "index": 28
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        507,
+                        504,
+                        531
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                507,
+                                505,
+                                520
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        507,
+                                        505,
+                                        520
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Emmanuel Bengio, Joelle Pineau, and Doina Precup. Interference and generalization in temporal",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                519,
+                                360,
+                                531
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        519,
+                                        360,
+                                        531
+                                    ],
+                                    "score": 1.0,
+                                    "content": "difference learning. arXiv preprint arXiv:2003.06350, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        }
+                    ],
+                    "index": 30.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        538,
+                        496,
+                        551
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                538,
+                                497,
+                                552
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        538,
+                                        497,
+                                        552
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Justin A Boyan. Least-squares temporal difference learning. In ICML, pp. 49–56. Citeseer, 1999.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        }
+                    ],
+                    "index": 32
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        558,
+                        504,
+                        581
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                558,
+                                505,
+                                570
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        558,
+                                        505,
+                                        570
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Greg Brockman, Vicki Cheung, Ludwig Pettersson, Jonas Schneider, John Schulman, Jie Tang, and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                568,
+                                277,
+                                581
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        568,
+                                        277,
+                                        581
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Wojciech Zaremba. Openai gym, 2016.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        }
+                    ],
+                    "index": 33.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        588,
+                        504,
+                        611
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                586,
+                                506,
+                                602
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        586,
+                                        506,
+                                        602
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Qi Cai, Zhuoran Yang, Jason D Lee, and Zhaoran Wang. Neural temporal-difference and q-learning",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                599,
+                                426,
+                                611
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        599,
+                                        426,
+                                        611
+                                    ],
+                                    "score": 1.0,
+                                    "content": "provably converge to global optima. arXiv preprint arXiv:1905.10027, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        }
+                    ],
+                    "index": 35.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        618,
+                        503,
+                        641
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                617,
+                                505,
+                                632
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        617,
+                                        505,
+                                        632
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Jinglin Chen and Nan Jiang. Information-theoretic considerations in batch reinforcement learning.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                628,
+                                170,
+                                642
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        628,
+                                        170,
+                                        642
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ICML, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        }
+                    ],
+                    "index": 37.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        648,
+                        503,
+                        682
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                649,
+                                505,
+                                661
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        649,
+                                        505,
+                                        661
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Bo Dai, Albert Shaw, Lihong Li, Lin Xiao, Niao He, Zhen Liu, Jianshu Chen, and Le Song. Sbeed:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                660,
+                                505,
+                                672
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        660,
+                                        505,
+                                        672
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Convergent reinforcement learning with nonlinear function approximation. In International Con-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                671,
+                                329,
+                                683
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        671,
+                                        329,
+                                        683
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ference on Machine Learning, pp. 1133–1142, 2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        }
+                    ],
+                    "index": 40
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        690,
+                        503,
+                        713
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                689,
+                                505,
+                                704
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        689,
+                                        505,
+                                        704
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Daniela Pucci De Farias. The linear programming approach to approximate dynamic programming:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        },
+                        {
+                            "bbox": [
+                                117,
+                                702,
+                                288,
+                                713
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        117,
+                                        702,
+                                        288,
+                                        713
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Theory and application. PhD thesis, 2002.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        }
+                    ],
+                    "index": 42.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        720,
+                        389,
+                        732
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                720,
+                                390,
+                                734
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        720,
+                                        390,
+                                        734
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Dean G Duffy. Green’s functions with applications. CRC Press, 2015.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        }
+                    ],
+                    "index": 44
+                }
+            ],
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+                792
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+                    "type": "discarded",
+                    "bbox": [
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+                        27,
+                        292,
+                        37
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+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                25,
+                                293,
+                                39
+                            ],
+                            "spans": [
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+                                        105,
+                                        25,
+                                        293,
+                                        39
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+                    ]
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+                    "type": "discarded",
+                    "bbox": [
+                        301,
+                        751,
+                        311,
+                        760
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+                    "lines": [
+                        {
+                            "bbox": [
+                                299,
+                                750,
+                                313,
+                                765
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+                            "spans": [
+                                {
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+                                        299,
+                                        750,
+                                        313,
+                                        765
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+                        225,
+                        93
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+                    "lines": [
+                        {
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+                                107,
+                                80,
+                                226,
+                                96
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+                            "spans": [
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+                        107,
+                        106,
+                        505,
+                        183
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+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                105,
+                                505,
+                                119
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        105,
+                                        505,
+                                        119
+                                    ],
+                                    "score": 1.0,
+                                    "content": "We thank Lihong Li, Aaron Courville, Aurick Zhou, Abhishek Gupta, George Tucker, Ofir Nachum,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                117,
+                                505,
+                                130
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        117,
+                                        505,
+                                        130
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Wesley Chung, Emmanuel Bengio, Zafarali Ahmed, and Jacob Buckman for feedback on an earlier",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                128,
+                                505,
+                                140
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        128,
+                                        505,
+                                        140
+                                    ],
+                                    "score": 1.0,
+                                    "content": "version of this paper. We thank Hossein Mobahi for insightful discussions about self-distillation",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                139,
+                                505,
+                                152
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        139,
+                                        505,
+                                        152
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and Hanie Sedghi for insightful discussions about implicit regularization and generalization in deep",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                150,
+                                505,
+                                163
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        150,
+                                        505,
+                                        163
+                                    ],
+                                    "score": 1.0,
+                                    "content": "networks. We additionally thank Michael Janner, Aaron Courville, Dale Schuurmans and Marc",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                160,
+                                505,
+                                174
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        160,
+                                        505,
+                                        174
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Bellemare for helpful discussions. AK was partly funded by the DARPA Assured Autonomy pro-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                172,
+                                493,
+                                186
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        172,
+                                        493,
+                                        186
+                                    ],
+                                    "score": 1.0,
+                                    "content": "gram, and DG was supported by a NSF graduate fellowship and compute support from Amazon.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        }
+                    ],
+                    "index": 4,
+                    "bbox_fs": [
+                        105,
+                        105,
+                        505,
+                        186
+                    ]
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        108,
+                        201,
+                        175,
+                        212
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                200,
+                                177,
+                                214
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        200,
+                                        177,
+                                        214
+                                    ],
+                                    "score": 1.0,
+                                    "content": "REFERENCES",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        }
+                    ],
+                    "index": 8
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        219,
+                        505,
+                        296
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                218,
+                                505,
+                                231
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        218,
+                                        505,
+                                        231
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Martin Abadi, Paul Barham, Jianmin Chen, Zhifeng Chen, Andy Davis, Jeffrey Dean, Matthieu",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                229,
+                                505,
+                                243
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        229,
+                                        505,
+                                        243
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Devin, Sanjay Ghemawat, Geoffrey Irving, Michael Isard, Manjunath Kudlur, Josh Levenberg,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                240,
+                                505,
+                                253
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        240,
+                                        505,
+                                        253
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Rajat Monga, Sherry Moore, Derek G. Murray, Benoit Steiner, Paul Tucker, Vijay Vasudevan,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                251,
+                                505,
+                                264
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        251,
+                                        505,
+                                        264
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Pete Warden, Martin Wicke, Yuan Yu, and Xiaoqiang Zheng. Tensorflow: A system for large-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                263,
+                                504,
+                                275
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        263,
+                                        504,
+                                        275
+                                    ],
+                                    "score": 1.0,
+                                    "content": "scale machine learning. In 12th USENIX Symposium on Operating Systems Design and Imple-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                274,
+                                504,
+                                286
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        274,
+                                        504,
+                                        286
+                                    ],
+                                    "score": 1.0,
+                                    "content": "mentation (OSDI 16), pp. 265–283, 2016. URL https://www.usenix.org/system/",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                284,
+                                361,
+                                297
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        284,
+                                        361,
+                                        297
+                                    ],
+                                    "score": 1.0,
+                                    "content": "files/conference/osdi16/osdi16-abadi.pdf.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        }
+                    ],
+                    "index": 12,
+                    "bbox_fs": [
+                        105,
+                        218,
+                        505,
+                        297
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        304,
+                        502,
+                        326
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                104,
+                                300,
+                                505,
+                                320
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        300,
+                                        505,
+                                        320
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Joshua Achiam, Ethan Knight, and Pieter Abbeel. Towards characterizing divergence in deep q-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                315,
+                                277,
+                                327
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        315,
+                                        277,
+                                        327
+                                    ],
+                                    "score": 1.0,
+                                    "content": "learning. ArXiv, abs/1903.08894, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        }
+                    ],
+                    "index": 16.5,
+                    "bbox_fs": [
+                        104,
+                        300,
+                        505,
+                        327
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        334,
+                        503,
+                        357
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                333,
+                                505,
+                                348
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        333,
+                                        505,
+                                        348
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Rishabh Agarwal, Dale Schuurmans, and Mohammad Norouzi. An optimistic perspective on offline",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                345,
+                                476,
+                                358
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        345,
+                                        476,
+                                        358
+                                    ],
+                                    "score": 1.0,
+                                    "content": "reinforcement learning. In International Conference on Machine Learning (ICML), 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        }
+                    ],
+                    "index": 18.5,
+                    "bbox_fs": [
+                        105,
+                        333,
+                        505,
+                        358
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        364,
+                        503,
+                        388
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                364,
+                                505,
+                                377
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        364,
+                                        505,
+                                        377
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Sanjeev Arora, Nadav Cohen, and Elad Hazan. On the optimization of deep networks: Implicit",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                375,
+                                432,
+                                388
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        375,
+                                        432,
+                                        388
+                                    ],
+                                    "score": 1.0,
+                                    "content": "acceleration by overparameterization. arXiv preprint arXiv:1802.06509, 2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        }
+                    ],
+                    "index": 20.5,
+                    "bbox_fs": [
+                        106,
+                        364,
+                        505,
+                        388
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        395,
+                        504,
+                        418
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                394,
+                                505,
+                                408
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        394,
+                                        505,
+                                        408
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Sanjeev Arora, Nadav Cohen, Wei Hu, and Yuping Luo. Implicit regularization in deep matrix",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                405,
+                                487,
+                                418
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        405,
+                                        487,
+                                        418
+                                    ],
+                                    "score": 1.0,
+                                    "content": "factorization. In Advances in Neural Information Processing Systems, pp. 7413–7424, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        }
+                    ],
+                    "index": 22.5,
+                    "bbox_fs": [
+                        106,
+                        394,
+                        505,
+                        418
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        425,
+                        504,
+                        459
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                425,
+                                505,
+                                438
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        425,
+                                        505,
+                                        438
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Marc G. Bellemare, Yavar Naddaf, Joel Veness, and Michael Bowling. The arcade learning envi-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                436,
+                                504,
+                                448
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        436,
+                                        504,
+                                        448
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ronment: An evaluation platform for general agents. J. Artif. Int. Res., 47(1):253–279, May 2013.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                447,
+                                189,
+                                458
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        447,
+                                        189,
+                                        458
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ISSN 1076-9757.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        }
+                    ],
+                    "index": 25,
+                    "bbox_fs": [
+                        105,
+                        425,
+                        505,
+                        458
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        466,
+                        504,
+                        500
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                467,
+                                505,
+                                479
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        467,
+                                        505,
+                                        479
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Marc G Bellemare, Will Dabney, and Remi Munos. A distributional perspective on reinforcement ´",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                478,
+                                505,
+                                490
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        478,
+                                        505,
+                                        490
+                                    ],
+                                    "score": 1.0,
+                                    "content": "learning. In Proceedings of the 34th International Conference on Machine Learning-Volume 70,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                489,
+                                245,
+                                501
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        489,
+                                        245,
+                                        501
+                                    ],
+                                    "score": 1.0,
+                                    "content": "pp. 449–458. JMLR. org, 2017.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        }
+                    ],
+                    "index": 28,
+                    "bbox_fs": [
+                        106,
+                        467,
+                        505,
+                        501
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        507,
+                        504,
+                        531
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                507,
+                                505,
+                                520
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        507,
+                                        505,
+                                        520
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Emmanuel Bengio, Joelle Pineau, and Doina Precup. Interference and generalization in temporal",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                519,
+                                360,
+                                531
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        519,
+                                        360,
+                                        531
+                                    ],
+                                    "score": 1.0,
+                                    "content": "difference learning. arXiv preprint arXiv:2003.06350, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        }
+                    ],
+                    "index": 30.5,
+                    "bbox_fs": [
+                        106,
+                        507,
+                        505,
+                        531
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        538,
+                        496,
+                        551
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                538,
+                                497,
+                                552
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        538,
+                                        497,
+                                        552
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Justin A Boyan. Least-squares temporal difference learning. In ICML, pp. 49–56. Citeseer, 1999.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        }
+                    ],
+                    "index": 32,
+                    "bbox_fs": [
+                        106,
+                        538,
+                        497,
+                        552
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        558,
+                        504,
+                        581
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                558,
+                                505,
+                                570
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        558,
+                                        505,
+                                        570
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Greg Brockman, Vicki Cheung, Ludwig Pettersson, Jonas Schneider, John Schulman, Jie Tang, and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                568,
+                                277,
+                                581
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        568,
+                                        277,
+                                        581
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Wojciech Zaremba. Openai gym, 2016.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        }
+                    ],
+                    "index": 33.5,
+                    "bbox_fs": [
+                        106,
+                        558,
+                        505,
+                        581
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        588,
+                        504,
+                        611
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                586,
+                                506,
+                                602
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        586,
+                                        506,
+                                        602
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Qi Cai, Zhuoran Yang, Jason D Lee, and Zhaoran Wang. Neural temporal-difference and q-learning",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                599,
+                                426,
+                                611
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        599,
+                                        426,
+                                        611
+                                    ],
+                                    "score": 1.0,
+                                    "content": "provably converge to global optima. arXiv preprint arXiv:1905.10027, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        }
+                    ],
+                    "index": 35.5,
+                    "bbox_fs": [
+                        106,
+                        586,
+                        506,
+                        611
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        618,
+                        503,
+                        641
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                617,
+                                505,
+                                632
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        617,
+                                        505,
+                                        632
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Jinglin Chen and Nan Jiang. Information-theoretic considerations in batch reinforcement learning.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                628,
+                                170,
+                                642
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        628,
+                                        170,
+                                        642
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ICML, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        }
+                    ],
+                    "index": 37.5,
+                    "bbox_fs": [
+                        105,
+                        617,
+                        505,
+                        642
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        648,
+                        503,
+                        682
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                649,
+                                505,
+                                661
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        649,
+                                        505,
+                                        661
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Bo Dai, Albert Shaw, Lihong Li, Lin Xiao, Niao He, Zhen Liu, Jianshu Chen, and Le Song. Sbeed:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                660,
+                                505,
+                                672
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        660,
+                                        505,
+                                        672
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Convergent reinforcement learning with nonlinear function approximation. In International Con-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                114,
+                                671,
+                                329,
+                                683
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        114,
+                                        671,
+                                        329,
+                                        683
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ference on Machine Learning, pp. 1133–1142, 2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        }
+                    ],
+                    "index": 40,
+                    "bbox_fs": [
+                        106,
+                        649,
+                        505,
+                        683
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        690,
+                        503,
+                        713
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                689,
+                                505,
+                                704
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        689,
+                                        505,
+                                        704
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Daniela Pucci De Farias. The linear programming approach to approximate dynamic programming:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        },
+                        {
+                            "bbox": [
+                                117,
+                                702,
+                                288,
+                                713
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        117,
+                                        702,
+                                        288,
+                                        713
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Theory and application. PhD thesis, 2002.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        }
+                    ],
+                    "index": 42.5,
+                    "bbox_fs": [
+                        105,
+                        689,
+                        505,
+                        713
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        720,
+                        389,
+                        732
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                720,
+                                390,
+                                734
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        720,
+                                        390,
+                                        734
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Dean G Duffy. Green’s functions with applications. CRC Press, 2015.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        }
+                    ],
+                    "index": 44,
+                    "bbox_fs": [
+                        106,
+                        720,
+                        390,
+                        734
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        82,
+                        504,
+                        105
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                80,
+                                505,
+                                96
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        80,
+                                        505,
+                                        96
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Damien Ernst, Pierre Geurts, and Louis Wehenkel. Tree-based batch mode reinforcement learning.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                93,
+                                372,
+                                106
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        93,
+                                        372,
+                                        106
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Journal of Machine Learning Research, 6(Apr):503–556, 2005.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        }
+                    ],
+                    "index": 0.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        113,
+                        504,
+                        136
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                112,
+                                505,
+                                126
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        112,
+                                        505,
+                                        126
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Amir-massoud Farahmand, Csaba Szepesvari, and R ´ emi Munos. Error propagation for approximate ´",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                124,
+                                504,
+                                137
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        124,
+                                        504,
+                                        137
+                                    ],
+                                    "score": 1.0,
+                                    "content": "policy and value iteration. In Advances in Neural Information Processing Systems (NIPS), 2010.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        }
+                    ],
+                    "index": 2.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        144,
+                        505,
+                        178
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                142,
+                                505,
+                                158
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        142,
+                                        505,
+                                        158
+                                    ],
+                                    "score": 1.0,
+                                    "content": "William Fedus, Dibya Ghosh, John D Martin, Marc G Bellemare, Yoshua Bengio, and Hugo",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                155,
+                                504,
+                                167
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        155,
+                                        504,
+                                        167
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Larochelle. On catastrophic interference in atari 2600 games. arXiv preprint arXiv:2002.12499,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                164,
+                                147,
+                                179
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        164,
+                                        147,
+                                        179
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2020a.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        }
+                    ],
+                    "index": 5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        186,
+                        506,
+                        220
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                186,
+                                505,
+                                199
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        186,
+                                        505,
+                                        199
+                                    ],
+                                    "score": 1.0,
+                                    "content": "William Fedus, Prajit Ramachandran, Rishabh Agarwal, Yoshua Bengio, Hugo Larochelle, Mark",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                197,
+                                505,
+                                210
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        197,
+                                        505,
+                                        210
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Rowland, and Will Dabney. Revisiting fundamentals of experience replay. arXiv preprint",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                209,
+                                224,
+                                219
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        209,
+                                        224,
+                                        219
+                                    ],
+                                    "score": 1.0,
+                                    "content": "arXiv:2007.06700, 2020b.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        }
+                    ],
+                    "index": 8
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        227,
+                        505,
+                        262
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                226,
+                                505,
+                                242
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        226,
+                                        505,
+                                        242
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Justin Fu, Aviral Kumar, Matthew Soh, and Sergey Levine. Diagnosing bottlenecks in deep q-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                238,
+                                505,
+                                253
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        238,
+                                        505,
+                                        253
+                                    ],
+                                    "score": 1.0,
+                                    "content": "learning algorithms. In Proceedings of the 36th International Conference on Machine Learning.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                250,
+                                173,
+                                262
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        250,
+                                        173,
+                                        262
+                                    ],
+                                    "score": 1.0,
+                                    "content": "PMLR, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        }
+                    ],
+                    "index": 11
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        270,
+                        504,
+                        293
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                268,
+                                505,
+                                285
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        268,
+                                        505,
+                                        285
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Dibya Ghosh and Marc G Bellemare. Representations for stable off-policy reinforcement learning.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                281,
+                                278,
+                                292
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        281,
+                                        278,
+                                        292
+                                    ],
+                                    "score": 1.0,
+                                    "content": "arXiv preprint arXiv:2007.05520, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        }
+                    ],
+                    "index": 13.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        300,
+                        504,
+                        335
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                300,
+                                505,
+                                314
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        300,
+                                        505,
+                                        314
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Caglar Gulcehre, Ziyu Wang, Alexander Novikov, Tom Le Paine, Sergio Gomez Colmenarejo, Kon- ´",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                312,
+                                505,
+                                324
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        312,
+                                        505,
+                                        324
+                                    ],
+                                    "score": 1.0,
+                                    "content": "rad Zolna, Rishabh Agarwal, Josh Merel, Daniel Mankowitz, Cosmin Paduraru, et al. Rl un-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                323,
+                                371,
+                                335
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        323,
+                                        371,
+                                        335
+                                    ],
+                                    "score": 1.0,
+                                    "content": "plugged: Benchmarks for offline reinforcement learning. 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        }
+                    ],
+                    "index": 16
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        342,
+                        505,
+                        377
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                342,
+                                505,
+                                356
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        342,
+                                        505,
+                                        356
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Suriya Gunasekar, Blake E Woodworth, Srinadh Bhojanapalli, Behnam Neyshabur, and Nati Srebro.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                353,
+                                505,
+                                368
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        353,
+                                        505,
+                                        368
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Implicit regularization in matrix factorization. In Advances in Neural Information Processing",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                365,
+                                244,
+                                378
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        365,
+                                        244,
+                                        378
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Systems, pp. 6151–6159, 2017.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        }
+                    ],
+                    "index": 19
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        385,
+                        505,
+                        418
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                384,
+                                506,
+                                398
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        384,
+                                        506,
+                                        398
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Suriya Gunasekar, Jason D Lee, Daniel Soudry, and Nati Srebro. Implicit bias of gradient descent",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                394,
+                                505,
+                                410
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        394,
+                                        505,
+                                        410
+                                    ],
+                                    "score": 1.0,
+                                    "content": "on linear convolutional networks. In Advances in Neural Information Processing Systems, pp.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                406,
+                                191,
+                                419
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        406,
+                                        191,
+                                        419
+                                    ],
+                                    "score": 1.0,
+                                    "content": "9461–9471, 2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        }
+                    ],
+                    "index": 22
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        426,
+                        505,
+                        461
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                426,
+                                505,
+                                440
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        426,
+                                        505,
+                                        440
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Tuomas Haarnoja, Aurick Zhou, Pieter Abbeel, and Sergey Levine. Soft actor-critic: Off-policy",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                438,
+                                505,
+                                450
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        438,
+                                        505,
+                                        450
+                                    ],
+                                    "score": 1.0,
+                                    "content": "maximum entropy deep reinforcement learning with a stochastic actor. CoRR, abs/1801.01290,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                448,
+                                356,
+                                462
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        448,
+                                        356,
+                                        462
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2018. URL http://arxiv.org/abs/1801.01290.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        }
+                    ],
+                    "index": 25
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        468,
+                        505,
+                        502
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                468,
+                                505,
+                                482
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        468,
+                                        505,
+                                        482
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Matteo Hessel, Joseph Modayil, Hado Van Hasselt, Tom Schaul, Georg Ostrovski, Will Dabney, Dan",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                480,
+                                505,
+                                492
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        480,
+                                        505,
+                                        492
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Horgan, Bilal Piot, Mohammad Azar, and David Silver. Rainbow: Combining improvements in",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                491,
+                                504,
+                                503
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        491,
+                                        504,
+                                        503
+                                    ],
+                                    "score": 1.0,
+                                    "content": "deep reinforcement learning. In Thirty-Second AAAI Conference on Artificial Intelligence, 2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        }
+                    ],
+                    "index": 28
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        510,
+                        505,
+                        555
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                509,
+                                506,
+                                523
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        509,
+                                        506,
+                                        523
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Edmund Hlawka, Rudolf Taschner, and Johannes Schoißengeier. The Dirichlet Approximation",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                521,
+                                505,
+                                534
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        521,
+                                        505,
+                                        534
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Theorem, pp. 1–18. Springer Berlin Heidelberg, Berlin, Heidelberg, 1991. ISBN 978-3-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                531,
+                                505,
+                                545
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        531,
+                                        505,
+                                        545
+                                    ],
+                                    "score": 1.0,
+                                    "content": "642-75306-0. doi: 10.1007/978-3-642-75306-0 1. URL https://doi.org/10.1007/",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                542,
+                                237,
+                                556
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        542,
+                                        237,
+                                        556
+                                    ],
+                                    "score": 1.0,
+                                    "content": "978-3-642-75306-0_1.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        }
+                    ],
+                    "index": 31.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        563,
+                        505,
+                        597
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                564,
+                                504,
+                                576
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        564,
+                                        504,
+                                        576
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Maximilian Igl, Gregory Farquhar, Jelena Luketina, Wendelin Boehmer, and Shimon Whiteson.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                574,
+                                505,
+                                587
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        574,
+                                        505,
+                                        587
+                                    ],
+                                    "score": 1.0,
+                                    "content": "The impact of non-stationarity on generalisation in deep reinforcement learning. arXiv preprint",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                586,
+                                219,
+                                597
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        586,
+                                        219,
+                                        597
+                                    ],
+                                    "score": 1.0,
+                                    "content": "arXiv:2006.05826, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        }
+                    ],
+                    "index": 35
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        605,
+                        504,
+                        629
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                604,
+                                505,
+                                618
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        604,
+                                        505,
+                                        618
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Arthur Jacot, Franck Gabriel, and Clement Hongler. Neural tangent kernel: Convergence and gen-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                617,
+                                503,
+                                630
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        617,
+                                        503,
+                                        630
+                                    ],
+                                    "score": 1.0,
+                                    "content": "eralization in neural networks. In Advances in Neural Information Processing Systems 31. 2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        }
+                    ],
+                    "index": 37.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        636,
+                        504,
+                        670
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                636,
+                                506,
+                                649
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        636,
+                                        506,
+                                        649
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Max Jaderberg, Volodymyr Mnih, Wojciech Marian Czarnecki, Tom Schaul, Joel Z Leibo, David",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                648,
+                                505,
+                                660
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        648,
+                                        505,
+                                        660
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Silver, and Koray Kavukcuoglu. Reinforcement learning with unsupervised auxiliary tasks. arXiv",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                659,
+                                254,
+                                671
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        659,
+                                        254,
+                                        671
+                                    ],
+                                    "score": 1.0,
+                                    "content": "preprint arXiv:1611.05397, 2016.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        }
+                    ],
+                    "index": 40
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        678,
+                        504,
+                        701
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                676,
+                                504,
+                                692
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        676,
+                                        504,
+                                        692
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Robert Johnson. Approximate irrational numbers by rational numbers, 2016. URL https://",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                689,
+                                366,
+                                702
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        689,
+                                        366,
+                                        702
+                                    ],
+                                    "score": 1.0,
+                                    "content": "math.stackexchange.com/questions/1829743/.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        }
+                    ],
+                    "index": 42.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        709,
+                        504,
+                        732
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                709,
+                                505,
+                                722
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        709,
+                                        505,
+                                        722
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Aviral Kumar, Abhishek Gupta, and Sergey Levine. Discor: Corrective feedback in reinforcement",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                720,
+                                427,
+                                733
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        720,
+                                        427,
+                                        733
+                                    ],
+                                    "score": 1.0,
+                                    "content": "learning via distribution correction. arXiv preprint arXiv:2003.07305, 2020a.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 45
+                        }
+                    ],
+                    "index": 44.5
+                }
+            ],
+            "page_idx": 10,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        107,
+                        27,
+                        293,
+                        37
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                26,
+                                293,
+                                38
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        26,
+                                        293,
+                                        38
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Published as a conference paper at ICLR 2021",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        300,
+                        751,
+                        310,
+                        760
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                299,
+                                750,
+                                312,
+                                765
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        299,
+                                        750,
+                                        312,
+                                        765
+                                    ],
+                                    "score": 1.0,
+                                    "content": "",
+                                    "type": "text",
+                                    "height": 15,
+                                    "width": 13
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        82,
+                        504,
+                        105
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                80,
+                                505,
+                                96
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        80,
+                                        505,
+                                        96
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Damien Ernst, Pierre Geurts, and Louis Wehenkel. Tree-based batch mode reinforcement learning.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                93,
+                                372,
+                                106
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        93,
+                                        372,
+                                        106
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Journal of Machine Learning Research, 6(Apr):503–556, 2005.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        }
+                    ],
+                    "index": 0.5,
+                    "bbox_fs": [
+                        105,
+                        80,
+                        505,
+                        106
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        113,
+                        504,
+                        136
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                112,
+                                505,
+                                126
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        112,
+                                        505,
+                                        126
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Amir-massoud Farahmand, Csaba Szepesvari, and R ´ emi Munos. Error propagation for approximate ´",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                124,
+                                504,
+                                137
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        124,
+                                        504,
+                                        137
+                                    ],
+                                    "score": 1.0,
+                                    "content": "policy and value iteration. In Advances in Neural Information Processing Systems (NIPS), 2010.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        }
+                    ],
+                    "index": 2.5,
+                    "bbox_fs": [
+                        106,
+                        112,
+                        505,
+                        137
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        144,
+                        505,
+                        178
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                142,
+                                505,
+                                158
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        142,
+                                        505,
+                                        158
+                                    ],
+                                    "score": 1.0,
+                                    "content": "William Fedus, Dibya Ghosh, John D Martin, Marc G Bellemare, Yoshua Bengio, and Hugo",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                155,
+                                504,
+                                167
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        155,
+                                        504,
+                                        167
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Larochelle. On catastrophic interference in atari 2600 games. arXiv preprint arXiv:2002.12499,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                164,
+                                147,
+                                179
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        164,
+                                        147,
+                                        179
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2020a.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        }
+                    ],
+                    "index": 5,
+                    "bbox_fs": [
+                        105,
+                        142,
+                        505,
+                        179
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        186,
+                        506,
+                        220
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                186,
+                                505,
+                                199
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        186,
+                                        505,
+                                        199
+                                    ],
+                                    "score": 1.0,
+                                    "content": "William Fedus, Prajit Ramachandran, Rishabh Agarwal, Yoshua Bengio, Hugo Larochelle, Mark",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                197,
+                                505,
+                                210
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        197,
+                                        505,
+                                        210
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Rowland, and Will Dabney. Revisiting fundamentals of experience replay. arXiv preprint",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                209,
+                                224,
+                                219
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        209,
+                                        224,
+                                        219
+                                    ],
+                                    "score": 1.0,
+                                    "content": "arXiv:2007.06700, 2020b.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        }
+                    ],
+                    "index": 8,
+                    "bbox_fs": [
+                        106,
+                        186,
+                        505,
+                        219
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        227,
+                        505,
+                        262
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                226,
+                                505,
+                                242
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        226,
+                                        505,
+                                        242
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Justin Fu, Aviral Kumar, Matthew Soh, and Sergey Levine. Diagnosing bottlenecks in deep q-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                238,
+                                505,
+                                253
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        238,
+                                        505,
+                                        253
+                                    ],
+                                    "score": 1.0,
+                                    "content": "learning algorithms. In Proceedings of the 36th International Conference on Machine Learning.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                250,
+                                173,
+                                262
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        250,
+                                        173,
+                                        262
+                                    ],
+                                    "score": 1.0,
+                                    "content": "PMLR, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        }
+                    ],
+                    "index": 11,
+                    "bbox_fs": [
+                        105,
+                        226,
+                        505,
+                        262
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        270,
+                        504,
+                        293
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                268,
+                                505,
+                                285
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        268,
+                                        505,
+                                        285
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Dibya Ghosh and Marc G Bellemare. Representations for stable off-policy reinforcement learning.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                281,
+                                278,
+                                292
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        281,
+                                        278,
+                                        292
+                                    ],
+                                    "score": 1.0,
+                                    "content": "arXiv preprint arXiv:2007.05520, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        }
+                    ],
+                    "index": 13.5,
+                    "bbox_fs": [
+                        105,
+                        268,
+                        505,
+                        292
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        300,
+                        504,
+                        335
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                300,
+                                505,
+                                314
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        300,
+                                        505,
+                                        314
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Caglar Gulcehre, Ziyu Wang, Alexander Novikov, Tom Le Paine, Sergio Gomez Colmenarejo, Kon- ´",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                312,
+                                505,
+                                324
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        312,
+                                        505,
+                                        324
+                                    ],
+                                    "score": 1.0,
+                                    "content": "rad Zolna, Rishabh Agarwal, Josh Merel, Daniel Mankowitz, Cosmin Paduraru, et al. Rl un-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                323,
+                                371,
+                                335
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        323,
+                                        371,
+                                        335
+                                    ],
+                                    "score": 1.0,
+                                    "content": "plugged: Benchmarks for offline reinforcement learning. 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        }
+                    ],
+                    "index": 16,
+                    "bbox_fs": [
+                        106,
+                        300,
+                        505,
+                        335
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        342,
+                        505,
+                        377
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                342,
+                                505,
+                                356
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        342,
+                                        505,
+                                        356
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Suriya Gunasekar, Blake E Woodworth, Srinadh Bhojanapalli, Behnam Neyshabur, and Nati Srebro.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                353,
+                                505,
+                                368
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        353,
+                                        505,
+                                        368
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Implicit regularization in matrix factorization. In Advances in Neural Information Processing",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                365,
+                                244,
+                                378
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        365,
+                                        244,
+                                        378
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Systems, pp. 6151–6159, 2017.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        }
+                    ],
+                    "index": 19,
+                    "bbox_fs": [
+                        105,
+                        342,
+                        505,
+                        378
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        385,
+                        505,
+                        418
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                384,
+                                506,
+                                398
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        384,
+                                        506,
+                                        398
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Suriya Gunasekar, Jason D Lee, Daniel Soudry, and Nati Srebro. Implicit bias of gradient descent",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                394,
+                                505,
+                                410
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        394,
+                                        505,
+                                        410
+                                    ],
+                                    "score": 1.0,
+                                    "content": "on linear convolutional networks. In Advances in Neural Information Processing Systems, pp.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                406,
+                                191,
+                                419
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        406,
+                                        191,
+                                        419
+                                    ],
+                                    "score": 1.0,
+                                    "content": "9461–9471, 2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        }
+                    ],
+                    "index": 22,
+                    "bbox_fs": [
+                        105,
+                        384,
+                        506,
+                        419
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        426,
+                        505,
+                        461
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                426,
+                                505,
+                                440
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        426,
+                                        505,
+                                        440
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Tuomas Haarnoja, Aurick Zhou, Pieter Abbeel, and Sergey Levine. Soft actor-critic: Off-policy",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                438,
+                                505,
+                                450
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        438,
+                                        505,
+                                        450
+                                    ],
+                                    "score": 1.0,
+                                    "content": "maximum entropy deep reinforcement learning with a stochastic actor. CoRR, abs/1801.01290,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                448,
+                                356,
+                                462
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        448,
+                                        356,
+                                        462
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2018. URL http://arxiv.org/abs/1801.01290.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        }
+                    ],
+                    "index": 25,
+                    "bbox_fs": [
+                        105,
+                        426,
+                        505,
+                        462
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        468,
+                        505,
+                        502
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                468,
+                                505,
+                                482
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        468,
+                                        505,
+                                        482
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Matteo Hessel, Joseph Modayil, Hado Van Hasselt, Tom Schaul, Georg Ostrovski, Will Dabney, Dan",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                480,
+                                505,
+                                492
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        480,
+                                        505,
+                                        492
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Horgan, Bilal Piot, Mohammad Azar, and David Silver. Rainbow: Combining improvements in",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                491,
+                                504,
+                                503
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        491,
+                                        504,
+                                        503
+                                    ],
+                                    "score": 1.0,
+                                    "content": "deep reinforcement learning. In Thirty-Second AAAI Conference on Artificial Intelligence, 2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        }
+                    ],
+                    "index": 28,
+                    "bbox_fs": [
+                        105,
+                        468,
+                        505,
+                        503
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        510,
+                        505,
+                        555
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                509,
+                                506,
+                                523
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        509,
+                                        506,
+                                        523
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Edmund Hlawka, Rudolf Taschner, and Johannes Schoißengeier. The Dirichlet Approximation",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                521,
+                                505,
+                                534
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        521,
+                                        505,
+                                        534
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Theorem, pp. 1–18. Springer Berlin Heidelberg, Berlin, Heidelberg, 1991. ISBN 978-3-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                531,
+                                505,
+                                545
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        531,
+                                        505,
+                                        545
+                                    ],
+                                    "score": 1.0,
+                                    "content": "642-75306-0. doi: 10.1007/978-3-642-75306-0 1. URL https://doi.org/10.1007/",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                542,
+                                237,
+                                556
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        542,
+                                        237,
+                                        556
+                                    ],
+                                    "score": 1.0,
+                                    "content": "978-3-642-75306-0_1.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        }
+                    ],
+                    "index": 31.5,
+                    "bbox_fs": [
+                        105,
+                        509,
+                        506,
+                        556
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        563,
+                        505,
+                        597
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                564,
+                                504,
+                                576
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        564,
+                                        504,
+                                        576
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Maximilian Igl, Gregory Farquhar, Jelena Luketina, Wendelin Boehmer, and Shimon Whiteson.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                574,
+                                505,
+                                587
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        574,
+                                        505,
+                                        587
+                                    ],
+                                    "score": 1.0,
+                                    "content": "The impact of non-stationarity on generalisation in deep reinforcement learning. arXiv preprint",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                586,
+                                219,
+                                597
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        586,
+                                        219,
+                                        597
+                                    ],
+                                    "score": 1.0,
+                                    "content": "arXiv:2006.05826, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        }
+                    ],
+                    "index": 35,
+                    "bbox_fs": [
+                        106,
+                        564,
+                        505,
+                        597
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        605,
+                        504,
+                        629
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                604,
+                                505,
+                                618
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        604,
+                                        505,
+                                        618
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Arthur Jacot, Franck Gabriel, and Clement Hongler. Neural tangent kernel: Convergence and gen-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                617,
+                                503,
+                                630
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        617,
+                                        503,
+                                        630
+                                    ],
+                                    "score": 1.0,
+                                    "content": "eralization in neural networks. In Advances in Neural Information Processing Systems 31. 2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        }
+                    ],
+                    "index": 37.5,
+                    "bbox_fs": [
+                        106,
+                        604,
+                        505,
+                        630
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        636,
+                        504,
+                        670
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                636,
+                                506,
+                                649
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        636,
+                                        506,
+                                        649
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Max Jaderberg, Volodymyr Mnih, Wojciech Marian Czarnecki, Tom Schaul, Joel Z Leibo, David",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                648,
+                                505,
+                                660
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        648,
+                                        505,
+                                        660
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Silver, and Koray Kavukcuoglu. Reinforcement learning with unsupervised auxiliary tasks. arXiv",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                659,
+                                254,
+                                671
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        659,
+                                        254,
+                                        671
+                                    ],
+                                    "score": 1.0,
+                                    "content": "preprint arXiv:1611.05397, 2016.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        }
+                    ],
+                    "index": 40,
+                    "bbox_fs": [
+                        105,
+                        636,
+                        506,
+                        671
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        678,
+                        504,
+                        701
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                676,
+                                504,
+                                692
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        676,
+                                        504,
+                                        692
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Robert Johnson. Approximate irrational numbers by rational numbers, 2016. URL https://",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                689,
+                                366,
+                                702
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        689,
+                                        366,
+                                        702
+                                    ],
+                                    "score": 1.0,
+                                    "content": "math.stackexchange.com/questions/1829743/.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        }
+                    ],
+                    "index": 42.5,
+                    "bbox_fs": [
+                        105,
+                        676,
+                        504,
+                        702
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        709,
+                        504,
+                        732
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                709,
+                                505,
+                                722
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        709,
+                                        505,
+                                        722
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Aviral Kumar, Abhishek Gupta, and Sergey Levine. Discor: Corrective feedback in reinforcement",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                720,
+                                427,
+                                733
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        720,
+                                        427,
+                                        733
+                                    ],
+                                    "score": 1.0,
+                                    "content": "learning via distribution correction. arXiv preprint arXiv:2003.07305, 2020a.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 45
+                        }
+                    ],
+                    "index": 44.5,
+                    "bbox_fs": [
+                        106,
+                        709,
+                        505,
+                        733
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        82,
+                        504,
+                        105
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                81,
+                                505,
+                                96
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        81,
+                                        505,
+                                        96
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Aviral Kumar, Aurick Zhou, George Tucker, and Sergey Levine. Conservative q-learning for offline",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                93,
+                                380,
+                                106
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        93,
+                                        380,
+                                        106
+                                    ],
+                                    "score": 1.0,
+                                    "content": "reinforcement learning. arXiv preprint arXiv:2006.04779, 2020b.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        }
+                    ],
+                    "index": 0.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        113,
+                        503,
+                        136
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                111,
+                                505,
+                                127
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        111,
+                                        505,
+                                        127
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Sascha Lange, Thomas Gabel, and Martin Riedmiller. Batch reinforcement learning. In Reinforce-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                124,
+                                286,
+                                136
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        124,
+                                        286,
+                                        136
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ment learning, pp. 45–73. Springer, 2012.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        }
+                    ],
+                    "index": 2.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        144,
+                        503,
+                        167
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                142,
+                                505,
+                                157
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        142,
+                                        505,
+                                        157
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Sergey Levine, Aviral Kumar, George Tucker, and Justin Fu. Offline reinforcement learning: Tuto-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                155,
+                                474,
+                                168
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        155,
+                                        474,
+                                        168
+                                    ],
+                                    "score": 1.0,
+                                    "content": "rial, review, and perspectives on open problems. arXiv preprint arXiv:2005.01643, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        }
+                    ],
+                    "index": 4.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        174,
+                        505,
+                        208
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                173,
+                                505,
+                                186
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        173,
+                                        505,
+                                        186
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Vincent Liu, Raksha Kumaraswamy, Lei Le, and Martha White. The utility of sparse representations",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                184,
+                                504,
+                                198
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        184,
+                                        504,
+                                        198
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for control in reinforcement learning. CoRR, abs/1811.06626, 2018. URL http://arxiv.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                196,
+                                229,
+                                208
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        196,
+                                        229,
+                                        208
+                                    ],
+                                    "score": 1.0,
+                                    "content": "org/abs/1811.06626.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        }
+                    ],
+                    "index": 7
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        216,
+                        505,
+                        282
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                216,
+                                505,
+                                229
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        216,
+                                        505,
+                                        229
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Xufang Luo, Qi Meng, Di He, Wei Chen, and Yunhong Wang. I4r: Promoting deep reinforcement",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                227,
+                                505,
+                                240
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        227,
+                                        505,
+                                        240
+                                    ],
+                                    "score": 1.0,
+                                    "content": "learning by the indicator for expressive representations. In Christian Bessiere (ed.), Proceed-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                115,
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+                        },
+                        {
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+                                        116,
+                                        249,
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+                                    "content": "2669–2675. International Joint Conferences on Artificial Intelligence Organization, 7 2020. doi:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
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+                            "spans": [
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+                                        259,
+                                        505,
+                                        273
+                                    ],
+                                    "score": 1.0,
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+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
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+                                270,
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+                                283
+                            ],
+                            "spans": [
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+                                    "bbox": [
+                                        115,
+                                        270,
+                                        142,
+                                        283
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+                        }
+                    ],
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+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        290,
+                        505,
+                        335
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                291,
+                                505,
+                                303
+                            ],
+                            "spans": [
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+                                    "bbox": [
+                                        106,
+                                        291,
+                                        505,
+                                        303
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Hamid R. Maei, Csaba Szepesvari, Shalabh Bhatnagar, Doina Precup, David Silver, and Richard S. ´",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                301,
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+                                315
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        301,
+                                        505,
+                                        315
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Sutton. Convergent temporal-difference learning with arbitrary smooth function approximation.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                312,
+                                505,
+                                326
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        312,
+                                        505,
+                                        326
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In Proceedings of the 22nd International Conference on Neural Information Processing Systems,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                323,
+                                142,
+                                335
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        323,
+                                        142,
+                                        335
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2009.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        }
+                    ],
+                    "index": 16.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        343,
+                        505,
+                        399
+                    ],
+                    "lines": [
+                        {
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+                                106,
+                                344,
+                                505,
+                                356
+                            ],
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+                                    "bbox": [
+                                        106,
+                                        344,
+                                        505,
+                                        356
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Volodymyr Mnih, Koray Kavukcuoglu, David Silver, Andrei A Rusu, Joel Veness, Marc G Belle-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                354,
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+                                367
+                            ],
+                            "spans": [
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+                                    "bbox": [
+                                        115,
+                                        354,
+                                        506,
+                                        367
+                                    ],
+                                    "score": 1.0,
+                                    "content": "mare, Alex Graves, Martin Riedmiller, Andreas K Fidjeland, Georg Ostrovski, Stig Petersen,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                117,
+                                366,
+                                504,
+                                378
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        117,
+                                        366,
+                                        504,
+                                        378
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Charles Beattie, Amir Sadik, Ioannis Antonoglou, Helen King, Dharshan Kumaran, Daan Wier-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                375,
+                                505,
+                                390
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        375,
+                                        505,
+                                        390
+                                    ],
+                                    "score": 1.0,
+                                    "content": "stra, Shane Legg, and Demis Hassabis. Human-level control through deep reinforcement learning.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                387,
+                                347,
+                                399
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        387,
+                                        347,
+                                        399
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Nature, 518(7540):529–533, feb 2015. ISSN 0028-0836.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        }
+                    ],
+                    "index": 21
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        406,
+                        504,
+                        430
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                406,
+                                505,
+                                420
+                            ],
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+                                    "bbox": [
+                                        106,
+                                        406,
+                                        505,
+                                        420
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Hossein Mobahi, Mehrdad Farajtabar, and Peter L Bartlett. Self-distillation amplifies regularization",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                116,
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+                                430
+                            ],
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+                                        116,
+                                        417,
+                                        345,
+                                        430
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+                            ],
+                            "index": 25
+                        }
+                    ],
+                    "index": 24.5
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+                                    "bbox": [
+                                        105,
+                                        437,
+                                        505,
+                                        451
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Remi Munos. Error bounds for approximate policy iteration. In ´ Proceedings of the Twentieth Inter-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                115,
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+                                462
+                            ],
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+                                    "bbox": [
+                                        115,
+                                        448,
+                                        505,
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+                                    "type": "text"
+                                }
+                            ],
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+                        },
+                        {
+                            "bbox": [
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+                                    "bbox": [
+                                        116,
+                                        460,
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+                                    "type": "text"
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+                            ],
+                            "index": 28
+                        }
+                    ],
+                    "index": 27
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        104,
+                        479,
+                        504,
+                        502
+                    ],
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+                            "bbox": [
+                                106,
+                                479,
+                                505,
+                                492
+                            ],
+                            "spans": [
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+                                    "bbox": [
+                                        106,
+                                        479,
+                                        505,
+                                        492
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Remi Munos and Csaba Szepesv ´ ari. Finite-time bounds for fitted value iteration. ´ Journal of Machine",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                490,
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+                                503
+                            ],
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+                                    "bbox": [
+                                        116,
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+                    ],
+                    "index": 29.5
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+                        587
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+                                    "bbox": [
+                                        106,
+                                        509,
+                                        505,
+                                        523
+                                    ],
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+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                521,
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+                                533
+                            ],
+                            "spans": [
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+                                        116,
+                                        521,
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+                                    "type": "text"
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+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                531,
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+                                {
+                                    "bbox": [
+                                        115,
+                                        531,
+                                        505,
+                                        545
+                                    ],
+                                    "score": 1.0,
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+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                542,
+                                505,
+                                556
+                            ],
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+                                {
+                                    "bbox": [
+                                        115,
+                                        542,
+                                        505,
+                                        556
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Lu Fang, Junjie Bai, and Soumith Chintala. Pytorch: An imperative style, high-performance",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                554,
+                                505,
+                                567
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        554,
+                                        505,
+                                        567
+                                    ],
+                                    "score": 1.0,
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+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                564,
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+                                578
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+                                    "bbox": [
+                                        115,
+                                        564,
+                                        506,
+                                        578
+                                    ],
+                                    "score": 1.0,
+                                    "content": "R. Garnett (eds.), Advances in Neural Information Processing Systems 32, pp. 8026–8037. Curran",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                576,
+                                209,
+                                587
+                            ],
+                            "spans": [
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+                                    "bbox": [
+                                        116,
+                                        576,
+                                        209,
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+                                    "type": "text"
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+                            ],
+                            "index": 37
+                        }
+                    ],
+                    "index": 34
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        595,
+                        504,
+                        618
+                    ],
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+                        {
+                            "bbox": [
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+                                609
+                            ],
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+                                    "bbox": [
+                                        105,
+                                        594,
+                                        505,
+                                        609
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Martin L Puterman. Markov Decision Processes: Discrete Stochastic Dynamic Programming. John",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                606,
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+                                619
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+                                    "bbox": [
+                                        116,
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+                                        222,
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+                                    "type": "text"
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+                        }
+                    ],
+                    "index": 38.5
+                },
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+                    "type": "text",
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+                        107,
+                        626,
+                        503,
+                        659
+                    ],
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+                                626,
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+                                639
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+                                    "bbox": [
+                                        105,
+                                        626,
+                                        505,
+                                        639
+                                    ],
+                                    "score": 1.0,
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+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
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+                                650
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+                                    "bbox": [
+                                        115,
+                                        638,
+                                        505,
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+                                    "type": "text"
+                                }
+                            ],
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+                        },
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+                            "bbox": [
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+                                    "bbox": [
+                                        115,
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+                                        106,
+                                        666,
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+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        },
+                        {
+                            "bbox": [
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+                                        313,
+                                        764
+                                    ],
+                                    "score": 1.0,
+                                    "content": "12",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        82,
+                        504,
+                        105
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                81,
+                                505,
+                                96
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        81,
+                                        505,
+                                        96
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Aviral Kumar, Aurick Zhou, George Tucker, and Sergey Levine. Conservative q-learning for offline",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                93,
+                                380,
+                                106
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        93,
+                                        380,
+                                        106
+                                    ],
+                                    "score": 1.0,
+                                    "content": "reinforcement learning. arXiv preprint arXiv:2006.04779, 2020b.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        }
+                    ],
+                    "index": 0.5,
+                    "bbox_fs": [
+                        105,
+                        81,
+                        505,
+                        106
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        113,
+                        503,
+                        136
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                111,
+                                505,
+                                127
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        111,
+                                        505,
+                                        127
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Sascha Lange, Thomas Gabel, and Martin Riedmiller. Batch reinforcement learning. In Reinforce-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                124,
+                                286,
+                                136
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        124,
+                                        286,
+                                        136
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ment learning, pp. 45–73. Springer, 2012.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        }
+                    ],
+                    "index": 2.5,
+                    "bbox_fs": [
+                        105,
+                        111,
+                        505,
+                        136
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        144,
+                        503,
+                        167
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                142,
+                                505,
+                                157
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        142,
+                                        505,
+                                        157
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Sergey Levine, Aviral Kumar, George Tucker, and Justin Fu. Offline reinforcement learning: Tuto-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                155,
+                                474,
+                                168
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        155,
+                                        474,
+                                        168
+                                    ],
+                                    "score": 1.0,
+                                    "content": "rial, review, and perspectives on open problems. arXiv preprint arXiv:2005.01643, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        }
+                    ],
+                    "index": 4.5,
+                    "bbox_fs": [
+                        105,
+                        142,
+                        505,
+                        168
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        174,
+                        505,
+                        208
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                173,
+                                505,
+                                186
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        173,
+                                        505,
+                                        186
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Vincent Liu, Raksha Kumaraswamy, Lei Le, and Martha White. The utility of sparse representations",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                184,
+                                504,
+                                198
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        184,
+                                        504,
+                                        198
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for control in reinforcement learning. CoRR, abs/1811.06626, 2018. URL http://arxiv.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                196,
+                                229,
+                                208
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        196,
+                                        229,
+                                        208
+                                    ],
+                                    "score": 1.0,
+                                    "content": "org/abs/1811.06626.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        }
+                    ],
+                    "index": 7,
+                    "bbox_fs": [
+                        106,
+                        173,
+                        505,
+                        208
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        216,
+                        505,
+                        282
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                216,
+                                505,
+                                229
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        216,
+                                        505,
+                                        229
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Xufang Luo, Qi Meng, Di He, Wei Chen, and Yunhong Wang. I4r: Promoting deep reinforcement",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                227,
+                                505,
+                                240
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        227,
+                                        505,
+                                        240
+                                    ],
+                                    "score": 1.0,
+                                    "content": "learning by the indicator for expressive representations. In Christian Bessiere (ed.), Proceed-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                236,
+                                505,
+                                253
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        236,
+                                        505,
+                                        253
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ings of the Twenty-Ninth International Joint Conference on Artificial Intelligence, IJCAI-20, pp.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                249,
+                                505,
+                                262
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        249,
+                                        505,
+                                        262
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2669–2675. International Joint Conferences on Artificial Intelligence Organization, 7 2020. doi:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                259,
+                                505,
+                                273
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        259,
+                                        505,
+                                        273
+                                    ],
+                                    "score": 1.0,
+                                    "content": "10.24963/ijcai.2020/370. URL https://doi.org/10.24963/ijcai.2020/370. Main",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                270,
+                                142,
+                                283
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        270,
+                                        142,
+                                        283
+                                    ],
+                                    "score": 1.0,
+                                    "content": "track.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        }
+                    ],
+                    "index": 11.5,
+                    "bbox_fs": [
+                        106,
+                        216,
+                        505,
+                        283
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        290,
+                        505,
+                        335
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                291,
+                                505,
+                                303
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        291,
+                                        505,
+                                        303
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Hamid R. Maei, Csaba Szepesvari, Shalabh Bhatnagar, Doina Precup, David Silver, and Richard S. ´",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                301,
+                                505,
+                                315
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        301,
+                                        505,
+                                        315
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Sutton. Convergent temporal-difference learning with arbitrary smooth function approximation.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                312,
+                                505,
+                                326
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        312,
+                                        505,
+                                        326
+                                    ],
+                                    "score": 1.0,
+                                    "content": "In Proceedings of the 22nd International Conference on Neural Information Processing Systems,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                323,
+                                142,
+                                335
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        323,
+                                        142,
+                                        335
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2009.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        }
+                    ],
+                    "index": 16.5,
+                    "bbox_fs": [
+                        106,
+                        291,
+                        505,
+                        335
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        343,
+                        505,
+                        399
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                344,
+                                505,
+                                356
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        344,
+                                        505,
+                                        356
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Volodymyr Mnih, Koray Kavukcuoglu, David Silver, Andrei A Rusu, Joel Veness, Marc G Belle-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                354,
+                                506,
+                                367
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        354,
+                                        506,
+                                        367
+                                    ],
+                                    "score": 1.0,
+                                    "content": "mare, Alex Graves, Martin Riedmiller, Andreas K Fidjeland, Georg Ostrovski, Stig Petersen,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                117,
+                                366,
+                                504,
+                                378
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        117,
+                                        366,
+                                        504,
+                                        378
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Charles Beattie, Amir Sadik, Ioannis Antonoglou, Helen King, Dharshan Kumaran, Daan Wier-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                375,
+                                505,
+                                390
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        375,
+                                        505,
+                                        390
+                                    ],
+                                    "score": 1.0,
+                                    "content": "stra, Shane Legg, and Demis Hassabis. Human-level control through deep reinforcement learning.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                387,
+                                347,
+                                399
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        387,
+                                        347,
+                                        399
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Nature, 518(7540):529–533, feb 2015. ISSN 0028-0836.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        }
+                    ],
+                    "index": 21,
+                    "bbox_fs": [
+                        106,
+                        344,
+                        506,
+                        399
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        406,
+                        504,
+                        430
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                406,
+                                505,
+                                420
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        406,
+                                        505,
+                                        420
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Hossein Mobahi, Mehrdad Farajtabar, and Peter L Bartlett. Self-distillation amplifies regularization",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                417,
+                                345,
+                                430
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        417,
+                                        345,
+                                        430
+                                    ],
+                                    "score": 1.0,
+                                    "content": "in hilbert space. arXiv preprint arXiv:2002.05715, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        }
+                    ],
+                    "index": 24.5,
+                    "bbox_fs": [
+                        106,
+                        406,
+                        505,
+                        430
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        437,
+                        504,
+                        471
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                437,
+                                505,
+                                451
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        437,
+                                        505,
+                                        451
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Remi Munos. Error bounds for approximate policy iteration. In ´ Proceedings of the Twentieth Inter-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                448,
+                                505,
+                                462
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        448,
+                                        505,
+                                        462
+                                    ],
+                                    "score": 1.0,
+                                    "content": "national Conference on International Conference on Machine Learning, ICML’03, pp. 560–567.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                460,
+                                276,
+                                471
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        460,
+                                        276,
+                                        471
+                                    ],
+                                    "score": 1.0,
+                                    "content": "AAAI Press, 2003. ISBN 1577351894.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        }
+                    ],
+                    "index": 27,
+                    "bbox_fs": [
+                        105,
+                        437,
+                        505,
+                        471
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        104,
+                        479,
+                        504,
+                        502
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                479,
+                                505,
+                                492
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        479,
+                                        505,
+                                        492
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Remi Munos and Csaba Szepesv ´ ari. Finite-time bounds for fitted value iteration. ´ Journal of Machine",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                490,
+                                294,
+                                503
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        490,
+                                        294,
+                                        503
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Learning Research, 9(May):815–857, 2008.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        }
+                    ],
+                    "index": 29.5,
+                    "bbox_fs": [
+                        106,
+                        479,
+                        505,
+                        503
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        510,
+                        505,
+                        587
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                509,
+                                505,
+                                523
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        509,
+                                        505,
+                                        523
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Adam Paszke, Sam Gross, Francisco Massa, Adam Lerer, James Bradbury, Gregory Chanan, Trevor",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                521,
+                                505,
+                                533
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        521,
+                                        505,
+                                        533
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Killeen, Zeming Lin, Natalia Gimelshein, Luca Antiga, Alban Desmaison, Andreas Kopf, Edward",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                531,
+                                505,
+                                545
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        531,
+                                        505,
+                                        545
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Yang, Zachary DeVito, Martin Raison, Alykhan Tejani, Sasank Chilamkurthy, Benoit Steiner,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                542,
+                                505,
+                                556
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        542,
+                                        505,
+                                        556
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Lu Fang, Junjie Bai, and Soumith Chintala. Pytorch: An imperative style, high-performance",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                554,
+                                505,
+                                567
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        554,
+                                        505,
+                                        567
+                                    ],
+                                    "score": 1.0,
+                                    "content": "deep learning library. In H. Wallach, H. Larochelle, A. Beygelzimer, F. dAlche-Buc, E. Fox, and ´",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                564,
+                                506,
+                                578
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        564,
+                                        506,
+                                        578
+                                    ],
+                                    "score": 1.0,
+                                    "content": "R. Garnett (eds.), Advances in Neural Information Processing Systems 32, pp. 8026–8037. Curran",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                576,
+                                209,
+                                587
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        576,
+                                        209,
+                                        587
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Associates, Inc., 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        }
+                    ],
+                    "index": 34,
+                    "bbox_fs": [
+                        106,
+                        509,
+                        506,
+                        587
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        595,
+                        504,
+                        618
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                594,
+                                505,
+                                609
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        594,
+                                        505,
+                                        609
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Martin L Puterman. Markov Decision Processes: Discrete Stochastic Dynamic Programming. John",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                606,
+                                222,
+                                619
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        606,
+                                        222,
+                                        619
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Wiley & Sons, Inc., 1994.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        }
+                    ],
+                    "index": 38.5,
+                    "bbox_fs": [
+                        105,
+                        594,
+                        505,
+                        619
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        626,
+                        503,
+                        659
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                626,
+                                505,
+                                639
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        626,
+                                        505,
+                                        639
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Martin Riedmiller. Neural fitted q iteration–first experiences with a data efficient neural reinforce-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                638,
+                                505,
+                                650
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        638,
+                                        505,
+                                        650
+                                    ],
+                                    "score": 1.0,
+                                    "content": "ment learning method. In European Conference on Machine Learning, pp. 317–328. Springer,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                646,
+                                143,
+                                660
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        646,
+                                        143,
+                                        660
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2005.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        }
+                    ],
+                    "index": 41,
+                    "bbox_fs": [
+                        105,
+                        626,
+                        505,
+                        660
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        667,
+                        504,
+                        691
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                666,
+                                505,
+                                681
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        666,
+                                        505,
+                                        681
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Axel Ruhe. On the closeness of eigenvalues and singular values for almost normal matrices. Linear",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                679,
+                                314,
+                                691
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        679,
+                                        314,
+                                        691
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Algebra and its Applications, 11(1):87–93, 1975.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        }
+                    ],
+                    "index": 43.5,
+                    "bbox_fs": [
+                        106,
+                        666,
+                        505,
+                        691
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        699,
+                        504,
+                        732
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                697,
+                                506,
+                                712
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        697,
+                                        506,
+                                        712
+                                    ],
+                                    "score": 1.0,
+                                    "content": "David Silver, Julian Schrittwieser, Karen Simonyan, Ioannis Antonoglou, Aja Huang, Arthur Guez,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 45
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                708,
+                                506,
+                                723
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        708,
+                                        506,
+                                        723
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Thomas Hubert, Lucas Baker, Matthew Lai, Adrian Bolton, et al. Mastering the game of go",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 46
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                720,
+                                369,
+                                732
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        720,
+                                        369,
+                                        732
+                                    ],
+                                    "score": 1.0,
+                                    "content": "without human knowledge. nature, 550(7676):354–359, 2017.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 47
+                        }
+                    ],
+                    "index": 46,
+                    "bbox_fs": [
+                        105,
+                        697,
+                        506,
+                        732
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        82,
+                        504,
+                        105
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                82,
+                                505,
+                                95
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        82,
+                                        505,
+                                        95
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Arun Suggala, Adarsh Prasad, and Pradeep K Ravikumar. Connecting optimization and regulariza-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                92,
+                                486,
+                                106
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        92,
+                                        486,
+                                        106
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tion paths. In Advances in Neural Information Processing Systems, pp. 10608–10619, 2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        }
+                    ],
+                    "index": 0.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        111,
+                        505,
+                        156
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                111,
+                                505,
+                                125
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        111,
+                                        505,
+                                        125
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Richard S. Sutton, Hamid Reza Maei, Doina Precup, Shalabh Bhatnagar, David Silver, Csaba",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                122,
+                                506,
+                                137
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        122,
+                                        506,
+                                        137
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Szepesvari, and Eric Wiewiora. Fast gradient-descent methods for temporal-difference learning ´",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                134,
+                                505,
+                                147
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        134,
+                                        505,
+                                        147
+                                    ],
+                                    "score": 1.0,
+                                    "content": "with linear function approximation. In International Conference on Machine Learning (ICML),",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                144,
+                                143,
+                                158
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        144,
+                                        143,
+                                        158
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2009.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        }
+                    ],
+                    "index": 3.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        164,
+                        504,
+                        186
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                163,
+                                504,
+                                176
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        163,
+                                        504,
+                                        176
+                                    ],
+                                    "score": 1.0,
+                                    "content": "James Townsend. Differentiating the singular value decomposition. Technical report, Technical",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                175,
+                                403,
+                                187
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        175,
+                                        403,
+                                        187
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Report 2016, https://j-towns. github. io/papers/svd-derivative . . . , 2016.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        }
+                    ],
+                    "index": 6.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        194,
+                        503,
+                        217
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                192,
+                                505,
+                                208
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        192,
+                                        505,
+                                        208
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Pan Xu and Quanquan Gu. A finite-time analysis of q-learning with neural network function ap-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                205,
+                                333,
+                                217
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        205,
+                                        333,
+                                        217
+                                    ],
+                                    "score": 1.0,
+                                    "content": "proximation. arXiv preprint arXiv:1912.04511, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        }
+                    ],
+                    "index": 8.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        223,
+                        503,
+                        246
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                222,
+                                505,
+                                238
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        222,
+                                        505,
+                                        238
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Xin Xu, Tao Xie, Dewen Hu, and Xicheng Lu. Kernel least-squares temporal difference learning.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                235,
+                                394,
+                                247
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        235,
+                                        394,
+                                        247
+                                    ],
+                                    "score": 1.0,
+                                    "content": "International Journal of Information Technology, 11(9):54–63, 2005.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        }
+                    ],
+                    "index": 10.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        253,
+                        504,
+                        277
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                253,
+                                505,
+                                266
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        253,
+                                        505,
+                                        266
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Xin Xu, Dewen Hu, and Xicheng Lu. Kernel-based least squares policy iteration for reinforcement",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                265,
+                                407,
+                                276
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        265,
+                                        407,
+                                        276
+                                    ],
+                                    "score": 1.0,
+                                    "content": "learning. IEEE Transactions on Neural Networks, 18(4):973–992, 2007.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        }
+                    ],
+                    "index": 12.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        283,
+                        504,
+                        307
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                282,
+                                505,
+                                298
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        282,
+                                        505,
+                                        298
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Yuzhe Yang, Guo Zhang, Zhi Xu, and Dina Katabi. Harnessing structures for value-based planning",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                294,
+                                393,
+                                307
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        294,
+                                        393,
+                                        307
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and reinforcement learning. arXiv preprint arXiv:1909.12255, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        }
+                    ],
+                    "index": 14.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        313,
+                        504,
+                        336
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                312,
+                                505,
+                                327
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        312,
+                                        505,
+                                        327
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Zhuoran Yang, Yuchen Xie, and Zhaoran Wang. A theoretical analysis of deep q-learning. In",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                325,
+                                376,
+                                337
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        325,
+                                        376,
+                                        337
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Learning for Dynamics and Control, pp. 486–489. PMLR, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        }
+                    ],
+                    "index": 16.5
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        343,
+                        504,
+                        366
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                107,
+                                343,
+                                505,
+                                356
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        343,
+                                        505,
+                                        356
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Yufeng Zhang, Qi Cai, Zhuoran Yang, Yongxin Chen, and Zhaoran Wang. Can temporal-difference",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                355,
+                                504,
+                                367
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        355,
+                                        504,
+                                        367
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and q-learning learn representation? a mean-field theory. arXiv preprint arXiv:2006.04761, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        }
+                    ],
+                    "index": 18.5
+                }
+            ],
+            "page_idx": 12,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        108,
+                        27,
+                        292,
+                        37
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                26,
+                                293,
+                                38
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        26,
+                                        293,
+                                        38
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Published as a conference paper at ICLR 2021",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                },
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        300,
+                        751,
+                        311,
+                        760
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                299,
+                                750,
+                                313,
+                                764
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        299,
+                                        750,
+                                        313,
+                                        764
+                                    ],
+                                    "score": 1.0,
+                                    "content": "13",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        82,
+                        504,
+                        105
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                82,
+                                505,
+                                95
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        82,
+                                        505,
+                                        95
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Arun Suggala, Adarsh Prasad, and Pradeep K Ravikumar. Connecting optimization and regulariza-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                92,
+                                486,
+                                106
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        92,
+                                        486,
+                                        106
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tion paths. In Advances in Neural Information Processing Systems, pp. 10608–10619, 2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        }
+                    ],
+                    "index": 0.5,
+                    "bbox_fs": [
+                        106,
+                        82,
+                        505,
+                        106
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        111,
+                        505,
+                        156
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                111,
+                                505,
+                                125
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        111,
+                                        505,
+                                        125
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Richard S. Sutton, Hamid Reza Maei, Doina Precup, Shalabh Bhatnagar, David Silver, Csaba",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                122,
+                                506,
+                                137
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        122,
+                                        506,
+                                        137
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Szepesvari, and Eric Wiewiora. Fast gradient-descent methods for temporal-difference learning ´",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                134,
+                                505,
+                                147
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        134,
+                                        505,
+                                        147
+                                    ],
+                                    "score": 1.0,
+                                    "content": "with linear function approximation. In International Conference on Machine Learning (ICML),",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                144,
+                                143,
+                                158
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        144,
+                                        143,
+                                        158
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2009.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        }
+                    ],
+                    "index": 3.5,
+                    "bbox_fs": [
+                        105,
+                        111,
+                        506,
+                        158
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        106,
+                        164,
+                        504,
+                        186
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                163,
+                                504,
+                                176
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        163,
+                                        504,
+                                        176
+                                    ],
+                                    "score": 1.0,
+                                    "content": "James Townsend. Differentiating the singular value decomposition. Technical report, Technical",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                175,
+                                403,
+                                187
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        175,
+                                        403,
+                                        187
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Report 2016, https://j-towns. github. io/papers/svd-derivative . . . , 2016.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        }
+                    ],
+                    "index": 6.5,
+                    "bbox_fs": [
+                        106,
+                        163,
+                        504,
+                        187
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        194,
+                        503,
+                        217
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                192,
+                                505,
+                                208
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        192,
+                                        505,
+                                        208
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Pan Xu and Quanquan Gu. A finite-time analysis of q-learning with neural network function ap-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                205,
+                                333,
+                                217
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        205,
+                                        333,
+                                        217
+                                    ],
+                                    "score": 1.0,
+                                    "content": "proximation. arXiv preprint arXiv:1912.04511, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        }
+                    ],
+                    "index": 8.5,
+                    "bbox_fs": [
+                        105,
+                        192,
+                        505,
+                        217
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        223,
+                        503,
+                        246
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                222,
+                                505,
+                                238
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        222,
+                                        505,
+                                        238
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Xin Xu, Tao Xie, Dewen Hu, and Xicheng Lu. Kernel least-squares temporal difference learning.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                235,
+                                394,
+                                247
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        235,
+                                        394,
+                                        247
+                                    ],
+                                    "score": 1.0,
+                                    "content": "International Journal of Information Technology, 11(9):54–63, 2005.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        }
+                    ],
+                    "index": 10.5,
+                    "bbox_fs": [
+                        105,
+                        222,
+                        505,
+                        247
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        253,
+                        504,
+                        277
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                253,
+                                505,
+                                266
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        253,
+                                        505,
+                                        266
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Xin Xu, Dewen Hu, and Xicheng Lu. Kernel-based least squares policy iteration for reinforcement",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                265,
+                                407,
+                                276
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        265,
+                                        407,
+                                        276
+                                    ],
+                                    "score": 1.0,
+                                    "content": "learning. IEEE Transactions on Neural Networks, 18(4):973–992, 2007.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        }
+                    ],
+                    "index": 12.5,
+                    "bbox_fs": [
+                        105,
+                        253,
+                        505,
+                        276
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        108,
+                        283,
+                        504,
+                        307
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                282,
+                                505,
+                                298
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        282,
+                                        505,
+                                        298
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Yuzhe Yang, Guo Zhang, Zhi Xu, and Dina Katabi. Harnessing structures for value-based planning",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                115,
+                                294,
+                                393,
+                                307
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        294,
+                                        393,
+                                        307
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and reinforcement learning. arXiv preprint arXiv:1909.12255, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        }
+                    ],
+                    "index": 14.5,
+                    "bbox_fs": [
+                        106,
+                        282,
+                        505,
+                        307
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        313,
+                        504,
+                        336
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                312,
+                                505,
+                                327
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        312,
+                                        505,
+                                        327
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Zhuoran Yang, Yuchen Xie, and Zhaoran Wang. A theoretical analysis of deep q-learning. In",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                325,
+                                376,
+                                337
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        116,
+                                        325,
+                                        376,
+                                        337
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Learning for Dynamics and Control, pp. 486–489. PMLR, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        }
+                    ],
+                    "index": 16.5,
+                    "bbox_fs": [
+                        105,
+                        312,
+                        505,
+                        337
+                    ]
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        107,
+                        343,
+                        504,
+                        366
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                107,
+                                343,
+                                505,
+                                356
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        343,
+                                        505,
+                                        356
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Yufeng Zhang, Qi Cai, Zhuoran Yang, Yongxin Chen, and Zhaoran Wang. Can temporal-difference",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                116,
+                                355,
+                                504,
+                                367
+                            ],
+                            "spans": [
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+                                    "bbox": [
+                                        116,
+                                        355,
+                                        504,
+                                        367
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and q-learning learn representation? a mean-field theory. arXiv preprint arXiv:2006.04761, 2020.",
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+                            ],
+                            "index": 19
+                        }
+                    ],
+                    "index": 18.5,
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+                                    "content": "A ADDITIONAL EVIDENCE FOR IMPLICIT UNDER-PARAMETERIZATION",
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+                                    "content": "• For the final point in this section, we verify if the non-stationarity of the policy in the Q-",
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+                                    "score": 1.0,
+                                    "content": "of the control objective. To illustrate this, we ran an experiment in the control setting",
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+                                    "score": 1.0,
+                                    "content": "(computed using tabular Q-evaluation) instead of using the bootstrap TD",
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+                                    "score": 1.0,
+                                    "content": "estimate. The results, shown in figure A.11a, show that the srank",
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+                                    "score": 1.0,
+                                    "content": "icantly when regressing to true control values and infact increases with more iterations as",
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+                                    "score": 1.0,
+                                    "content": "compared to Figure 6a where rank drops with bootstrapping. This experiment, alongside",
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+                        },
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+                                    "score": 1.0,
+                                    "content": "with experiments discussed above, ablating bootstrapping in the stationary policy evalua-",
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+                                    "content": "A.4 HOW DOES IMPLICIT REGULARIZATION INHIBIT DATA-EFFICIENT RL?",
+                                    "type": "text"
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+                                    "content": "Implicit under-parameterization leads to a trade-off between minimizing the TD error vs. encourag-",
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+                                    "score": 1.0,
+                                    "content": "ing low rank features as shown in Figure 4b. This trade-off often results in decrease in effective rank,",
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+                                    "score": 1.0,
+                                    "content": "at the expense of increase in TD error, resulting in lower performance. Here we present additional",
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+                                    "score": 1.0,
+                                    "content": "evidence to support this.",
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+                                    "score": 1.0,
+                                    "content": "• For the final point in this section, we verify if the non-stationarity of the policy in the Q-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
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+                            "spans": [
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+                                    "score": 1.0,
+                                    "content": "learning (control) setting, i.e., when the Bellman optimality operator is used is not a reason",
+                                    "type": "text"
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+                                    "score": 1.0,
+                                    "content": "behind the emergence of implicit under-parameterization. The non-stationary policy in a",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
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+                            "spans": [
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "control setting causes the targets to change and, as a consequence, leads to non-zero er-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "rors. However, rank drop is primarily caused by bootstrapping rather than non-stationarity",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
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+                                    "score": 1.0,
+                                    "content": "of the control objective. To illustrate this, we ran an experiment in the control setting",
+                                    "type": "text"
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+                                    "score": 1.0,
+                                    "content": "on Gridworld, regressing to the target computed using the true value function",
+                                    "type": "text"
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+                                    "type": "inline_equation"
+                                },
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+                                    "score": 1.0,
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+                                    "type": "text"
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+                                    "type": "inline_equation"
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+                                    "score": 1.0,
+                                    "content": "(computed using tabular Q-evaluation) instead of using the bootstrap TD",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
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+                                    "score": 1.0,
+                                    "content": "estimate. The results, shown in figure A.11a, show that the srank",
+                                    "type": "text"
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+                                    "type": "inline_equation"
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+                                {
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+                                    "score": 1.0,
+                                    "content": "doesn’t decrease signif-",
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+                                    "score": 1.0,
+                                    "content": "icantly when regressing to true control values and infact increases with more iterations as",
+                                    "type": "text"
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+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
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+                                    "score": 1.0,
+                                    "content": "compared to Figure 6a where rank drops with bootstrapping. This experiment, alongside",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "with experiments discussed above, ablating bootstrapping in the stationary policy evalua-",
+                                    "type": "text"
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+                            ],
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+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "tion setting shows that rank-deficiency is caused due to bootstrapping.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
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+                    ],
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+                                    "score": 1.0,
+                                    "content": "A.4 HOW DOES IMPLICIT REGULARIZATION INHIBIT DATA-EFFICIENT RL?",
+                                    "type": "text"
+                                }
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+                                    "content": "Implicit under-parameterization leads to a trade-off between minimizing the TD error vs. encourag-",
+                                    "type": "text"
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+                                    "score": 1.0,
+                                    "content": "ing low rank features as shown in Figure 4b. This trade-off often results in decrease in effective rank,",
+                                    "type": "text"
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+                                    "score": 1.0,
+                                    "content": "at the expense of increase in TD error, resulting in lower performance. Here we present additional",
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+                                    "score": 1.0,
+                                    "content": "evidence to support this.",
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+                                    "score": 1.0,
+                                    "content": "Figure A.11b shows a gridworld problem with one-hot features, which naturally leads to reduced",
+                                    "type": "text"
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+                                    "score": 1.0,
+                                    "content": "for longer can increase feature rank. This",
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+                                    "score": 1.0,
+                                    "content": "experiment uses a policy iteration style",
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+                                    "score": 1.0,
+                                    "content": "setup but the essential trend of rank drop",
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+                                    "score": 1.0,
+                                    "content": "as we train more does not occur.",
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+                                    "type": "inline_equation"
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+                                    "type": "text"
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+                                    "score": 1.0,
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+                                    "type": "text"
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+                                    "type": "text"
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+                                    "content": "decreases unlike the case in Figure 4a, where it remains same or even increases. The method is able",
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+                                    "score": 1.0,
+                                    "content": "decreases unlike the case in Figure 4a, where it remains same or even increases. The method is able",
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+                                    "content": "to learn policies that attain good performance as well. Hence, this justifies that when there’s very",
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+                                    "score": 1.0,
+                                    "content": ". This provides evidence showing that typical Q-networks learn",
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+                                    "content": "{ \\bf R } + \\gamma P ^ { \\pi } { \\bf Q } _ { k }",
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+                                            "content": "Figure A.12: TD error vs. Effective rank on Atari. We observe that Huber-loss TD error is often higher when",
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+                                    "score": 1.0,
+                                    "content": "with and without penalty respectively.",
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+                                    "content": "Theorem 4.1 also holds approximately as we discuss at the end of Appendix C.",
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+                                    "content": ". Since eigenvalues are only defined for a square matrix",
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+                                    "score": 1.0,
+                                    "content": "retical abstraction that cannot be computed in practice as it depends on the Green’s kernel (Duffy,",
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+                                    "content": "2015) obtained by assuming that the neural network behaves as a kernel regressor. Instead, we com-",
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+                                    "score": 1.0,
+                                    "content": "is the practical counterpart for the matrix, S, when",
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+                                    "score": 1.0,
+                                    "content": "using neural networks (as also indicated by the analysis in Section 4.2). In fact, on the gridworld",
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+                                    "score": 1.0,
+                                    "content": "(Figure A.21), we experiment with a feature",
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+                                    "score": 1.0,
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+                                    "content": "\\dim ( \\phi ( \\mathbf { s } , \\mathbf { a } ) ) = | S | | { \\mathcal { A } } |",
+                                    "type": "inline_equation"
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+                                    "content": ", with the same number of parameters as a kernel parameterization",
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+                                    "content": "\\begin{array} { r } { Q ( \\mathbf { s } , \\mathbf { a } ) = \\sum _ { \\mathbf { s } ^ { \\prime } , \\mathbf { a } ^ { \\prime } } \\mathbf { w } ( \\mathbf { s } ^ { \\prime } , \\mathbf { a } ^ { \\prime } ) k ( \\mathbf { s } , \\mathbf { a } , \\mathbf { s } ^ { \\prime } , \\mathbf { a } ^ { \\prime } ) } \\end{array}",
+                                    "type": "inline_equation"
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+                                    "score": 1.0,
+                                    "content": ". This can also be considered as perform-",
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+                                    "score": 1.0,
+                                    "content": "ing gradient descent on a “wide” linear network , and we measure the feature rank while observing",
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+                                    "score": 1.0,
+                                    "content": ", and we find that in practical scenarios (Figures A.20 and A.21), sran",
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+                                    "content": "\\qquad \\leqslant \\delta \\bigl ( \\Phi \\bigr ) \\approx",
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+                                    "score": 1.0,
+                                    "content": "with an extremely similar qualitative trend we believe that Theorem 4.1 still explains",
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+                                    "score": 1.0,
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+                                    "score": 1.0,
+                                    "content": "with an extremely similar qualitative trend we believe that Theorem 4.1 still explains",
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+                                            "content": "on the gridworld in the offline setting (left) and the",
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+                                            "content": "\\mathrm { d i m } ( \\phi ( \\mathbf { s } , \\mathbf { a } ) ) = | S | | \\mathcal { A } |",
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+                                            "score": 1.0,
+                                            "content": ". Note that both notions",
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+                                    "score": 1.0,
+                                    "content": "corresponding unnormalized plots are found in Figure A.6). In these plots, each unit on the",
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+                                    "content": "consists of a 256-cell grid, with walls arising randomly with a probability of 0.2. Each state allows 5",
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+                                    "content": ". The features for this Q-function",
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+                                    "content": "semi-definite, since all eigenvalues are positive and real. Now by using the proof for Lemma C.1.1,",
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+                                    "content": "note that the above argument applies even with the approximation, proving the required result on the",
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+                                    "score": 1.0,
+                                    "content": ". Earlier in this proof, we showed that the ratio",
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+                                    "score": 1.0,
+                                    "content": "between singular values is bounded above by a monotonically decreasing function",
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+                                    "content": "semi-definite, since all eigenvalues are positive and real. Now by using the proof for Lemma C.1.1,",
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+                                    "content": "equation. In order to do so, we make an assumption similar to but not identical as Arora et al. (2018),",
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+                                    "content": "for all fitting iterations",
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+                                    "score": 1.0,
+                                    "content": ". Assume balanced initialization only for the first",
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+                                    "content": "N - 1",
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+                                    "content": "layers, i.e.,",
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+                                    "content": "\\mathbf { W } _ { j + 1 } ( 0 , 0 ) ^ { T } \\mathbf { W } _ { j + 1 } ( 0 , 0 ) =",
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+                                    "content": "\\mathbf { W } _ { j } ( 0 , 0 ) \\mathbf { W } _ { j } ( 0 , 0 ) ^ { T } , \\forall j \\in { 1 , \\cdots , N - 2 } .",
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+                                    "content": ". Then the weights remain balanced throughout, i.e.",
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+                                    "content": ". Assume balanced initialization only for the first",
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+                                    "content": "\\mathbf { W } _ { j } ( 0 , 0 ) \\mathbf { W } _ { j } ( 0 , 0 ) ^ { T } , \\forall j \\in { 1 , \\cdots , N - 2 } .",
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+                                    "score": 1.0,
+                                    "content": ". Then the weights remain balanced throughout, i.e.",
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+                                    "content": "loss function. Formalizing this, we can show inductively that the weights will remain balanced",
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+                                    "score": 1.0,
+                                    "content": "within each fitting iteration. Thus, we have shown the",
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+                                    "score": 1.0,
+                                    "content": "result in Equation D.4.",
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+                                    "score": 1.0,
+                                    "content": "techniques and results from Arora et al. (2019) to study properties of the singular value evolution",
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+                                    "content": "and hence, discuss properties related to the effective rank of the matrix,",
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+                                    "content": "Lemma D.0.2 ((Extension of Theorem 1 from Arora et al. (2018)). Under conditions specified in",
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+                                    "content": "\\begin{array} { r } { \\dot { N } _ { \\phi } ( k , t ) = - \\eta \\sum _ { j = 1 } ^ { N - 1 } \\left[ \\mathbf { W } _ { \\phi } ( k , t ) \\mathbf { W } _ { \\phi } ( k , t ) ^ { T } \\right] ^ { \\frac { N - j } { N - 1 } } \\cdot \\mathbf { W } _ { N } ( k , t ) ^ { T } \\frac { d L _ { k } ( \\mathbf { W } _ { N + 1 } ( k , t ) ) } { d \\mathbf { W } _ { N - 1 } } \\cdot \\left[ \\mathbf { W } _ { \\phi } ( k , t ) ^ { T } \\mathbf { W } _ { \\phi } ( k , t ) \\right] ^ { \\frac { j - 1 } { N - 1 } } . } \\end{array}",
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+                                    "type": "inline_equation"
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+                                    "content": ". The belancedness condition re-written using SVD of the weight matrices is equivalent to",
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+                                    "score": 1.0,
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+                                    "score": 1.0,
+                                    "content": "take are the same. Note the distinction from Arora et al. (2018), where they apply balancedness on",
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+                                    "content": "all matrices, and that in our case would trivially give a rank-1 matrix.",
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+                                    "content": "\\begin{array} { r } { \\dot { N } _ { \\phi } ( k , t ) = - \\eta \\sum _ { j = 1 } ^ { N - 1 } \\left[ \\mathbf { W } _ { \\phi } ( k , t ) \\mathbf { W } _ { \\phi } ( k , t ) ^ { T } \\right] ^ { \\frac { N - j } { N - 1 } } \\cdot \\mathbf { W } _ { N } ( k , t ) ^ { T } \\frac { d L _ { k } ( \\mathbf { W } _ { N + 1 } ( k , t ) ) } { d \\mathbf { W } _ { N - 1 } } \\cdot \\left[ \\mathbf { W } _ { \\phi } ( k , t ) ^ { T } \\mathbf { W } _ { \\phi } ( k , t ) \\right] ^ { \\frac { j - 1 } { N - 1 } } . } \\end{array}",
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+                                    "score": 1.0,
+                                    "content": "in this section, for ease of notation.",
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+                                    "content": ". The belancedness condition re-written using SVD of the weight matrices is equivalent to",
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+                                    "content": "Proof of Proposition 4.1. Finally, we are ready to use Lemma D.0.2 to prove the relationship with",
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+                                            "content": "grow at a disproportionately higher rate than other smaller singular values as described by equation 4 .",
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+                                    "score": 1.0,
+                                    "content": ". To see this, let’s",
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+                                    "score": 1.0,
+                                    "content": "et al. (2019)). Thus, we can assume that",
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+                                    "content": "\\dot { \\sigma } _ { r } ( k , t ) = - N \\left( \\sigma _ { r } ^ { 2 } ( k , t ) \\right) ^ { 1 - 1 / N } \\cdot \\mathbf { f } ( k , t ) \\cdot \\mathbf { e } _ { r } \\cdot \\mathbf { d } _ { r } .",
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+                                    "content": "is multiplied to the expression of the gradient in our case.",
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+                                    "score": 1.0,
+                                    "content": "By using the fact that the expression for",
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+                                    "score": 1.0,
+                                    "content": "is shared across all singular values, we can obtain",
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+                                    "type": "text"
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+                                    "score": 1.0,
+                                    "content": ". Integrating, we can show",
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+                                    "score": 1.0,
+                                    "content": "that depending upon the ratio",
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+                                    "content": "\\frac { \\mathbf { e } _ { r } { \\cdot } \\mathbf { d } _ { r } } { \\mathbf { e } _ { r ^ { \\prime } } { \\cdot } \\mathbf { d } _ { r ^ { \\prime } } }",
+                                    "type": "inline_equation"
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+                                    "content": ", and the value of",
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+                                    "content": "\\sigma _ { r ^ { \\prime } } ( k , t )",
+                                    "type": "inline_equation"
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+                            ],
+                            "index": 7
+                        },
+                        {
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "will take on different magnitude values, in particular, they will grow at disproportionate rates. By",
+                                    "type": "text"
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+                            ],
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+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "then appealing to the result from Proposition 4.1 in Section 4.1 (kernel regression argument), we can",
+                                    "type": "text"
+                                }
+                            ],
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+                        },
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+                                    "content": "(see Equation D.10 and Arora et al. (2019), Equation 11) and hence, the value of",
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+                                    "score": 1.0,
+                                    "content": "at a given iteration gets propagated into the next iteration. We first illustrate this compounding effect",
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+                                    "content": "and then discuss Theorem 4.2 as a special case of this phenomenon.",
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+                                    "content": "then appealing to the result from Proposition 4.1 in Section 4.1 (kernel regression argument), we can",
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+                                    "content": "). Now, we will argue that for a given",
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+                                    "score": 1.0,
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+                                    "content": "indicating a non-zero value of regularization.",
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+                                    "content": "D.2 PROOF OF PROPOSITION 4.2: COMPOUNDING RANK DROP IN SECTION 4.2",
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+                                    "content": "In this section, we illustrate that the rank drop effect compounds due to bootstrapping and prove",
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+                                    "content": "Proposition 4.2 formally. Our goal is to demonstrate the compounding effect: a change in the rank",
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+                                    "score": 1.0,
+                                    "content": "at a given iteration gets propagated into the next iteration. We first illustrate this compounding effect",
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+                                    "content": "and then discuss Theorem 4.2 as a special case of this phenomenon.",
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+                                    "content": ". That is, if",
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+                                    "content": "ping, note that we can use Assumption D.2 and D.1 to observe the following relation:",
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+                                    "content": "\\begin{array} { r l r } { \\mathrm { s r a n k } _ { \\delta } ( \\mathbf { W } _ { \\phi } ( k ) ) } & { \\leq \\mathrm { s r a n k } _ { \\delta } ( \\mathbf { W } _ { \\phi } ^ { P } ( k ) ) - \\displaystyle \\frac { | | \\mathbf { Q } _ { k } - \\mathbf { y } _ { k } | | } { \\lambda _ { k } } } & { \\mathrm { ( s i n c e ~ w e ~ c a n ~ c o p y ~ o v e r ~ t h e ~ w e i g h t s ) } } \\\\ & { \\leq \\mathrm { s r a n k } _ { \\delta } ( \\mathbf { W } _ { \\phi } ( k - 1 ) ) + c _ { k } - \\displaystyle \\frac { | | \\mathbf { Q } _ { k } - \\mathbf { y } _ { k } | | } { \\lambda _ { k } } } & { \\mathrm { ( u s i n g ~ A s s u m p t i o n ~ D . 2 ) } } \\\\ & { \\leq \\mathrm { s r a n k } _ { \\delta } ( \\mathbf { W } _ { \\phi } ( k - 2 ) ) + c _ { k - 1 } - \\displaystyle \\frac { | | \\mathbf { Q } _ { k - 1 } - \\mathbf { y } _ { k - 1 } | | } { \\lambda _ { k - 1 } } + c _ { k } - \\displaystyle \\frac { | | \\mathbf { Q } _ { k } - \\mathbf { y } _ { k } | | } { \\lambda _ { k } } } \\\\ & { \\mathrm { s r a n k } _ { \\delta } ( \\mathbf { W } _ { \\phi } ( k ) ) \\leq \\left| \\mathrm { s r a n k } _ { \\delta } ( \\mathbf { W } _ { \\phi } ( 0 ) ) + \\displaystyle \\sum _ { j = 1 } ^ { k } c _ { j } - \\displaystyle \\sum _ { j = 1 } ^ { k } \\displaystyle \\frac { | | \\mathbf { Q } _ { j } - \\mathbf { y } _ { j } | | } { \\lambda _ { j } } \\right| } & { \\mathrm { ( D ~ } } \\end{array}",
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+                                    "content": "point with an equal srank, we will obtain a better solution at the optimum with a smaller srank",
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+                                    "content": "in Equation 5. We then use Assumption D.2 to relate",
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+                                    "content": ", which gives us a recursive inequality. Finally, the last two",
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+                                    "score": 1.0,
+                                    "content": "Now if the decrease in effective rank due to accumulating TD errors is larger than the possible",
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+                                    "content": ", then we observe a rank drop. Also note that",
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+                                    "content": "can be negative, in which case both terms contribute to a drop in rank. But in the most general",
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+                                    "content": ", can also be positive for some iterations. This equation indicates how a change in in rank in",
+                                    "type": "text"
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+                        },
+                        {
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+                                    "content": "one iteration gets compounded on the next iteration due to bootstrapping.",
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+                    ],
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+                                    "content": "What can we comment about the general value of",
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+                                    "content": "can be positive, for example when the ad-",
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+                                    "score": 1.0,
+                                    "content": "dition of the reward and dynamics projection increases srank.",
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+                                    "score": 1.0,
+                                    "content": "Our current set of assumptions are insufficient to guarantee",
+                                    "type": "text"
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+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "something about",
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+                                    "score": 1.0,
+                                    "content": "in the general case and more assumptions",
+                                    "type": "text"
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+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "are needed. For instance, as shown in Theorem 4.2, under",
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+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "Assumption D.1, we obtain that if we are in a small neighbor-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "hood around the fixed point, we will find that",
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+                                    "content": "c _ { k } \\leq 0",
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+                                    "score": 1.0,
+                                    "content": ".",
+                                    "type": "text"
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+                    "type": "text",
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+                                    "content": "Empirical verification: While our analysis does not dictate",
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+                                    "score": 1.0,
+                                    "content": ", we performed an experiment on Seaquest",
+                                    "type": "text"
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+                                    "content": "to approximately visualize",
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+                                    "content": "\\begin{array} { r l r } { \\mathrm { s r a n k } _ { \\delta } ( \\mathbf { W } _ { \\phi } ( k ) ) } & { \\leq \\mathrm { s r a n k } _ { \\delta } ( \\mathbf { W } _ { \\phi } ^ { P } ( k ) ) - \\displaystyle \\frac { | | \\mathbf { Q } _ { k } - \\mathbf { y } _ { k } | | } { \\lambda _ { k } } } & { \\mathrm { ( s i n c e ~ w e ~ c a n ~ c o p y ~ o v e r ~ t h e ~ w e i g h t s ) } } \\\\ & { \\leq \\mathrm { s r a n k } _ { \\delta } ( \\mathbf { W } _ { \\phi } ( k - 1 ) ) + c _ { k } - \\displaystyle \\frac { | | \\mathbf { Q } _ { k } - \\mathbf { y } _ { k } | | } { \\lambda _ { k } } } & { \\mathrm { ( u s i n g ~ A s s u m p t i o n ~ D . 2 ) } } \\\\ & { \\leq \\mathrm { s r a n k } _ { \\delta } ( \\mathbf { W } _ { \\phi } ( k - 2 ) ) + c _ { k - 1 } - \\displaystyle \\frac { | | \\mathbf { Q } _ { k - 1 } - \\mathbf { y } _ { k - 1 } | | } { \\lambda _ { k - 1 } } + c _ { k } - \\displaystyle \\frac { | | \\mathbf { Q } _ { k } - \\mathbf { y } _ { k } | | } { \\lambda _ { k } } } \\\\ & { \\mathrm { s r a n k } _ { \\delta } ( \\mathbf { W } _ { \\phi } ( k ) ) \\leq \\left| \\mathrm { s r a n k } _ { \\delta } ( \\mathbf { W } _ { \\phi } ( 0 ) ) + \\displaystyle \\sum _ { j = 1 } ^ { k } c _ { j } - \\displaystyle \\sum _ { j = 1 } ^ { k } \\displaystyle \\frac { | | \\mathbf { Q } _ { j } - \\mathbf { y } _ { j } | | } { \\lambda _ { j } } \\right| } & { \\mathrm { ( D ~ } } \\end{array}",
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+                                    "content": ", which gives us a recursive inequality. Finally, the last two",
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+                                    "content": "can be negative, in which case both terms contribute to a drop in rank. But in the most general",
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+                                    "content": ", can also be positive for some iterations. This equation indicates how a change in in rank in",
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+                                    "content": "can be positive, for example when the ad-",
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+                                    "content": "dition of the reward and dynamics projection increases srank.",
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+                                    "score": 1.0,
+                                    "content": ". As shown in Figure D.2, the value of the",
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+                                    "content": "\\displaystyle \\ d _ { \\mathrm { : } } ( W _ { \\phi } ( k , T ) )",
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+                                    "content": "(Assumption D.1) from Section D.2.",
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diff --git a/parse/train/O9bnihsFfXU/O9bnihsFfXU_model.json b/parse/train/O9bnihsFfXU/O9bnihsFfXU_model.json
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index 0000000000000000000000000000000000000000..e533e3c75be6792ca5ca17586426ae5c49cf6dc8
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diff --git a/parse/train/z-X_PpwaroO/z-X_PpwaroO.md b/parse/train/z-X_PpwaroO/z-X_PpwaroO.md
new file mode 100644
index 0000000000000000000000000000000000000000..6b532652488c1ce1d724d39bd1a4359c23384483
--- /dev/null
+++ b/parse/train/z-X_PpwaroO/z-X_PpwaroO.md
@@ -0,0 +1,271 @@
+# Computer-Aided Design as Language
+
+Yaroslav Ganin1∗ Sergey Bartunov1 Yujia Li1 Ethan Keller2 Stefano Saliceti1 1DeepMind 2Onshape
+
+# Abstract
+
+Computer-Aided Design (CAD) applications are used in manufacturing to model everything from coffee mugs to sports cars. These programs are complex and require years of training and experience to master. A component of all CAD models particularly difficult to make are the highly structured 2D sketches that lie at the heart of every 3D construction. In this work, we propose a machine learning model capable of automatically generating such sketches. Through this, we pave the way for developing intelligent tools that would help engineers create better designs with less effort. The core of our method is a combination of a generalpurpose language modeling technique alongside an off-the-shelf data serialization protocol. Additionally, we explore several extensions allowing us to gain finer control over the generation process. We show that our approach has enough flexibility to accommodate the complexity of the domain and performs well for both unconditional synthesis and image-to-sketch translation.
+
+# 1 Introduction
+
+Computer-Aided Design (CAD) is used in the production of most manufactured objects: from cars to robots to stents to power plants. CAD has replaced pencil drawings with precise computer sketches, enabling unparalleled precision, flexibility, and speed. Despite these improvements the CAD engineer must still develop, relate and annotate all the minutiae of their designs with the same attention to detail as their draftingtable forebears. CAD productivity might be improved by the careful application of machine learning to automate predictable design tasks and free the engineer to focus on the bigger picture. The flexibility and power of deep learning is uniquely suited to the complexity of design.
+
+Sketches are at the heart of mechanical CAD. They are the skeleton from which three dimensional forms are made. A sketch consists of various geometric entities (e.g., lines, arcs, splines and circles) related by specific constraints such as tangency, perpendicularity and symmetry. Figure 1 illustrates how entities and constraints work in tandem to create well-defined shapes. Geometric entities lie on a single plane and together form enclosed regions used by subsequent construction operations such as lofts and extrusions to generate complex
+
+![](images/801c01a8f7ad74854fddf78e6c8c49c6d66b6df145afc636cd0e89cfc38f010b.jpg)  
+Figure 1: The anatomy of a CAD sketch. Sketches are the main building block of every 3D construction. A sketch consists of entities (e.g., lines and arcs) and constraints (e.g., tangent and mirror). The dotted curve shows what happens if we drop some of the constraints — the design idea is lost.
+
+![](images/768010495993ed4419100a195bad75e3db43476e171ff7bd23282a293c1f8bdc.jpg)  
+Figure 2: Interpreter-guided generation of a sketch. At each point in time, a Transformer [33] outputs a raw value which is fed into an interpreter that decides which field of a Protocol Buffers message this value corresponds to. Once the field is populated the interpreter communicates $( -  )$ its decision back to the Transformer and transitions $( \nrightarrow )$ to the next state.
+
+3D geometry. Well-chosen sketch constraints are essential to properly convey design intent [2] and facilitate the sketch’s resilience to successive parameters modifications which is often understood as a measure of the quality of a design document [8]. The dotted curve in Figure 1 shows what happens when some of the constraints are dropped – the design idea is lost.
+
+The complexities of sketch construction are analogous to those of natural language modeling. Selecting the next constraint or entity in a sketch is like the generation of the next word in a sentence. In both contexts, the selection must function grammatically (form a consistent constraint system in the case of the sketch) and work towards some cohesive meaning (preserve design intent). Luckily, machine learning has proved highly successful in generating natural language — especially the Transformer [33] trained on vast amounts of real-world data [26, 6]. It is therefore a promising choice for adapting to the task of sketch generation. This work is our take at this adaptation.
+
+We make the following contributions: (1) We devise a method for describing structured objects using Protocol Buffers [32] and demonstrate its flexibility on the domain of natural CAD sketches. (2) We propose several techniques for capturing distributions of objects represented as serialized Protocol Buffers. Our approach draws inspiration from recent advances in language modeling while focusing on eliminating data redundancy. (3) We collect a dataset of over $4 . 7 \mathbf { M }$ of carefully preprocessed parametric CAD sketches and use this dataset to validate the proposed generative models. To our knowledge, the experiments presented in this work significantly surpass the scale of those reported in the literature both in terms of the amount of training data and the model capacity.
+
+# 2 Related work
+
+Datasets and generative models for CAD. Until recently there were very few parametric CAD datasets large and varied enough to serve as training data for machine learning. This situation had started to change with the release of the ABC dataset [16] containing a collection of 3D shapes from the Onshape public repository [22]. Unfortunately, the main focus of [16] revolves around meshes and, as a result, the dataset is difficult to use for sketch modeling.
+
+Several works concurrent with ours deal with the symbolic representation of CAD constructions. Seff et al. [31] center their attention on contributing a better dataset of 2D sketches but also provide a proof-of-concept model predicting a selected subset of object attributes. Willis et al. [37] use the dataset from [31] to train a modification of [21] which demonstrates a boost in generation quality but is designed to only work for sketch entities. The latter is addressed in our present work and in a subsequent paper by Para et al. [24]. While [24] employ very similar ideas to ours they do not support certain features of the CAD data and their proposed model is a more direct adaptation of [21] and therefore cannot handle arbitrary orderings of entities and constraints. In Section 5, we show that object ordering has a substantial impact on the performance.
+
+Fusion 360 Gallery [36] attacks CAD data from a different angle. Here, the task is to recover a sequence of extrusion operations that gives rise to a particular target 3D shape. Despite dealing with 3D, this setting is deliberately limited: sketches are assumed to be given and the proposed model only decides on which sketch to extrude and to what extent. [38] considers a more general scenario where extrusion profiles are not provided and need to be synthesized from scratch. Although both of these works make initial steps towards full parametric CAD generation, they rely on significant simplifying assumptions and therefore it is unclear how well they will scale to more real-world scenarios. Our approach, on the other hand, is designed to be flexible and domain-agnostic and is only limited by the data availability.
+
+Vector image generation and inference. Synthesizing CAD sketches bears a lot of similarities with predicting vector graphics. In this field, several recent works Carlier et al. [7] and Reddy et al. [30] using different vector object representations to define generative models of vector images. Egiazarian et al. [13] take a more traditional computer vision approach and propose a multi-stage pipeline for vectorizing technical drawings. All of these methods use highly domain-dependent architectures and, therefore, it would be a non-trivial task to adapt them for generation of complex sketch objects. CAD community has also been concerned with a similar task of image to CAD conversion [20, 34, 10, 11], largely focusing on heuristic object recognition while our work relies more on learning the recognition from data.
+
+Transformers for sequence modeling. In our work, we employ Transfomers [33] as a computational backbone for the proposed approach. Due to its scalability and excellent performance [29, 9, 6, 27], this architecture has become the dominating approach in many sequence modeling applications. Our method can be seen as generalization of PolyGen [21], a Transformer-based generative model for 3D meshes. Similarly to [21], we use Pointer Networks [35] to relate items in the synthesized sequence. Unlike PolyGen, however, our framework can handle non-homogeneous structures of arbitrary complexity. Moreover, we simplify the architecture to use a single neural network to generate the entire object of interest. All these improvements make our approach a good fit for modeling CAD sketches and potentially other components of CAD constructions.
+
+# 3 Data
+
+Formally, a CAD sketch is defined by two collections of objects: entities and constraints. Each object is generally represented as a set of attribute-value pairs where a value can be either primitive (e.g., integer or floating-point) or complex (e.g., an array or another object). Sketches that we use in this work originate from the Onshape platform [22] which provides them in JSON format [25]. As the first step in our processing pipeline we convert JSON messages into Protocol Buffers (PB) [32]. In order to keep the pipeline as domain-agnostic and as widely applicable as possible, we aim to avoid any significant changes to the data and largely retain the original structures of objects. The benefit of converting into PB is twofold: the resulting data occupies less space because unnecessary information is removed, but also, unlike JSON, PB provide a convenient way to define precise specifications for structures of arbitrary complexity.
+
+Listing 1a shows how we represent the line entity and the mirror constraint (see Appendix A for an extensive list of supported objects). The line specification is straightforward: we first need to decide whether our entity should be treated as a construction geometry2 and then provide pairs of coordinates for the beginning and end of the segment. The MirrorConstraint is used to force an arbitrary number of pairs of geometries (i.e., mirrored_pairs) to be symmetrical with respect to some axis (i.e., mirror). Constraints rely on the Pointer data type to specify entities they act upon. In practice, a pointer is simply an index in the table of all the eligible pointees (i.e., entities and their parts).
+
+message LineEntity { bool is_construction $\ c = ~ 1$ ; message Vector $\{ \begin{array} { r l } \end{array}  / / $ 2D coordinate. double $\texttt { x } = \texttt { 1 }$ ; double $\tt { y } = 2$ ; } Vector start $= ~ 2$ ; // Start point. Vector end $\ c = \ 3$ ; // End point.   
+}   
+message MirrorConstraint { Pointer mirror $\ c = ~ 1$ ; // Axis of symmetry. message Pair { // Mirrored objects. Pointer first $\ l = \ 1$ ; Pointer second $= ~ 2$ ; } repeated Pair mirrored_pairs $= ~ 2$ ;   
+}
+
+(a) Entities and constraints have similar structures. Pointers refer to entities that constraints are applied to.
+
+message Entity { oneof kind { LineEntity line $\ l = \ 1$ ; // And other entity types. }   
+}   
+message Object { oneof kind { Entity entity $\ l = \ 1$ ; Constraint constraint $= ~ 2$ ; }   
+}   
+message Constraint { // Defined similarly to Entity.   
+}   
+message Sketch { repeated Object objects $\ c = ~ 1$ ;   
+}
+
+(b) A full sketch is defined as a sequence of objects each of which can be either an entity or a constraint.
+
+Listing 1: Examples of object specifications. We represent objects using Protocol Buffers. Protocol Buffers allow us to easily write specifications for structured objects of varying complexity.
+
+Our ultimate goal is to build a machine learning model of sketch objects. To that end, we process the data even further and represent these objects as sequences of tokens. This allows us to pose sketch generation as language modeling (LM) and take advantage of the recent progress in this area [26, 6]. To achieve this, we pack first collections of entities and constraints into one Protocol Buffer message (see Listing 1b) assuming some ordering of objects. We discuss different orderings in Section 5.
+
+There are a few ways to obtaining a sequence of tokens from a sketch message. Arguably the most intuitive one is to format messages as text. For a line entity connecting (0.0, 0.1) and $( - 0 . 5 , 0 . 2 )$ this will result in:
+
+{ is_construction: true, start { x: 0.0, y: 0.1 }, end { x: -0.5, y: 0.2 } }
+
+Since this format contains both the structure and the content of the data, the resulting sequences end up being prohibitively long. Additionally, the model would have to generate valid syntax, which would take up some portion of the model’s capacity. To overcome these challenges, we work with two flavours of serialized PB messages.
+
+The first one is a sequences of bytes obtained by calling the SerializeToString() method of a message. Such sequences are much shorter since the structure is handled by an external parser automatically generated from the data specification. The parser’s task is to interpret the incoming stream of unstructured bytes and populate the fields of PB messages. However, like the text format, not every sequence of bytes results in a valid PB message.
+
+Going one step further, we can utilize the structure of the sketch format more directly, and build a custom interpreter, that takes as input a sequence of tokens each representing a valid choice at various decision steps [4] in the sketch creation process. We designed this interpreter in such a way that all sequences of tokens in this format lead to valid PB messages. More specifically, we represent a message as a sequence of triplets $( d _ { i } , c _ { i } , f _ { i } )$ where $i$ is an index of the token. The majority of tokens describe basic fields of the sketch objects with each token representing exactly one field. The first two positions in each triplet are allocated for a discrete value and a continuous value respectively. Since each field in a message is either discrete or continuous only one of two positions is active at a time (the other one is set to a default zero value). The third component is a boolean flag signifying the end of a repeated field3 which contains a list of elements of the same type. An example sequence for a sketch containing a line and a point placed at one of its ends is shown in Table 1 (Triplet column).
+
+<table><tr><td>Triplet</td><td>Field</td><td></td><td>Triplet</td><td>Field</td></tr><tr><td>1.</td><td>(0,0.0,False)</td><td>objects.kind</td><td>8. (0,0.0,False)</td><td>objects.kind</td></tr><tr><td>2.</td><td>(0,0.0,False)</td><td>entity.kind</td><td>9. (1, 0.0,False)</td><td>entity.kind</td></tr><tr><td>3.</td><td>(1,0.0,False)</td><td>line.is_constr</td><td>10. (0, 0.0,False)</td><td>Point point.is_const</td></tr><tr><td>4.</td><td>(0, 0.0,False)</td><td>line.start.x</td><td>11. (0, 0.0,False)</td><td>point .x</td></tr><tr><td>5.</td><td>(0,0.1,False)</td><td>line.start.y</td><td>12. (0,0.1,False)</td><td>point.y</td></tr><tr><td>6.</td><td>(0,-0.5,False)</td><td>line.end.x</td><td>13. (0, 0.0, True)</td><td>objects.kind</td></tr><tr><td>7.</td><td>(0, 0.2,False)</td><td>line.end.y</td><td></td><td></td></tr></table>
+
+Table 1: A triplet representation of a simple sketch. The sketch contains and a line and a point. Within each triplet in the left column, the active component (the value that is actually used) is highlighted in bold. The right column shows which field of the object the triplet is associated with.
+
+Given a sequence of such triplets, it is possible to infer which exact field each token corresponds to. Indeed, the very first token $( d _ { 1 } , c _ { 1 } , f _ { 1 } )$ is always associated with objects.kind since it is the first choice that needs to be made to create a Sketch message (see Listing 1b). The second field depends on the concrete value of $d _ { 1 }$ . If $d _ { 1 } = 0$ then the first object is an entity which means that the second token corresponds to entity.kind . The rest of the sequence is associated in a similar fashion. Field identifiers along with their locations within an object form the context of the tokens. We use this contextual information as an additional input for our machine learning models since it makes it easier to interpret the meaning of the triplet values and to be aware of the overall structure of the data.
+
+# 4 Model
+
+In order to estimate the distribution $p _ { \mathrm { d a t a } }$ of 2D sketches in a dataset $\mathcal { D }$ , we decompose the joint distribution over the sequence of tokens [19] $\mathbf { t } = ( t _ { 1 } , \ldots , t _ { N } )$ in an autoregressive fashion, representing each conditional with a neural network parameterized by $\theta$ and pose the estimation of $p _ { \mathrm { d a t a } }$ as maximization of the log-likelihood of $\mathcal { D }$ , i.e.,
+
+$$
+p ( t ; \theta ) = \prod _ { i = 1 } ^ { N } p ( t _ { i } \mid t _ { < i } ; \theta ) , \quad \sum _ { t \in \mathcal { D } } \log p ( t ; \theta ) \to \operatorname* { m a x } _ { \theta } ,
+$$
+
+where $N$ is the length of the sequence and $t _ { < i }$ denotes all the tokens preceding $t _ { i }$ .
+
+More concretely, we employ the Transformer decoder architecture [33] that takes an embedding of the token $\pmb { e } _ { i - 1 } \overset { \cdot } { = } \mathrm { e m b e d } _ { i } ^ { \cdot } ( t _ { i - 1 } ^ { \cdot } ) \in \mathbb { R } ^ { D }$ and maps it into another vector $\boldsymbol { h } _ { i }$ of the same dimensionality. The latter is decoded into parameters of $p ( t _ { i } \mid t _ { < i } )$ by a learned mapping $\mathsf { d i s t } _ { i } ( \cdot )$ .4
+
+Byte representation When dealing with the bytes of a PB message, each token is simply a discrete value in the range $\{ 0 , \dots , 2 5 5 \} \cup \{ \bar { \bf E 0 S } \}$ and therefore $p ( t _ { i } \mid t _ { < i } ; \bar { \theta ( \mathbf { \Sigma } ) }$ can be modeled as a categorical distribution similar to how it’s done in typical LM approaches [5]. In this setting, for each time step $i$ of the sequence we have
+
+$$
+\mathbf { e m b e d } _ { i } ( t _ { i - 1 } ) = V [ t _ { i - 1 } ] + e _ { i } ^ { \mathrm { p o s } } ,
+$$
+
+where $[ \cdot ]$ denotes the lookup operation and $e _ { i } ^ { \mathrm { p o s } }$ is a position embedding for position $i$ . Both $V$ and $e _ { i } ^ { \mathrm { p o s } }$ are learned. Moreover, $\forall i \ \mathtt { d i s t } _ { i }$ is the same linear projection into $\mathbb { R } ^ { 2 5 7 }$ (256 values and EOS) and the output is treated as logits of the distribution.
+
+Triplet representation In case of the triplet representation, we follow a slightly more involved procedure. As outlined in Section 3, tokens can be either discrete or continuous. Additionally, different discrete tokens may have different ranges of values. For example, there are only two possible values for the object.kind token – either to an entity or a constraint. On the other hand, the range of the entity.kind token has cardinality of 4 since we support 4 different types of sketch entities. This means that we can’t naively describe each conditional in Equation 1 using the same template distribution like we did for the bytes. We circumvent this by introducing the notion of token groups.
+
+A token group $\mathcal { G }$ is a collection of related token types that can be handled in a similar fashion. Specifically, we use the same embedding function and the same projection for every $t$ such that
+
+![](images/023d60da6886256697dbccdb13316caf4b192be89fcc2c3abc16679bb42ccf08.jpg)
+
+(a) Unconditional byte model.
+
+(b) Unconditional triplet model.
+
+![](images/6a078adb38e4e5126f04a58c9d202baf6dc4394bfc33aa9ce47e076d2e729d83.jpg)  
+Figure 3: Synthesized sketches and data. (a)–(c) show samples from various proposed models (we use Nucleus Sampling with top- $p = 0 . 9 ,$ ). In (c), the output is rendered in a slightly thicker style. (d) demonstrates samples from the unconditional model after applying predicted constraints (the output is in blue). (e) shows examples from the dataset.
+
+$\mathsf { t y p e } ( t ) \in \mathcal { G }$ . For instance, we might want to group all the tokens associated with coordinates. In the example from Table 1, tokens with indices 4–7 and 11–12 will all end up in the same $\mathcal { G } ^ { 5 }$ . Naturally, we use the same functional form for the output distribution $p ( t _ { i } \mid t _ { < i } ; \boldsymbol { \theta } )$ within each group.
+
+We embed $t _ { i - 1 }$ that belongs to the group $\mathcal { G }$ as (note the difference with Equation 2):
+
+$$
+K [ \mathbf { f i e l d } ( t _ { i - 1 } ) ] + V ^ { \mathcal { G } } [ t _ { i - 1 } ] + e _ { n } ^ { \mathrm { o b j } } + e _ { m } ^ { \mathrm { r e l } } ,
+$$
+
+where field $( t )$ returns the field of $t$ (e.g., objects.kind or line.start. $\mathtt { x }$ ) and $K$ is a collection of learnable embeddings for every possible field type. Unlike in Equation 2, instead of using global position embedding eposi w e describe the location with the index $n$ of the current object as well as the relative position $m$ of $t _ { i - 1 }$ within an object.
+
+We handle the “end” tokens (i.e., $f _ { i } = \mathrm { T r u e } )$ similarly to EOS in Section 4 — the output projection produces an additional logit used to compute the probability of ending the repetition. Since $f _ { i }$ is only expected to be True at particular points in the sequence (i.e., right after tokens forming a whole element of the list) we mask out the extra logit everywhere else. This ensures that the “end” token can’t be predicted prematurely and also eliminates its unnecessary contribution to the optimized objective.
+
+One significant difference between the byte setting and the triplet setting is how we process pointer fields. In the former, pointers do not get any special treatment and are generated just like any other integer field. We rely on the model’s capability to make sense of the entity part index and relate it to the corresponding locations in the sequence via attention weights. This seems to be a viable strategy since Transformers have demonstrated an impressive referencing capacity in recent works [6].
+
+Since the triplet representation provides us with direct access to the semantics of tokens it’s possible to relate pointers to their pointees more explicitly by using Pointer Networks [35]. The approach we are taking here is similar to [21]. In order to compute $p ( t _ { i } \mid t _ { < i } ; \theta )$ , we first project the output of the Transformer $\boldsymbol { h } _ { i }$ into the final pointer vector $p _ { i } = { W _ { \mathrm { p t r } } h _ { i } }$ . The conditional is then obtained as follows:
+
+$$
+\begin{array} { r } { p ( t _ { i } \mathrm { ~ p o i n t s ~ t o ~ } t _ { i k } \mid t _ { < i } ; \theta ) = \mathrm { s o f t m a x } _ { k } ( \pmb { p } _ { i } ^ { T } H _ { i } ) , \quad H _ { i } = [ \pmb { h } _ { i 1 } , \dots , \pmb { h } _ { i k } , \dots , \pmb { h } _ { i M } ] , } \end{array}
+$$
+
+where $\operatorname { s o f t m a x } _ { k }$ is the $k$ -th element of the softmax vector and $\boldsymbol { r } _ { i } = \{ t _ { i 1 } , . . . , t _ { i M } \}$ is the set of tokens that $t _ { i }$ can point to. Naturally, $\mathbf { \nabla } _ { \mathbf { r } _ { i } }$ only contains tokens from $t _ { < i }$ . This is different from [35, 21] where $\textstyle r _ { i } \equiv r$ is external to the predicted sequence and remains immutable throughout the generation process.
+
+In Onshape, constraints can be applied not only to whole entities but also to their subparts (e.g., the center of a circle or the end points of a line segment). To handle this, we introduce special referrable tokens decoupling pointees from the object attribute tokens. Referrables are injected after each entity and have the same identifier within each entity type. In order to let the model distinguish between different subparts, we adjust Equation 3 to use a learnable embedding of a part index instead of $V ^ { \mathcal { G } } [ t _ { i - 1 } ]$ . As referrable tokens do not need to be predicted the respective terms are removed from Equation 1. For the same reason, in Equation 4, $\boldsymbol { h } _ { i k }$ corresponds to the time step where $t _ { i k }$ is the output and not the input. This allows us to avoid having unused Transformer outputs.
+
+Finally, we need to specify how we embed pointers as inputs to the Transformer network. Following [35, 21] we could reuse $h _ { j }$ for tokens that point to $t _ { j }$ . Unfortunately, this creates output-to-input connections which are extremely detrimental to the efficiency of the Transformer architecture — different time steps can no longer be processed in parallel during training. Instead, we opt for a simpler solution and employ the standard embedding scheme for discrete tokens (Equation 3).
+
+Sampling from the model Sampling from the byte model is identical to sampling from any typical Transformer-based LM. The triplet model, on the other hand, requires slightly more bespoke handling. Figure 2 illustrates the procedure. We start by embedding and feeding a special BOS token into the Transformer. The Transformer then outputs a collection of triplets, one for each possible token group. In order to determine which concrete token needs to be emitted, we employ an interpreter (a state machine) automatically generated from the data specification. Knowing the current state allows us to choose the right token group and associate the active component of the triplet with a field in the synthesized object. Once the appropriate field is populated the interpreter transitions to the next state and produces an output token which is then fed back into the model. The process stops when the state machine receives the “end” triplet for the outermost repeated field (i.e., object.kind ).
+
+Conditional generation In addition to the unconditional model described above, we explore a variant that allows us to translate bitmaps into sketches. Here, we simply let the main Transformer cross-attend to the features extracted from the input image by a ViT network [12]. The specific setup is detailed in Appendix C.
+
+# 5 Experiments
+
+We validate our proposed approaches on the data that we obtained from the repository of documents publicly available on the Onshape platform [22]. Following the standard evaluation methodology for autoregressive generative models [23, 21] we use log-likelihood as our primary quantitative metric. Additionally, we provide a variety of random and selected model samples for qualitative assessment (Figure 3).
+
+Dataset Unlike the majority of the existing works dealing with CAD sketch generation [31, 37, 24] we do not rely on SketchGraphs [31]. Instead, we collect the largest to date dataset of engineering sketches addressing the main disadvantage of [31], severe data duplication. The acquisition and the filtering procedures
+
+Table 2: Test likelihoods of various models. The object column is computed as the average number of bits per object in a sketch averaged across test examples. The sketch column is similar except we do not divide by the number of objects.   
+
+<table><tr><td rowspan="2">Model</td><td rowspan="2"> Sequence</td><td colspan="2">Average bits per</td></tr><tr><td>object</td><td>sketch</td></tr><tr><td>Uniform</td><td>unord. bytes</td><td>112.23</td><td>3683.56</td></tr><tr><td></td><td>unord. triplets</td><td>25.34</td><td>847.52</td></tr><tr><td>Text</td><td>interleaved</td><td>4.622</td><td>139.687</td></tr><tr><td>Byte</td><td>concatenated</td><td>4.381</td><td>132.621</td></tr><tr><td rowspan="3">Triplet</td><td>interleaved</td><td>4.252</td><td>127.495</td></tr><tr><td>concatenated</td><td>4.218</td><td>127.913</td></tr><tr><td>interleaved</td><td>4.103</td><td>123.213</td></tr><tr><td>Cond.</td><td>interleaved</td><td>1.570</td><td>53.730</td></tr></table>
+
+![](images/2059d907b811a8da4ce130202c27c31b776e49951b3446b4a44e0a7efa04fa39.jpg)  
+Figure 4: Distribution of various sketch statistics for samples drawn from our unconditional models. The top- $p$ parameter for Nucleus Sampling is shown in parentheses.
+
+are detailed in Appendix D. For our experiments we split the dataset randomly into 3 parts: 4,656,607   
+examples for the training set and 50,000 sketches for each the validation and the test set.6
+
+Unconditional generation. In this series of experiments, the goal is to determine how well our models capture the distribution of sketches in the dataset. We use the same network architecture for both the byte and the triplet settings.7 We compare two orderings of objects: in the first one (concatenated), constraints go after the last entity while in the second (interleaved), a constraint object is injected immediately after the entities it operates on. In both cases, the relative orderings within both the sequence of entities and the sequence of constraints are taken directly from the original JSON messages.
+
+Table 2 shows test log-likelihoods obtained by different models. Unsurprisingly, our proposed methods (rows 4–7) significantly outperform the weak baselines (rows 1–2). The difference between the two uniform settings is due to the fact that the byte description of a PB message is usually longer than the triplet one: $2 3 9 \nu s . 4 5 6$ tokens on average with the maximum length of 959 vs. 1987. Additionally, the tokens in the triplet representation tend to have smaller range of values $( i . e . , < 2 5 7 )$ ).
+
+These differences between representations may partially explain why triplet models demonstrate better performance on the hold-out test set. It’s also worth emphasizing that the byte model does not receive any explicit information about the parsing state. This seem to make learning more challenging and as a result compared to the triplet model it takes roughly 3 times more network updates to reach the highest data likelihood on the validation.
+
+Another important factor affecting the performance of the models is the choice of the object ordering. As it is evident from Table 2, the interleaved ordering consistently leads to better results. One explanation for this is that at any point in time, the model has more explicit information about the relations between the sketch entities produced so far.
+
+In the row 3 of Table 2, we also provide the test log-likelihood for a conventional language modeling baseline trained on the text representation of PB messages (see Section 3). Here, we employ the SentencePiece tokenizer [17] with fairly aggressive settings (8000 words in the vocabulary; splitting at whitespaces switched off) to be able to keep the sequences within the budget of 1024 tokens. As can be seen from the table, the resulting Transformer model (of exactly the same architecture as other entries) despite being better than the uniform baselines is still substantially worse than the proposed methods.
+
+In addition to measuring likelihoods, we sampled 10,000 sketches from the best performing byte and triplet models and computed distributions of various high-level statistics (Figure 4 and Figure 6 in the appendix). We repeated this procedure both with and without using Nucleus Sampling (NS) [15]. Both models follow the data distribution closely when we use samples from the unmodified model output. In this setting, however, a significant fraction of sketches is either malformed (e.g., the generated PB message cannot be parsed) or unsolvable: $3 6 \%$ for the byte model and $1 4 \%$ for the triplet model. NS with top- $p = 0 . 9$ skews the sample distribution and seems to have a more pronounced negative effect on the byte model. The upside is that the resulting sketches become “cleaner”: the percentage of invalid samples goes down to $2 5 \%$ and $6 \%$ for the byte and the triplet settings respectively.
+
+![](images/5d620b9ee341dd09d6ee279fd7943e89afcaaee0b870754354379fa1d011f84b.jpg)  
+Figure 5: Entities and constraints sampled from the unconditional (top) and the conditional (bottom) triplet models. The first column of nodes represents different entities (all parts are folded into a single node). The order of nodes (top to bottom) follows the generation order. The second column represents different constraints also ordered by their index in the sequence. Finally, the third column is reserved for constraint types, from the most to the least frequent.
+
+Figures 3a and 3b show renders of random samples from several proposed models. Overall, generated sketches look plausible and exhibit a lot of desired properties: closedness of regions, regularity, symmetry, a non-trivial amount of fine detail. We observe that the byte model produces slightly less complex samples with fewer open arcs but this could be a side effect of a particular top- $p$ value. We also note that the model does not always synthesize sensible sketches — just like any other typical autoregressive model trained with teacher forcing it suffers from not being able to recover from mistakes made early on in the sequence [28]. This can potentially be addressed by fine-tuning using, for example, reinforcement learning.
+
+We show a more detailed sample from the triplet model in Figure 5. While not perfect, the inferred constraints are reasonable most of the time. The model does a good job at connecting entities using Coincident constraints but also successfully detects more complex relations spanning more than two primitives (e.g., Mirror). Having access to constraints gives us opportunity to correct mistakes in entity prediction by applying an external sketch solver (see Figure 3d). Although this aspect of sketching was not the main focus of this work, we believe that a tighter integration between the model and the CAD software will lead to a significant boost in generation quality.
+
+Conditional generation. As discussed in Section 4, we also trained an image-conditional model using the same regime as for the unconditional one. As expected, it achieves a significantly better fit (the last row of Table 2) but at the same time retains a non-trivial amount of uncertainty. The latter is arising, in particular, from the fact that different permutations of entities result in the same rendered image. Image-conditional samples can be found in Figure 3c. The model was able to nearly perfectly reconstruct simpler sketches and mostly made mistakes in the presence of a large number of fine details. Additionally, we compared our system against the nearest neighbour baseline in terms of visual reconstruction error as measured by Chamfer distance. We found that the proposed method reduces the error by $\approx 8 0 \%$ (see Appendix H). In order to test the out-of-distribution performance, we supply the model with several custom-made drawings. Surprisingly, after minor post-processing to account for the short sequence bias the system manages to produce reasonable reconstructions (see the bottom example in Figure 5). We detail this experiment in Appendix I.
+
+# 6 Discussion
+
+In this work, we have demonstrated how a combination of a general-purpose language modeling technique alongside an off-the-shelf data serialization protocol can be used to effectively solve generation of complex structured objects. We showcased the proposed system on the domain of 2D CAD drawings and developed models that can synthesize geometric primitives and relations between them both unconditionally as well as using a bitmap as a reference. These are only initial proof-of-concept experiments and we are hoping to see more applications taking advantage of the flexibility of the developed interface: conditioning on various sketch properties, inferring constraints given entities and automatically completing drawings, to name a few.
+
+Although we focused our attention on a particular dataset we argue that the approach described in this paper is largely domain-agnostic. In order to adapt the system to a new kind of data, the algorithm designer only needs to provide an appropriate Protocol Buffer specification and if the PB language is too restrictive one can always replace it with a more powerful interpreter. As a straightforward direction for future work, we can consider extending the method to handle 3D. In Onshape, 3D operations bear a lot of similarities with sketch constraints — just like constraints, they can be represented as nested messages containing references to the geometries existing in the scene. Thus, most of the ideas from the present work can be taken verbatim to this new setting.
+
+We hope that this work will serve as a stepping stone for further advances in the field of automated CAD but also inspire new ideas and approaches to generative modeling of arbitrary structured data.
+
+# Acknowledgments and Disclosure of Funding
+
+The authors would like to thank Charlie Nash, Georg Ostrovski, and Adam Kosiorek for helping with the manuscript preparation as well as Igor Babuschkin, David Choi, Nate Kushman, Andrew Kimpton, Jake Rosenfeld, Lana Saksonov, John Rousseau, Greg Guarriello, Andy Brock, Francesco Nori, Aäron van den Oord, and Oriol Vinyals for insightful discussions and support.
+
+YG, SB, YL, and SS are funded by DeepMind. EK is funded by PTC.
+
+# References
+
+[1] J. Alakuijala, A. Farruggia, P. Ferragina, E. Kliuchnikov, R. Obryk, Z. Szabadka, and L. Vandevenne. Brotli: A general-purpose data compressor. TOIS, 2018.   
+[2] H. K. Ault. Using geometric constraints to capture design intent. JGG, 1999.   
+[3] H. G. Barrow, J. M. Tenenbaum, R. C. Bolles, and H. C. Wolf. Parametric correspondence and chamfer matching: Two new techniques for image matching. Technical report, SRI INTERNATIONAL MENLO PARK CA ARTIFICIAL INTELLIGENCE CENTER, 1977.   
+[4] R. Bavishi, C. Lemieux, R. Fox, K. Sen, and I. Stoica. AutoPandas: Neural-backed generators for program synthesis. In OOPSLA, 2019.   
+[5] Y. Bengio, R. Ducharme, P. Vincent, and C. Janvin. A neural probabilistic language model. JMLR, 2003.   
+[6] T. B. Brown, B. Mann, N. Ryder, M. Subbiah, J. Kaplan, P. Dhariwal, A. Neelakantan, P. Shyam, G. Sastry, A. Askell, et al. Language models are few-shot learners. arXiv preprint arXiv:2005.14165, 2020.   
+[7] A. Carlier, M. Danelljan, A. Alahi, and R. Timofte. DeepSVG: A hierarchical generative network for vector graphics animation. arXiv preprint arXiv:2007.11301, 2020.   
+[8] P. Company, F. Naya, M. Contero, and J. Camba. On the role of geometric constraints to support design intent communication and model reusability. Computer-Aided Design and Applications, 2019.   
+[9] P. Dhariwal, H. Jun, C. Payne, J. W. Kim, A. Radford, and I. Sutskever. Jukebox: A generative model for music. arXiv preprint arXiv:2005.00341, 2020.   
+[10] D. Dori and K. Tombre. From engineering drawings to 3d CAD models: are we ready now? Computer-Aided Design, 1995.   
+[11] D. Dori and L. Wenyin. Automated cad conversion with the machine drawing understanding system: concepts, algorithms, and performance. SMC, 1999.   
+[12] A. Dosovitskiy, L. Beyer, A. Kolesnikov, D. Weissenborn, X. Zhai, T. Unterthiner, M. Dehghani, M. Minderer, G. Heigold, S. Gelly, et al. An image is worth 16x16 words: Transformers for image recognition at scale. arXiv preprint arXiv:2010.11929, 2020.   
+[13] V. Egiazarian, O. Voynov, A. Artemov, D. Volkhonskiy, A. Safin, M. Taktasheva, D. Zorin, and E. Burnaev. Deep vectorization of technical drawings. In ECCV, 2020.   
+[14] Y. Ganin, T. Kulkarni, I. Babuschkin, S. A. Eslami, and O. Vinyals. Synthesizing programs for images using reinforced adversarial learning. In ICML, 2018.   
+[15] A. Holtzman, J. Buys, L. Du, M. Forbes, and Y. Choi. The curious case of neural text degeneration. arXiv preprint arXiv:1904.09751, 2019.   
+[16] S. Koch, A. Matveev, Z. Jiang, F. Williams, A. Artemov, E. Burnaev, M. Alexa, D. Zorin, and D. Panozzo. ABC: A big CAD model dataset for geometric deep learning. In CVPR, 2019.   
+[17] T. Kudo and J. Richardson. Sentencepiece: A simple and language independent subword tokenizer and detokenizer for neural text processing. arXiv preprint arXiv:1808.06226, 2018.   
+[18] A. Meurer, C. P. Smith, M. Paprocki, O. Certík, S. B. Kirpichev, M. Rocklin, A. Kumar, ˇ S. Ivanov, J. K. Moore, S. Singh, et al. SymPy: symbolic computing in Python. PeerJ Computer Science, 2017.   
+[19] T. Mikolov, M. Karafiát, L. Burget, J. Cernock ˇ y, and S. Khudanpur. Recurrent neural network \` based language model. In INTERSPEECH, 2010.   
+[20] V. Nagasamy and N. A. Langrana. Engineering drawing processing and vectorization system. CVGIP, 1990.   
+[21] C. Nash, Y. Ganin, S. A. Eslami, and P. Battaglia. PolyGen: An autoregressive generative model of 3D meshes. In ICML, 2020.   
+[22] Onshape developers. Onshape website. https://www.onshape.com/. Accessed: 2021-03-10.   
+[23] A. v. d. Oord, N. Kalchbrenner, O. Vinyals, L. Espeholt, A. Graves, and K. Kavukcuoglu. Conditional image generation with PixelCNN decoders. arXiv preprint arXiv:1606.05328, 2016.   
+[24] W. R. Para, S. F. Bhat, P. Guerrero, T. Kelly, N. Mitra, L. Guibas, and P. Wonka. SketchGen: Generating constrained CAD sketches. arXiv preprint arXiv:2106.02711, 2021.   
+[25] F. Pezoa, J. L. Reutter, F. Suarez, M. Ugarte, and D. Vrgoc. Foundations of JSON schema. In ˇ WWW, 2016.   
+[26] A. Radford, J. Wu, R. Child, D. Luan, D. Amodei, and I. Sutskever. Language models are unsupervised multitask learners. OpenAI blog, 2019.   
+[27] A. Ramesh, M. Pavlov, G. Goh, S. Gray, C. Voss, A. Radford, M. Chen, and I. Sutskever. Zero-shot text-to-image generation. arXiv preprint arXiv:2102.12092, 2021.   
+[28] M. Ranzato, S. Chopra, M. Auli, and W. Zaremba. Sequence level training with recurrent neural networks. arXiv preprint arXiv:1511.06732, 2015.   
+[29] A. Razavi, A. v. d. Oord, and O. Vinyals. Generating diverse high-fidelity images with VQVAE-2. arXiv preprint arXiv:1906.00446, 2019.   
+[30] P. Reddy, M. Gharbi, M. Lukac, and N. J. Mitra. Im2Vec: Synthesizing vector graphics without vector supervision. arXiv preprint arXiv:2102.02798, 2021.   
+[31] A. Seff, Y. Ovadia, W. Zhou, and R. P. Adams. Sketchgraphs: A large-scale dataset for modeling relational geometry in computer-aided design. arXiv preprint arXiv:2007.08506, 2020.   
+[32] K. Varda. Google protocol buffers: Google’s data interchange format. Technical report, 2008.   
+[33] A. Vaswani, N. Shazeer, N. Parmar, J. Uszkoreit, L. Jones, A. N. Gomez, L. Kaiser, and I. Polosukhin. Attention is all you need. arXiv preprint arXiv:1706.03762, 2017.   
+[34] P. Vaxiviere and K. Tombre. Celesstin: CAD conversion of mechanical drawings. Computer, 1992.   
+[35] O. Vinyals, M. Fortunato, and N. Jaitly. Pointer networks. In NeurIPS, 2015.   
+[36] K. D. Willis, Y. Pu, J. Luo, H. Chu, T. Du, J. G. Lambourne, A. Solar-Lezama, and W. Matusik. Fusion 360 gallery: A dataset and environment for programmatic CAD reconstruction. arXiv preprint arXiv:2010.02392, 2020.   
+[37] K. D. Willis, P. K. Jayaraman, J. G. Lambourne, H. Chu, and Y. Pu. Engineering sketch generation for computer-aided design. arXiv preprint arXiv:2104.09621, 2021.   
+[38] R. Wu, C. Xiao, and C. Zheng. DeepCAD: A deep generative network for computer-aided design models. In ICCV, 2021.
+
+# Checklist
+
+1. For all authors...
+
+(a) Do the main claims made in the abstract and introduction accurately reflect the paper’s contributions and scope? [Yes]   
+(b) Did you describe the limitations of your work? [Yes]   
+(c) Did you discuss any potential negative societal impacts of your work? [No] The method presented in this work is a general machine learning framework and it is not immediately obvious how it could negatively impact the society.   
+(d) Have you read the ethics review guidelines and ensured that your paper conforms to them? [Yes]
+
+2. If you are including theoretical results...
+
+(a) Did you state the full set of assumptions of all theoretical results? [N/A] (b) Did you include complete proofs of all theoretical results? [N/A]
+
+3. If you ran experiments...
+
+(a) Did you include the code, data, and instructions needed to reproduce the main experimental results (either in the supplemental material or as a URL)? [No] The code is proprietary but may be open-sourced in the future. The dataset will be released shortly.   
+(b) Did you specify all the training details (e.g., data splits, hyperparameters, how they were chosen)? [Yes]   
+(c) Did you report error bars (e.g., with respect to the random seed after running experiments multiple times)? [No] The experiments in the paper are expensive to run. Moreover, we did not observe any significant fluctuations in the validation metrics between different training runs with the same hyperparameters.   
+(d) Did you include the total amount of compute and the type of resources used (e.g., type of GPUs, internal cluster, or cloud provider)? [Yes]
+
+4. If you are using existing assets (e.g., code, data, models) or curating/releasing new assets...
+
+(a) If your work uses existing assets, did you cite the creators? [Yes] We use data coming from a publicly available platform and we give credit to the platform in the paper.   
+(b) Did you mention the license of the assets? [N/A]   
+(c) Did you include any new assets either in the supplemental material or as a URL? [No]   
+(d) Did you discuss whether and how consent was obtained from people whose data you’re using/curating? [N/A]
+
+(e) Did you discuss whether the data you are using/curating contains personally identifiable information or offensive content? [N/A]
+
+5. If you used crowdsourcing or conducted research with human subjects...
+
+(a) Did you include the full text of instructions given to participants and screenshots, if applicable? [N/A]   
+(b) Did you describe any potential participant risks, with links to Institutional Review Board (IRB) approvals, if applicable? [N/A]   
+(c) Did you include the estimated hourly wage paid to participants and the total amount spent on participant compensation? [N/A]
\ No newline at end of file
diff --git a/parse/train/z-X_PpwaroO/z-X_PpwaroO_content_list.json b/parse/train/z-X_PpwaroO/z-X_PpwaroO_content_list.json
new file mode 100644
index 0000000000000000000000000000000000000000..cc0e5476c41ded27a266d4c93b566c5358a56792
--- /dev/null
+++ b/parse/train/z-X_PpwaroO/z-X_PpwaroO_content_list.json
@@ -0,0 +1,1228 @@
+[
+    {
+        "type": "text",
+        "text": "Computer-Aided Design as Language ",
+        "text_level": 1,
+        "bbox": [
+            271,
+            122,
+            727,
+            147
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Yaroslav Ganin1∗ Sergey Bartunov1 Yujia Li1 Ethan Keller2 Stefano Saliceti1 1DeepMind 2Onshape ",
+        "bbox": [
+            197,
+            199,
+            794,
+            236
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Abstract ",
+        "text_level": 1,
+        "bbox": [
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+            287
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Computer-Aided Design (CAD) applications are used in manufacturing to model everything from coffee mugs to sports cars. These programs are complex and require years of training and experience to master. A component of all CAD models particularly difficult to make are the highly structured 2D sketches that lie at the heart of every 3D construction. In this work, we propose a machine learning model capable of automatically generating such sketches. Through this, we pave the way for developing intelligent tools that would help engineers create better designs with less effort. The core of our method is a combination of a generalpurpose language modeling technique alongside an off-the-shelf data serialization protocol. Additionally, we explore several extensions allowing us to gain finer control over the generation process. We show that our approach has enough flexibility to accommodate the complexity of the domain and performs well for both unconditional synthesis and image-to-sketch translation. ",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1 Introduction ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            507,
+            310,
+            525
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Computer-Aided Design (CAD) is used in the production of most manufactured objects: from cars to robots to stents to power plants. CAD has replaced pencil drawings with precise computer sketches, enabling unparalleled precision, flexibility, and speed. Despite these improvements the CAD engineer must still develop, relate and annotate all the minutiae of their designs with the same attention to detail as their draftingtable forebears. CAD productivity might be improved by the careful application of machine learning to automate predictable design tasks and free the engineer to focus on the bigger picture. The flexibility and power of deep learning is uniquely suited to the complexity of design. ",
+        "bbox": [
+            174,
+            540,
+            531,
+            733
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Sketches are at the heart of mechanical CAD. They are the skeleton from which three dimensional forms are made. A sketch consists of various geometric entities (e.g., lines, arcs, splines and circles) related by specific constraints such as tangency, perpendicularity and symmetry. Figure 1 illustrates how entities and constraints work in tandem to create well-defined shapes. Geometric entities lie on a single plane and together form enclosed regions used by subsequent construction operations such as lofts and extrusions to generate complex ",
+        "bbox": [
+            174,
+            739,
+            529,
+            877
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/801c01a8f7ad74854fddf78e6c8c49c6d66b6df145afc636cd0e89cfc38f010b.jpg",
+        "image_caption": [
+            "Figure 1: The anatomy of a CAD sketch. Sketches are the main building block of every 3D construction. A sketch consists of entities (e.g., lines and arcs) and constraints (e.g., tangent and mirror). The dotted curve shows what happens if we drop some of the constraints — the design idea is lost. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            553,
+            515,
+            812,
+            770
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/768010495993ed4419100a195bad75e3db43476e171ff7bd23282a293c1f8bdc.jpg",
+        "image_caption": [
+            "Figure 2: Interpreter-guided generation of a sketch. At each point in time, a Transformer [33] outputs a raw value which is fed into an interpreter that decides which field of a Protocol Buffers message this value corresponds to. Once the field is populated the interpreter communicates $( -  )$ its decision back to the Transformer and transitions $( \\nrightarrow )$ to the next state. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+            108,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "3D geometry. Well-chosen sketch constraints are essential to properly convey design intent [2] and facilitate the sketch’s resilience to successive parameters modifications which is often understood as a measure of the quality of a design document [8]. The dotted curve in Figure 1 shows what happens when some of the constraints are dropped – the design idea is lost. ",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "The complexities of sketch construction are analogous to those of natural language modeling. Selecting the next constraint or entity in a sketch is like the generation of the next word in a sentence. In both contexts, the selection must function grammatically (form a consistent constraint system in the case of the sketch) and work towards some cohesive meaning (preserve design intent). Luckily, machine learning has proved highly successful in generating natural language — especially the Transformer [33] trained on vast amounts of real-world data [26, 6]. It is therefore a promising choice for adapting to the task of sketch generation. This work is our take at this adaptation. ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "We make the following contributions: (1) We devise a method for describing structured objects using Protocol Buffers [32] and demonstrate its flexibility on the domain of natural CAD sketches. (2) We propose several techniques for capturing distributions of objects represented as serialized Protocol Buffers. Our approach draws inspiration from recent advances in language modeling while focusing on eliminating data redundancy. (3) We collect a dataset of over $4 . 7 \\mathbf { M }$ of carefully preprocessed parametric CAD sketches and use this dataset to validate the proposed generative models. To our knowledge, the experiments presented in this work significantly surpass the scale of those reported in the literature both in terms of the amount of training data and the model capacity. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "2 Related work ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Datasets and generative models for CAD. Until recently there were very few parametric CAD datasets large and varied enough to serve as training data for machine learning. This situation had started to change with the release of the ABC dataset [16] containing a collection of 3D shapes from the Onshape public repository [22]. Unfortunately, the main focus of [16] revolves around meshes and, as a result, the dataset is difficult to use for sketch modeling. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Several works concurrent with ours deal with the symbolic representation of CAD constructions. Seff et al. [31] center their attention on contributing a better dataset of 2D sketches but also provide a proof-of-concept model predicting a selected subset of object attributes. Willis et al. [37] use the dataset from [31] to train a modification of [21] which demonstrates a boost in generation quality but is designed to only work for sketch entities. The latter is addressed in our present work and in a subsequent paper by Para et al. [24]. While [24] employ very similar ideas to ours they do not support certain features of the CAD data and their proposed model is a more direct adaptation of [21] and therefore cannot handle arbitrary orderings of entities and constraints. In Section 5, we show that object ordering has a substantial impact on the performance. ",
+        "bbox": [
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+        "type": "text",
+        "text": "",
+        "bbox": [
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "Fusion 360 Gallery [36] attacks CAD data from a different angle. Here, the task is to recover a sequence of extrusion operations that gives rise to a particular target 3D shape. Despite dealing with 3D, this setting is deliberately limited: sketches are assumed to be given and the proposed model only decides on which sketch to extrude and to what extent. [38] considers a more general scenario where extrusion profiles are not provided and need to be synthesized from scratch. Although both of these works make initial steps towards full parametric CAD generation, they rely on significant simplifying assumptions and therefore it is unclear how well they will scale to more real-world scenarios. Our approach, on the other hand, is designed to be flexible and domain-agnostic and is only limited by the data availability. ",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Vector image generation and inference. Synthesizing CAD sketches bears a lot of similarities with predicting vector graphics. In this field, several recent works Carlier et al. [7] and Reddy et al. [30] using different vector object representations to define generative models of vector images. Egiazarian et al. [13] take a more traditional computer vision approach and propose a multi-stage pipeline for vectorizing technical drawings. All of these methods use highly domain-dependent architectures and, therefore, it would be a non-trivial task to adapt them for generation of complex sketch objects. CAD community has also been concerned with a similar task of image to CAD conversion [20, 34, 10, 11], largely focusing on heuristic object recognition while our work relies more on learning the recognition from data. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Transformers for sequence modeling. In our work, we employ Transfomers [33] as a computational backbone for the proposed approach. Due to its scalability and excellent performance [29, 9, 6, 27], this architecture has become the dominating approach in many sequence modeling applications. Our method can be seen as generalization of PolyGen [21], a Transformer-based generative model for 3D meshes. Similarly to [21], we use Pointer Networks [35] to relate items in the synthesized sequence. Unlike PolyGen, however, our framework can handle non-homogeneous structures of arbitrary complexity. Moreover, we simplify the architecture to use a single neural network to generate the entire object of interest. All these improvements make our approach a good fit for modeling CAD sketches and potentially other components of CAD constructions. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "3 Data ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Formally, a CAD sketch is defined by two collections of objects: entities and constraints. Each object is generally represented as a set of attribute-value pairs where a value can be either primitive (e.g., integer or floating-point) or complex (e.g., an array or another object). Sketches that we use in this work originate from the Onshape platform [22] which provides them in JSON format [25]. As the first step in our processing pipeline we convert JSON messages into Protocol Buffers (PB) [32]. In order to keep the pipeline as domain-agnostic and as widely applicable as possible, we aim to avoid any significant changes to the data and largely retain the original structures of objects. The benefit of converting into PB is twofold: the resulting data occupies less space because unnecessary information is removed, but also, unlike JSON, PB provide a convenient way to define precise specifications for structures of arbitrary complexity. ",
+        "bbox": [
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "Listing 1a shows how we represent the line entity and the mirror constraint (see Appendix A for an extensive list of supported objects). The line specification is straightforward: we first need to decide whether our entity should be treated as a construction geometry2 and then provide pairs of coordinates for the beginning and end of the segment. The MirrorConstraint is used to force an arbitrary number of pairs of geometries (i.e., mirrored_pairs) to be symmetrical with respect to some axis (i.e., mirror). Constraints rely on the Pointer data type to specify entities they act upon. In practice, a pointer is simply an index in the table of all the eligible pointees (i.e., entities and their parts). ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "message LineEntity { bool is_construction $\\ c = ~ 1$ ; message Vector $\\{ \\begin{array} { r l } \\end{array}  / / $ 2D coordinate. double $\\texttt { x } = \\texttt { 1 }$ ; double $\\tt { y } = 2$ ; } Vector start $= ~ 2$ ; // Start point. Vector end $\\ c = \\ 3$ ; // End point.   \n}   \nmessage MirrorConstraint { Pointer mirror $\\ c = ~ 1$ ; // Axis of symmetry. message Pair { // Mirrored objects. Pointer first $\\ l = \\ 1$ ; Pointer second $= ~ 2$ ; } repeated Pair mirrored_pairs $= ~ 2$ ;   \n} ",
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+        "text": "(a) Entities and constraints have similar structures. Pointers refer to entities that constraints are applied to. ",
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+        "type": "text",
+        "text": "message Entity { oneof kind { LineEntity line $\\ l = \\ 1$ ; // And other entity types. }   \n}   \nmessage Object { oneof kind { Entity entity $\\ l = \\ 1$ ; Constraint constraint $= ~ 2$ ; }   \n}   \nmessage Constraint { // Defined similarly to Entity.   \n}   \nmessage Sketch { repeated Object objects $\\ c = ~ 1$ ;   \n} ",
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+    {
+        "type": "text",
+        "text": "(b) A full sketch is defined as a sequence of objects each of which can be either an entity or a constraint. ",
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+    {
+        "type": "text",
+        "text": "Listing 1: Examples of object specifications. We represent objects using Protocol Buffers. Protocol Buffers allow us to easily write specifications for structured objects of varying complexity. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Our ultimate goal is to build a machine learning model of sketch objects. To that end, we process the data even further and represent these objects as sequences of tokens. This allows us to pose sketch generation as language modeling (LM) and take advantage of the recent progress in this area [26, 6]. To achieve this, we pack first collections of entities and constraints into one Protocol Buffer message (see Listing 1b) assuming some ordering of objects. We discuss different orderings in Section 5. ",
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+    {
+        "type": "text",
+        "text": "There are a few ways to obtaining a sequence of tokens from a sketch message. Arguably the most intuitive one is to format messages as text. For a line entity connecting (0.0, 0.1) and $( - 0 . 5 , 0 . 2 )$ this will result in: ",
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+        "type": "text",
+        "text": "{ is_construction: true, start { x: 0.0, y: 0.1 }, end { x: -0.5, y: 0.2 } } ",
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+        "type": "text",
+        "text": "Since this format contains both the structure and the content of the data, the resulting sequences end up being prohibitively long. Additionally, the model would have to generate valid syntax, which would take up some portion of the model’s capacity. To overcome these challenges, we work with two flavours of serialized PB messages. ",
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+        "type": "text",
+        "text": "The first one is a sequences of bytes obtained by calling the SerializeToString() method of a message. Such sequences are much shorter since the structure is handled by an external parser automatically generated from the data specification. The parser’s task is to interpret the incoming stream of unstructured bytes and populate the fields of PB messages. However, like the text format, not every sequence of bytes results in a valid PB message. ",
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+        "type": "text",
+        "text": "Going one step further, we can utilize the structure of the sketch format more directly, and build a custom interpreter, that takes as input a sequence of tokens each representing a valid choice at various decision steps [4] in the sketch creation process. We designed this interpreter in such a way that all sequences of tokens in this format lead to valid PB messages. More specifically, we represent a message as a sequence of triplets $( d _ { i } , c _ { i } , f _ { i } )$ where $i$ is an index of the token. The majority of tokens describe basic fields of the sketch objects with each token representing exactly one field. The first two positions in each triplet are allocated for a discrete value and a continuous value respectively. Since each field in a message is either discrete or continuous only one of two positions is active at a time (the other one is set to a default zero value). The third component is a boolean flag signifying the end of a repeated field3 which contains a list of elements of the same type. An example sequence for a sketch containing a line and a point placed at one of its ends is shown in Table 1 (Triplet column). ",
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+    {
+        "type": "table",
+        "img_path": "images/adcfd069a5f960c85bcb146cfc971043babc429a1ecbc2eb31d46ce9af854b1e.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Triplet</td><td>Field</td><td></td><td>Triplet</td><td>Field</td></tr><tr><td>1.</td><td>(0,0.0,False)</td><td>objects.kind</td><td>8. (0,0.0,False)</td><td>objects.kind</td></tr><tr><td>2.</td><td>(0,0.0,False)</td><td>entity.kind</td><td>9. (1, 0.0,False)</td><td>entity.kind</td></tr><tr><td>3.</td><td>(1,0.0,False)</td><td>line.is_constr</td><td>10. (0, 0.0,False)</td><td>Point point.is_const</td></tr><tr><td>4.</td><td>(0, 0.0,False)</td><td>line.start.x</td><td>11. (0, 0.0,False)</td><td>point .x</td></tr><tr><td>5.</td><td>(0,0.1,False)</td><td>line.start.y</td><td>12. (0,0.1,False)</td><td>point.y</td></tr><tr><td>6.</td><td>(0,-0.5,False)</td><td>line.end.x</td><td>13. (0, 0.0, True)</td><td>objects.kind</td></tr><tr><td>7.</td><td>(0, 0.2,False)</td><td>line.end.y</td><td></td><td></td></tr></table>",
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+        "page_idx": 4
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+    {
+        "type": "text",
+        "text": "Table 1: A triplet representation of a simple sketch. The sketch contains and a line and a point. Within each triplet in the left column, the active component (the value that is actually used) is highlighted in bold. The right column shows which field of the object the triplet is associated with. ",
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+        "type": "text",
+        "text": "Given a sequence of such triplets, it is possible to infer which exact field each token corresponds to. Indeed, the very first token $( d _ { 1 } , c _ { 1 } , f _ { 1 } )$ is always associated with objects.kind since it is the first choice that needs to be made to create a Sketch message (see Listing 1b). The second field depends on the concrete value of $d _ { 1 }$ . If $d _ { 1 } = 0$ then the first object is an entity which means that the second token corresponds to entity.kind . The rest of the sequence is associated in a similar fashion. Field identifiers along with their locations within an object form the context of the tokens. We use this contextual information as an additional input for our machine learning models since it makes it easier to interpret the meaning of the triplet values and to be aware of the overall structure of the data. ",
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+    {
+        "type": "text",
+        "text": "4 Model ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "In order to estimate the distribution $p _ { \\mathrm { d a t a } }$ of 2D sketches in a dataset $\\mathcal { D }$ , we decompose the joint distribution over the sequence of tokens [19] $\\mathbf { t } = ( t _ { 1 } , \\ldots , t _ { N } )$ in an autoregressive fashion, representing each conditional with a neural network parameterized by $\\theta$ and pose the estimation of $p _ { \\mathrm { d a t a } }$ as maximization of the log-likelihood of $\\mathcal { D }$ , i.e., ",
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+    {
+        "type": "equation",
+        "img_path": "images/ec608e7217825af4fed5a80aef0f730b0d4ba8b8ae594a7120a0ecbefaf95868.jpg",
+        "text": "$$\np ( t ; \\theta ) = \\prod _ { i = 1 } ^ { N } p ( t _ { i } \\mid t _ { < i } ; \\theta ) , \\quad \\sum _ { t \\in \\mathcal { D } } \\log p ( t ; \\theta ) \\to \\operatorname* { m a x } _ { \\theta } ,\n$$",
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+    {
+        "type": "text",
+        "text": "where $N$ is the length of the sequence and $t _ { < i }$ denotes all the tokens preceding $t _ { i }$ . ",
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+        "type": "text",
+        "text": "More concretely, we employ the Transformer decoder architecture [33] that takes an embedding of the token $\\pmb { e } _ { i - 1 } \\overset { \\cdot } { = } \\mathrm { e m b e d } _ { i } ^ { \\cdot } ( t _ { i - 1 } ^ { \\cdot } ) \\in \\mathbb { R } ^ { D }$ and maps it into another vector $\\boldsymbol { h } _ { i }$ of the same dimensionality. The latter is decoded into parameters of $p ( t _ { i } \\mid t _ { < i } )$ by a learned mapping $\\mathsf { d i s t } _ { i } ( \\cdot )$ .4 ",
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+        "type": "text",
+        "text": "Byte representation When dealing with the bytes of a PB message, each token is simply a discrete value in the range $\\{ 0 , \\dots , 2 5 5 \\} \\cup \\{ \\bar { \\bf E 0 S } \\}$ and therefore $p ( t _ { i } \\mid t _ { < i } ; \\bar { \\theta ( \\mathbf { \\Sigma } ) }$ can be modeled as a categorical distribution similar to how it’s done in typical LM approaches [5]. In this setting, for each time step $i$ of the sequence we have ",
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+    {
+        "type": "equation",
+        "img_path": "images/fc29416e72b54ccb357d9cd503c309b9320c76706fdd1e30b0d599d9e13d8fd0.jpg",
+        "text": "$$\n\\mathbf { e m b e d } _ { i } ( t _ { i - 1 } ) = V [ t _ { i - 1 } ] + e _ { i } ^ { \\mathrm { p o s } } ,\n$$",
+        "text_format": "latex",
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+    },
+    {
+        "type": "text",
+        "text": "where $[ \\cdot ]$ denotes the lookup operation and $e _ { i } ^ { \\mathrm { p o s } }$ is a position embedding for position $i$ . Both $V$ and $e _ { i } ^ { \\mathrm { p o s } }$ are learned. Moreover, $\\forall i \\ \\mathtt { d i s t } _ { i }$ is the same linear projection into $\\mathbb { R } ^ { 2 5 7 }$ (256 values and EOS) and the output is treated as logits of the distribution. ",
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+    {
+        "type": "text",
+        "text": "Triplet representation In case of the triplet representation, we follow a slightly more involved procedure. As outlined in Section 3, tokens can be either discrete or continuous. Additionally, different discrete tokens may have different ranges of values. For example, there are only two possible values for the object.kind token – either to an entity or a constraint. On the other hand, the range of the entity.kind token has cardinality of 4 since we support 4 different types of sketch entities. This means that we can’t naively describe each conditional in Equation 1 using the same template distribution like we did for the bytes. We circumvent this by introducing the notion of token groups. ",
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+        "type": "text",
+        "text": "A token group $\\mathcal { G }$ is a collection of related token types that can be handled in a similar fashion. Specifically, we use the same embedding function and the same projection for every $t$ such that ",
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+    {
+        "type": "image",
+        "img_path": "images/023d60da6886256697dbccdb13316caf4b192be89fcc2c3abc16679bb42ccf08.jpg",
+        "image_caption": [],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "(a) Unconditional byte model. ",
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+    {
+        "type": "text",
+        "text": "(b) Unconditional triplet model. ",
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+        "type": "image",
+        "img_path": "images/6a078adb38e4e5126f04a58c9d202baf6dc4394bfc33aa9ce47e076d2e729d83.jpg",
+        "image_caption": [
+            "Figure 3: Synthesized sketches and data. (a)–(c) show samples from various proposed models (we use Nucleus Sampling with top- $p = 0 . 9 ,$ ). In (c), the output is rendered in a slightly thicker style. (d) demonstrates samples from the unconditional model after applying predicted constraints (the output is in blue). (e) shows examples from the dataset. "
+        ],
+        "image_footnote": [],
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+    },
+    {
+        "type": "text",
+        "text": "$\\mathsf { t y p e } ( t ) \\in \\mathcal { G }$ . For instance, we might want to group all the tokens associated with coordinates. In the example from Table 1, tokens with indices 4–7 and 11–12 will all end up in the same $\\mathcal { G } ^ { 5 }$ . Naturally, we use the same functional form for the output distribution $p ( t _ { i } \\mid t _ { < i } ; \\boldsymbol { \\theta } )$ within each group. ",
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+    {
+        "type": "text",
+        "text": "We embed $t _ { i - 1 }$ that belongs to the group $\\mathcal { G }$ as (note the difference with Equation 2): ",
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+        "page_idx": 5
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+    {
+        "type": "equation",
+        "img_path": "images/6187811b2facd16f51c3ced7cc3f023802faef96c81beb2f67c43a83b0629102.jpg",
+        "text": "$$\nK [ \\mathbf { f i e l d } ( t _ { i - 1 } ) ] + V ^ { \\mathcal { G } } [ t _ { i - 1 } ] + e _ { n } ^ { \\mathrm { o b j } } + e _ { m } ^ { \\mathrm { r e l } } ,\n$$",
+        "text_format": "latex",
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where field $( t )$ returns the field of $t$ (e.g., objects.kind or line.start. $\\mathtt { x }$ ) and $K$ is a collection of learnable embeddings for every possible field type. Unlike in Equation 2, instead of using global position embedding eposi w e describe the location with the index $n$ of the current object as well as the relative position $m$ of $t _ { i - 1 }$ within an object. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We handle the “end” tokens (i.e., $f _ { i } = \\mathrm { T r u e } )$ similarly to EOS in Section 4 — the output projection produces an additional logit used to compute the probability of ending the repetition. Since $f _ { i }$ is only expected to be True at particular points in the sequence (i.e., right after tokens forming a whole element of the list) we mask out the extra logit everywhere else. This ensures that the “end” token can’t be predicted prematurely and also eliminates its unnecessary contribution to the optimized objective. ",
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+    {
+        "type": "text",
+        "text": "One significant difference between the byte setting and the triplet setting is how we process pointer fields. In the former, pointers do not get any special treatment and are generated just like any other integer field. We rely on the model’s capability to make sense of the entity part index and relate it to the corresponding locations in the sequence via attention weights. This seems to be a viable strategy since Transformers have demonstrated an impressive referencing capacity in recent works [6]. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Since the triplet representation provides us with direct access to the semantics of tokens it’s possible to relate pointers to their pointees more explicitly by using Pointer Networks [35]. The approach we are taking here is similar to [21]. In order to compute $p ( t _ { i } \\mid t _ { < i } ; \\theta )$ , we first project the output of the Transformer $\\boldsymbol { h } _ { i }$ into the final pointer vector $p _ { i } = { W _ { \\mathrm { p t r } } h _ { i } }$ . The conditional is then obtained as follows: ",
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+    {
+        "type": "equation",
+        "img_path": "images/9ac78d8e1391073d825dc80ed6a0c040b7b3d2ab49408020279bca3188d51aef.jpg",
+        "text": "$$\n\\begin{array} { r } { p ( t _ { i } \\mathrm { ~ p o i n t s ~ t o ~ } t _ { i k } \\mid t _ { < i } ; \\theta ) = \\mathrm { s o f t m a x } _ { k } ( \\pmb { p } _ { i } ^ { T } H _ { i } ) , \\quad H _ { i } = [ \\pmb { h } _ { i 1 } , \\dots , \\pmb { h } _ { i k } , \\dots , \\pmb { h } _ { i M } ] , } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "where $\\operatorname { s o f t m a x } _ { k }$ is the $k$ -th element of the softmax vector and $\\boldsymbol { r } _ { i } = \\{ t _ { i 1 } , . . . , t _ { i M } \\}$ is the set of tokens that $t _ { i }$ can point to. Naturally, $\\mathbf { \\nabla } _ { \\mathbf { r } _ { i } }$ only contains tokens from $t _ { < i }$ . This is different from [35, 21] where $\\textstyle r _ { i } \\equiv r$ is external to the predicted sequence and remains immutable throughout the generation process. ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "In Onshape, constraints can be applied not only to whole entities but also to their subparts (e.g., the center of a circle or the end points of a line segment). To handle this, we introduce special referrable tokens decoupling pointees from the object attribute tokens. Referrables are injected after each entity and have the same identifier within each entity type. In order to let the model distinguish between different subparts, we adjust Equation 3 to use a learnable embedding of a part index instead of $V ^ { \\mathcal { G } } [ t _ { i - 1 } ]$ . As referrable tokens do not need to be predicted the respective terms are removed from Equation 1. For the same reason, in Equation 4, $\\boldsymbol { h } _ { i k }$ corresponds to the time step where $t _ { i k }$ is the output and not the input. This allows us to avoid having unused Transformer outputs. ",
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Finally, we need to specify how we embed pointers as inputs to the Transformer network. Following [35, 21] we could reuse $h _ { j }$ for tokens that point to $t _ { j }$ . Unfortunately, this creates output-to-input connections which are extremely detrimental to the efficiency of the Transformer architecture — different time steps can no longer be processed in parallel during training. Instead, we opt for a simpler solution and employ the standard embedding scheme for discrete tokens (Equation 3). ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Sampling from the model Sampling from the byte model is identical to sampling from any typical Transformer-based LM. The triplet model, on the other hand, requires slightly more bespoke handling. Figure 2 illustrates the procedure. We start by embedding and feeding a special BOS token into the Transformer. The Transformer then outputs a collection of triplets, one for each possible token group. In order to determine which concrete token needs to be emitted, we employ an interpreter (a state machine) automatically generated from the data specification. Knowing the current state allows us to choose the right token group and associate the active component of the triplet with a field in the synthesized object. Once the appropriate field is populated the interpreter transitions to the next state and produces an output token which is then fed back into the model. The process stops when the state machine receives the “end” triplet for the outermost repeated field (i.e., object.kind ). ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Conditional generation In addition to the unconditional model described above, we explore a variant that allows us to translate bitmaps into sketches. Here, we simply let the main Transformer cross-attend to the features extracted from the input image by a ViT network [12]. The specific setup is detailed in Appendix C. ",
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+    },
+    {
+        "type": "text",
+        "text": "5 Experiments ",
+        "text_level": 1,
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+        "text": "We validate our proposed approaches on the data that we obtained from the repository of documents publicly available on the Onshape platform [22]. Following the standard evaluation methodology for autoregressive generative models [23, 21] we use log-likelihood as our primary quantitative metric. Additionally, we provide a variety of random and selected model samples for qualitative assessment (Figure 3). ",
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+        "text": "Dataset Unlike the majority of the existing works dealing with CAD sketch generation [31, 37, 24] we do not rely on SketchGraphs [31]. Instead, we collect the largest to date dataset of engineering sketches addressing the main disadvantage of [31], severe data duplication. The acquisition and the filtering procedures ",
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+            "Table 2: Test likelihoods of various models. The object column is computed as the average number of bits per object in a sketch averaged across test examples. The sketch column is similar except we do not divide by the number of objects. "
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+        "table_body": "<table><tr><td rowspan=\"2\">Model</td><td rowspan=\"2\"> Sequence</td><td colspan=\"2\">Average bits per</td></tr><tr><td>object</td><td>sketch</td></tr><tr><td>Uniform</td><td>unord. bytes</td><td>112.23</td><td>3683.56</td></tr><tr><td></td><td>unord. triplets</td><td>25.34</td><td>847.52</td></tr><tr><td>Text</td><td>interleaved</td><td>4.622</td><td>139.687</td></tr><tr><td>Byte</td><td>concatenated</td><td>4.381</td><td>132.621</td></tr><tr><td rowspan=\"3\">Triplet</td><td>interleaved</td><td>4.252</td><td>127.495</td></tr><tr><td>concatenated</td><td>4.218</td><td>127.913</td></tr><tr><td>interleaved</td><td>4.103</td><td>123.213</td></tr><tr><td>Cond.</td><td>interleaved</td><td>1.570</td><td>53.730</td></tr></table>",
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+        "image_caption": [
+            "Figure 4: Distribution of various sketch statistics for samples drawn from our unconditional models. The top- $p$ parameter for Nucleus Sampling is shown in parentheses. "
+        ],
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+        "type": "text",
+        "text": "are detailed in Appendix D. For our experiments we split the dataset randomly into 3 parts: 4,656,607   \nexamples for the training set and 50,000 sketches for each the validation and the test set.6 ",
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+        "text": "Unconditional generation. In this series of experiments, the goal is to determine how well our models capture the distribution of sketches in the dataset. We use the same network architecture for both the byte and the triplet settings.7 We compare two orderings of objects: in the first one (concatenated), constraints go after the last entity while in the second (interleaved), a constraint object is injected immediately after the entities it operates on. In both cases, the relative orderings within both the sequence of entities and the sequence of constraints are taken directly from the original JSON messages. ",
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+        "text": "Table 2 shows test log-likelihoods obtained by different models. Unsurprisingly, our proposed methods (rows 4–7) significantly outperform the weak baselines (rows 1–2). The difference between the two uniform settings is due to the fact that the byte description of a PB message is usually longer than the triplet one: $2 3 9 \\nu s . 4 5 6$ tokens on average with the maximum length of 959 vs. 1987. Additionally, the tokens in the triplet representation tend to have smaller range of values $( i . e . , < 2 5 7 )$ ). ",
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+        "text": "These differences between representations may partially explain why triplet models demonstrate better performance on the hold-out test set. It’s also worth emphasizing that the byte model does not receive any explicit information about the parsing state. This seem to make learning more challenging and as a result compared to the triplet model it takes roughly 3 times more network updates to reach the highest data likelihood on the validation. ",
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+        "text": "Another important factor affecting the performance of the models is the choice of the object ordering. As it is evident from Table 2, the interleaved ordering consistently leads to better results. One explanation for this is that at any point in time, the model has more explicit information about the relations between the sketch entities produced so far. ",
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+        "text": "In the row 3 of Table 2, we also provide the test log-likelihood for a conventional language modeling baseline trained on the text representation of PB messages (see Section 3). Here, we employ the SentencePiece tokenizer [17] with fairly aggressive settings (8000 words in the vocabulary; splitting at whitespaces switched off) to be able to keep the sequences within the budget of 1024 tokens. As can be seen from the table, the resulting Transformer model (of exactly the same architecture as other entries) despite being better than the uniform baselines is still substantially worse than the proposed methods. ",
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+        "text": "In addition to measuring likelihoods, we sampled 10,000 sketches from the best performing byte and triplet models and computed distributions of various high-level statistics (Figure 4 and Figure 6 in the appendix). We repeated this procedure both with and without using Nucleus Sampling (NS) [15]. Both models follow the data distribution closely when we use samples from the unmodified model output. In this setting, however, a significant fraction of sketches is either malformed (e.g., the generated PB message cannot be parsed) or unsolvable: $3 6 \\%$ for the byte model and $1 4 \\%$ for the triplet model. NS with top- $p = 0 . 9$ skews the sample distribution and seems to have a more pronounced negative effect on the byte model. The upside is that the resulting sketches become “cleaner”: the percentage of invalid samples goes down to $2 5 \\%$ and $6 \\%$ for the byte and the triplet settings respectively. ",
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+            "Figure 5: Entities and constraints sampled from the unconditional (top) and the conditional (bottom) triplet models. The first column of nodes represents different entities (all parts are folded into a single node). The order of nodes (top to bottom) follows the generation order. The second column represents different constraints also ordered by their index in the sequence. Finally, the third column is reserved for constraint types, from the most to the least frequent. "
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+        "text": "Figures 3a and 3b show renders of random samples from several proposed models. Overall, generated sketches look plausible and exhibit a lot of desired properties: closedness of regions, regularity, symmetry, a non-trivial amount of fine detail. We observe that the byte model produces slightly less complex samples with fewer open arcs but this could be a side effect of a particular top- $p$ value. We also note that the model does not always synthesize sensible sketches — just like any other typical autoregressive model trained with teacher forcing it suffers from not being able to recover from mistakes made early on in the sequence [28]. This can potentially be addressed by fine-tuning using, for example, reinforcement learning. ",
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+        "text": "We show a more detailed sample from the triplet model in Figure 5. While not perfect, the inferred constraints are reasonable most of the time. The model does a good job at connecting entities using Coincident constraints but also successfully detects more complex relations spanning more than two primitives (e.g., Mirror). Having access to constraints gives us opportunity to correct mistakes in entity prediction by applying an external sketch solver (see Figure 3d). Although this aspect of sketching was not the main focus of this work, we believe that a tighter integration between the model and the CAD software will lead to a significant boost in generation quality. ",
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+        "text": "Conditional generation. As discussed in Section 4, we also trained an image-conditional model using the same regime as for the unconditional one. As expected, it achieves a significantly better fit (the last row of Table 2) but at the same time retains a non-trivial amount of uncertainty. The latter is arising, in particular, from the fact that different permutations of entities result in the same rendered image. Image-conditional samples can be found in Figure 3c. The model was able to nearly perfectly reconstruct simpler sketches and mostly made mistakes in the presence of a large number of fine details. Additionally, we compared our system against the nearest neighbour baseline in terms of visual reconstruction error as measured by Chamfer distance. We found that the proposed method reduces the error by $\\approx 8 0 \\%$ (see Appendix H). In order to test the out-of-distribution performance, we supply the model with several custom-made drawings. Surprisingly, after minor post-processing to account for the short sequence bias the system manages to produce reasonable reconstructions (see the bottom example in Figure 5). We detail this experiment in Appendix I. ",
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+    {
+        "type": "text",
+        "text": "6 Discussion ",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "In this work, we have demonstrated how a combination of a general-purpose language modeling technique alongside an off-the-shelf data serialization protocol can be used to effectively solve generation of complex structured objects. We showcased the proposed system on the domain of 2D CAD drawings and developed models that can synthesize geometric primitives and relations between them both unconditionally as well as using a bitmap as a reference. These are only initial proof-of-concept experiments and we are hoping to see more applications taking advantage of the flexibility of the developed interface: conditioning on various sketch properties, inferring constraints given entities and automatically completing drawings, to name a few. ",
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+    {
+        "type": "text",
+        "text": "Although we focused our attention on a particular dataset we argue that the approach described in this paper is largely domain-agnostic. In order to adapt the system to a new kind of data, the algorithm designer only needs to provide an appropriate Protocol Buffer specification and if the PB language is too restrictive one can always replace it with a more powerful interpreter. As a straightforward direction for future work, we can consider extending the method to handle 3D. In Onshape, 3D operations bear a lot of similarities with sketch constraints — just like constraints, they can be represented as nested messages containing references to the geometries existing in the scene. Thus, most of the ideas from the present work can be taken verbatim to this new setting. ",
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+    {
+        "type": "text",
+        "text": "We hope that this work will serve as a stepping stone for further advances in the field of automated CAD but also inspire new ideas and approaches to generative modeling of arbitrary structured data. ",
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+    {
+        "type": "text",
+        "text": "Acknowledgments and Disclosure of Funding ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The authors would like to thank Charlie Nash, Georg Ostrovski, and Adam Kosiorek for helping with the manuscript preparation as well as Igor Babuschkin, David Choi, Nate Kushman, Andrew Kimpton, Jake Rosenfeld, Lana Saksonov, John Rousseau, Greg Guarriello, Andy Brock, Francesco Nori, Aäron van den Oord, and Oriol Vinyals for insightful discussions and support. ",
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+    {
+        "type": "text",
+        "text": "YG, SB, YL, and SS are funded by DeepMind. EK is funded by PTC. ",
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+    {
+        "type": "text",
+        "text": "References ",
+        "text_level": 1,
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+        "text": "[1] J. Alakuijala, A. Farruggia, P. Ferragina, E. Kliuchnikov, R. Obryk, Z. Szabadka, and L. Vandevenne. Brotli: A general-purpose data compressor. TOIS, 2018.   \n[2] H. K. Ault. Using geometric constraints to capture design intent. JGG, 1999.   \n[3] H. G. Barrow, J. M. Tenenbaum, R. C. Bolles, and H. C. Wolf. Parametric correspondence and chamfer matching: Two new techniques for image matching. Technical report, SRI INTERNATIONAL MENLO PARK CA ARTIFICIAL INTELLIGENCE CENTER, 1977.   \n[4] R. Bavishi, C. Lemieux, R. Fox, K. Sen, and I. Stoica. AutoPandas: Neural-backed generators for program synthesis. In OOPSLA, 2019.   \n[5] Y. Bengio, R. Ducharme, P. Vincent, and C. Janvin. A neural probabilistic language model. JMLR, 2003.   \n[6] T. B. Brown, B. Mann, N. Ryder, M. Subbiah, J. Kaplan, P. Dhariwal, A. Neelakantan, P. Shyam, G. Sastry, A. Askell, et al. Language models are few-shot learners. arXiv preprint arXiv:2005.14165, 2020.   \n[7] A. Carlier, M. Danelljan, A. Alahi, and R. Timofte. DeepSVG: A hierarchical generative network for vector graphics animation. arXiv preprint arXiv:2007.11301, 2020.   \n[8] P. Company, F. Naya, M. Contero, and J. Camba. On the role of geometric constraints to support design intent communication and model reusability. Computer-Aided Design and Applications, 2019.   \n[9] P. Dhariwal, H. Jun, C. Payne, J. W. Kim, A. Radford, and I. Sutskever. Jukebox: A generative model for music. arXiv preprint arXiv:2005.00341, 2020.   \n[10] D. Dori and K. Tombre. From engineering drawings to 3d CAD models: are we ready now? Computer-Aided Design, 1995.   \n[11] D. Dori and L. Wenyin. Automated cad conversion with the machine drawing understanding system: concepts, algorithms, and performance. SMC, 1999.   \n[12] A. Dosovitskiy, L. Beyer, A. Kolesnikov, D. Weissenborn, X. Zhai, T. Unterthiner, M. Dehghani, M. Minderer, G. Heigold, S. Gelly, et al. An image is worth 16x16 words: Transformers for image recognition at scale. arXiv preprint arXiv:2010.11929, 2020.   \n[13] V. Egiazarian, O. Voynov, A. Artemov, D. Volkhonskiy, A. Safin, M. Taktasheva, D. Zorin, and E. Burnaev. Deep vectorization of technical drawings. In ECCV, 2020.   \n[14] Y. Ganin, T. Kulkarni, I. Babuschkin, S. A. Eslami, and O. Vinyals. Synthesizing programs for images using reinforced adversarial learning. In ICML, 2018.   \n[15] A. Holtzman, J. Buys, L. Du, M. Forbes, and Y. Choi. The curious case of neural text degeneration. arXiv preprint arXiv:1904.09751, 2019.   \n[16] S. Koch, A. Matveev, Z. Jiang, F. Williams, A. Artemov, E. Burnaev, M. Alexa, D. Zorin, and D. Panozzo. ABC: A big CAD model dataset for geometric deep learning. In CVPR, 2019.   \n[17] T. Kudo and J. Richardson. Sentencepiece: A simple and language independent subword tokenizer and detokenizer for neural text processing. arXiv preprint arXiv:1808.06226, 2018.   \n[18] A. Meurer, C. P. Smith, M. Paprocki, O. Certík, S. B. Kirpichev, M. Rocklin, A. Kumar, ˇ S. Ivanov, J. K. Moore, S. Singh, et al. SymPy: symbolic computing in Python. PeerJ Computer Science, 2017.   \n[19] T. Mikolov, M. Karafiát, L. Burget, J. Cernock ˇ y, and S. Khudanpur. Recurrent neural network \\` based language model. In INTERSPEECH, 2010.   \n[20] V. Nagasamy and N. A. Langrana. Engineering drawing processing and vectorization system. CVGIP, 1990.   \n[21] C. Nash, Y. Ganin, S. A. Eslami, and P. Battaglia. PolyGen: An autoregressive generative model of 3D meshes. In ICML, 2020.   \n[22] Onshape developers. Onshape website. https://www.onshape.com/. Accessed: 2021-03-10.   \n[23] A. v. d. Oord, N. Kalchbrenner, O. Vinyals, L. Espeholt, A. Graves, and K. Kavukcuoglu. Conditional image generation with PixelCNN decoders. arXiv preprint arXiv:1606.05328, 2016.   \n[24] W. R. Para, S. F. Bhat, P. Guerrero, T. Kelly, N. Mitra, L. Guibas, and P. Wonka. SketchGen: Generating constrained CAD sketches. arXiv preprint arXiv:2106.02711, 2021.   \n[25] F. Pezoa, J. L. Reutter, F. Suarez, M. Ugarte, and D. Vrgoc. Foundations of JSON schema. In ˇ WWW, 2016.   \n[26] A. Radford, J. Wu, R. Child, D. Luan, D. Amodei, and I. Sutskever. Language models are unsupervised multitask learners. OpenAI blog, 2019.   \n[27] A. Ramesh, M. Pavlov, G. Goh, S. Gray, C. Voss, A. Radford, M. Chen, and I. Sutskever. Zero-shot text-to-image generation. arXiv preprint arXiv:2102.12092, 2021.   \n[28] M. Ranzato, S. Chopra, M. Auli, and W. Zaremba. Sequence level training with recurrent neural networks. arXiv preprint arXiv:1511.06732, 2015.   \n[29] A. Razavi, A. v. d. Oord, and O. Vinyals. Generating diverse high-fidelity images with VQVAE-2. arXiv preprint arXiv:1906.00446, 2019.   \n[30] P. Reddy, M. Gharbi, M. Lukac, and N. J. Mitra. Im2Vec: Synthesizing vector graphics without vector supervision. arXiv preprint arXiv:2102.02798, 2021.   \n[31] A. Seff, Y. Ovadia, W. Zhou, and R. P. Adams. Sketchgraphs: A large-scale dataset for modeling relational geometry in computer-aided design. arXiv preprint arXiv:2007.08506, 2020.   \n[32] K. Varda. Google protocol buffers: Google’s data interchange format. Technical report, 2008.   \n[33] A. Vaswani, N. Shazeer, N. Parmar, J. Uszkoreit, L. Jones, A. N. Gomez, L. Kaiser, and I. Polosukhin. Attention is all you need. arXiv preprint arXiv:1706.03762, 2017.   \n[34] P. Vaxiviere and K. Tombre. Celesstin: CAD conversion of mechanical drawings. Computer, 1992.   \n[35] O. Vinyals, M. Fortunato, and N. Jaitly. Pointer networks. In NeurIPS, 2015.   \n[36] K. D. Willis, Y. Pu, J. Luo, H. Chu, T. Du, J. G. Lambourne, A. Solar-Lezama, and W. Matusik. Fusion 360 gallery: A dataset and environment for programmatic CAD reconstruction. arXiv preprint arXiv:2010.02392, 2020.   \n[37] K. D. Willis, P. K. Jayaraman, J. G. Lambourne, H. Chu, and Y. Pu. Engineering sketch generation for computer-aided design. arXiv preprint arXiv:2104.09621, 2021.   \n[38] R. Wu, C. Xiao, and C. Zheng. DeepCAD: A deep generative network for computer-aided design models. In ICCV, 2021. ",
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+        "text": "(a) Do the main claims made in the abstract and introduction accurately reflect the paper’s contributions and scope? [Yes]   \n(b) Did you describe the limitations of your work? [Yes]   \n(c) Did you discuss any potential negative societal impacts of your work? [No] The method presented in this work is a general machine learning framework and it is not immediately obvious how it could negatively impact the society.   \n(d) Have you read the ethics review guidelines and ensured that your paper conforms to them? [Yes] ",
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+        "text": "(a) Did you state the full set of assumptions of all theoretical results? [N/A] (b) Did you include complete proofs of all theoretical results? [N/A] ",
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+        "text": "(a) Did you include the code, data, and instructions needed to reproduce the main experimental results (either in the supplemental material or as a URL)? [No] The code is proprietary but may be open-sourced in the future. The dataset will be released shortly.   \n(b) Did you specify all the training details (e.g., data splits, hyperparameters, how they were chosen)? [Yes]   \n(c) Did you report error bars (e.g., with respect to the random seed after running experiments multiple times)? [No] The experiments in the paper are expensive to run. Moreover, we did not observe any significant fluctuations in the validation metrics between different training runs with the same hyperparameters.   \n(d) Did you include the total amount of compute and the type of resources used (e.g., type of GPUs, internal cluster, or cloud provider)? [Yes] ",
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diff --git a/parse/train/z-X_PpwaroO/z-X_PpwaroO_middle.json b/parse/train/z-X_PpwaroO/z-X_PpwaroO_middle.json
new file mode 100644
index 0000000000000000000000000000000000000000..b953a856b864af363ec062c15d90e5859a6a0b42
--- /dev/null
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+                                    "content": "a subsequent paper by Para et al. [24]. While [24] employ very similar ideas to ours they do not",
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+                                    "type": "text"
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+                            ],
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+                                    "content": "work originate from the Onshape platform [22] which provides them in JSON format [25]. As the",
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+                                    "content": "first step in our processing pipeline we convert JSON messages into Protocol Buffers (PB) [32]. In",
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+                            ],
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+                                    "score": 1.0,
+                                    "content": "integer or floating-point) or complex (e.g., an array or another object). Sketches that we use in this",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
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+                                    "score": 1.0,
+                                    "content": "work originate from the Onshape platform [22] which provides them in JSON format [25]. As the",
+                                    "type": "text"
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+                            ],
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+                        {
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+                                    "score": 1.0,
+                                    "content": "first step in our processing pipeline we convert JSON messages into Protocol Buffers (PB) [32]. In",
+                                    "type": "text"
+                                }
+                            ],
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+                        {
+                            "bbox": [
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "order to keep the pipeline as domain-agnostic and as widely applicable as possible, we aim to avoid",
+                                    "type": "text"
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+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "any significant changes to the data and largely retain the original structures of objects. The benefit of",
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+                            ],
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+                            "bbox": [
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "converting into PB is twofold: the resulting data occupies less space because unnecessary information",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        },
+                        {
+                            "bbox": [
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+                                    "score": 1.0,
+                                    "content": "is removed, but also, unlike JSON, PB provide a convenient way to define precise specifications for",
+                                    "type": "text"
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+                            ],
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+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "structures of arbitrary complexity.",
+                                    "type": "text"
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+                            ],
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+                        }
+                    ],
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+                                    "content": "Listing 1a shows how we represent the line entity and the mirror constraint (see Appendix A for",
+                                    "type": "text"
+                                }
+                            ],
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+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "an extensive list of supported objects). The line specification is straightforward: we first need to",
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+                            ],
+                            "index": 45
+                        },
+                        {
+                            "bbox": [
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "decide whether our entity should be treated as a construction geometry2 and then provide pairs of",
+                                    "type": "text"
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+                            ],
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+                        {
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+                                    "score": 1.0,
+                                    "content": "coordinates for the beginning and end of the segment. The MirrorConstraint is used to force an",
+                                    "type": "text"
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+                            ],
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+                        },
+                        {
+                            "bbox": [
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+                                    "bbox": [
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+                                    "type": "text"
+                                }
+                            ],
+                            "index": 48
+                        },
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+                                    "score": 1.0,
+                                    "content": "some axis (i.e., mirror). Constraints rely on the Pointer data type to specify entities they act upon.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 49
+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "In practice, a pointer is simply an index in the table of all the eligible pointees (i.e., entities and their",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 50
+                        },
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+                                    "score": 1.0,
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+                                    "content": "\\texttt { x } = \\texttt { 1 }",
+                                    "type": "inline_equation"
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+                                    "score": 1.0,
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+                                    "score": 1.0,
+                                    "content": "; // Start point.",
+                                    "type": "text"
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+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
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+                                    "type": "text"
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+                                    "score": 0.73,
+                                    "content": "\\ c = \\ 3",
+                                    "type": "inline_equation"
+                                },
+                                {
+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "; // End point.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
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+                                    "content": "}",
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+                    ],
+                    "index": 4
+                },
+                {
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+                                    "type": "text"
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+                            ],
+                            "index": 9
+                        },
+                        {
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+                                    "type": "text"
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+                                    "type": "inline_equation"
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+                                {
+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "; // Axis of symmetry.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
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+                                    "content": "message Pair { // Mirrored objects.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
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+                                    "type": "text"
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+                                    "type": "inline_equation"
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+                                {
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+                                    "type": "text"
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+                                    "type": "text"
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+                                    "type": "inline_equation"
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+                                {
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+                                    "score": 1.0,
+                                    "content": "repeated Pair mirrored_pairs",
+                                    "type": "text"
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+                                {
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+                                    "content": "}",
+                                    "type": "text"
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+                                    "content": "(see Listing 1b) assuming some ordering of objects. We discuss different orderings in Section 5.",
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+                                    "content": "a message. Such sequences are much shorter since the structure is handled by an external parser",
+                                    "type": "text"
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+                            ],
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+                        },
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+                                    "score": 1.0,
+                                    "content": "automatically generated from the data specification. The parser’s task is to interpret the incoming",
+                                    "type": "text"
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+                            ],
+                            "index": 54
+                        },
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+                                    "score": 1.0,
+                                    "content": "stream of unstructured bytes and populate the fields of PB messages. However, like the text format,",
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+                                    "score": 1.0,
+                                    "content": "not every sequence of bytes results in a valid PB message.",
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+                        }
+                    ],
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+                },
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+                                    "score": 1.0,
+                                    "content": "Going one step further, we can utilize the structure of the sketch format more directly, and build a",
+                                    "type": "text"
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+                            ],
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+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "custom interpreter, that takes as input a sequence of tokens each representing a valid choice at various",
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+                        },
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+                                    "score": 1.0,
+                                    "content": "decision steps [4] in the sketch creation process. We designed this interpreter in such a way that",
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+                            ],
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+                        },
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+                                    "content": "all sequences of tokens in this format lead to valid PB messages. More specifically, we represent a",
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+                        },
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+                                    "score": 0.93,
+                                    "content": "( d _ { i } , c _ { i } , f _ { i } )",
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+                                    "score": 1.0,
+                                    "content": "describe basic fields of the sketch objects with each token representing exactly one field. The first two",
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+                            ],
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+                                    "score": 1.0,
+                                    "content": "each field in a message is either discrete or continuous only one of two positions is active at a time",
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+                        },
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+                                    "content": "(the other one is set to a default zero value). The third component is a boolean flag signifying the end",
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+                        },
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+                                    "score": 1.0,
+                                    "content": "of a repeated field3 which contains a list of elements of the same type. An example sequence for a",
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+                        },
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+                                    "content": "sketch containing a line and a point placed at one of its ends is shown in Table 1 (Triplet column).",
+                                    "type": "text"
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+                        }
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+                                    "type": "text"
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+                                    "type": "text"
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+                                    "content": "(see Listing 1b) assuming some ordering of objects. We discuss different orderings in Section 5.",
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+                                    "score": 1.0,
+                                    "content": "Since this format contains both the structure and the content of the data, the resulting sequences end",
+                                    "type": "text"
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+                            ],
+                            "index": 48
+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "up being prohibitively long. Additionally, the model would have to generate valid syntax, which",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 49
+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "would take up some portion of the model’s capacity. To overcome these challenges, we work with",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 50
+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "two flavours of serialized PB messages.",
+                                    "type": "text"
+                                }
+                            ],
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+                    ],
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+                                    "content": "The first one is a sequences of bytes obtained by calling the SerializeToString() method of",
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+                            ],
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+                                    "content": "a message. Such sequences are much shorter since the structure is handled by an external parser",
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+                                    "score": 1.0,
+                                    "content": "automatically generated from the data specification. The parser’s task is to interpret the incoming",
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+                            ],
+                            "index": 54
+                        },
+                        {
+                            "bbox": [
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+                                    "score": 1.0,
+                                    "content": "stream of unstructured bytes and populate the fields of PB messages. However, like the text format,",
+                                    "type": "text"
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+                            ],
+                            "index": 55
+                        },
+                        {
+                            "bbox": [
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+                                    "score": 1.0,
+                                    "content": "not every sequence of bytes results in a valid PB message.",
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+                            "index": 56
+                        }
+                    ],
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "Going one step further, we can utilize the structure of the sketch format more directly, and build a",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 57
+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "custom interpreter, that takes as input a sequence of tokens each representing a valid choice at various",
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+                                    "score": 1.0,
+                                    "content": "decision steps [4] in the sketch creation process. We designed this interpreter in such a way that",
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+                            ],
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+                                    "score": 1.0,
+                                    "content": "all sequences of tokens in this format lead to valid PB messages. More specifically, we represent a",
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+                                    "score": 1.0,
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+                                    "score": 0.93,
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+                                    "content": "i",
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+                                    "score": 1.0,
+                                    "content": "is an index of the token. The majority of tokens",
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+                            "index": 61
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+                            "bbox": [
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+                                    "score": 1.0,
+                                    "content": "describe basic fields of the sketch objects with each token representing exactly one field. The first two",
+                                    "type": "text"
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+                                    "score": 1.0,
+                                    "content": "positions in each triplet are allocated for a discrete value and a continuous value respectively. Since",
+                                    "type": "text"
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+                            ],
+                            "index": 63
+                        },
+                        {
+                            "bbox": [
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+                                    "score": 1.0,
+                                    "content": "each field in a message is either discrete or continuous only one of two positions is active at a time",
+                                    "type": "text"
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+                            ],
+                            "index": 64
+                        },
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+                                    "score": 1.0,
+                                    "content": "(the other one is set to a default zero value). The third component is a boolean flag signifying the end",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 65
+                        },
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+                                    "score": 1.0,
+                                    "content": "of a repeated field3 which contains a list of elements of the same type. An example sequence for a",
+                                    "type": "text"
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+                            ],
+                            "index": 66
+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "sketch containing a line and a point placed at one of its ends is shown in Table 1 (Triplet column).",
+                                    "type": "text"
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+                        }
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+                                            "html": "<table><tr><td>Triplet</td><td>Field</td><td></td><td>Triplet</td><td>Field</td></tr><tr><td>1.</td><td>(0,0.0,False)</td><td>objects.kind</td><td>8. (0,0.0,False)</td><td>objects.kind</td></tr><tr><td>2.</td><td>(0,0.0,False)</td><td>entity.kind</td><td>9. (1, 0.0,False)</td><td>entity.kind</td></tr><tr><td>3.</td><td>(1,0.0,False)</td><td>line.is_constr</td><td>10. (0, 0.0,False)</td><td>Point point.is_const</td></tr><tr><td>4.</td><td>(0, 0.0,False)</td><td>line.start.x</td><td>11. (0, 0.0,False)</td><td>point .x</td></tr><tr><td>5.</td><td>(0,0.1,False)</td><td>line.start.y</td><td>12. (0,0.1,False)</td><td>point.y</td></tr><tr><td>6.</td><td>(0,-0.5,False)</td><td>line.end.x</td><td>13. (0, 0.0, True)</td><td>objects.kind</td></tr><tr><td>7.</td><td>(0, 0.2,False)</td><td>line.end.y</td><td></td><td></td></tr></table>",
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+                                    "content": "Table 1: A triplet representation of a simple sketch. The sketch contains and a line and a point.",
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+                                    "content": "Within each triplet in the left column, the active component (the value that is actually used) is",
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+                                    "score": 1.0,
+                                    "content": "highlighted in bold. The right column shows which field of the object the triplet is associated with.",
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+                    ],
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+                                    "content": "Given a sequence of such triplets, it is possible to infer which exact field each token corresponds to.",
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+                                    "score": 1.0,
+                                    "content": "Indeed, the very first token",
+                                    "type": "text"
+                                },
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+                                    "score": 0.93,
+                                    "content": "( d _ { 1 } , c _ { 1 } , f _ { 1 } )",
+                                    "type": "inline_equation"
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+                                    "score": 1.0,
+                                    "content": "is always associated with objects.kind since it is the first",
+                                    "type": "text"
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+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
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+                                    "score": 1.0,
+                                    "content": "choice that needs to be made to create a Sketch message (see Listing 1b). The second field depends",
+                                    "type": "text"
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+                            ],
+                            "index": 8
+                        },
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+                                    "score": 1.0,
+                                    "content": "on the concrete value of",
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+                                    "content": ". If",
+                                    "type": "text"
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+                                    "score": 0.92,
+                                    "content": "d _ { 1 } = 0",
+                                    "type": "inline_equation"
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+                                {
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+                                    "score": 1.0,
+                                    "content": "then the first object is an entity which means that the second",
+                                    "type": "text"
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+                            ],
+                            "index": 9
+                        },
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+                                    "content": "This means that we can’t naively describe each conditional in Equation 1 using the same template",
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+                                            "html": "<table><tr><td>Triplet</td><td>Field</td><td></td><td>Triplet</td><td>Field</td></tr><tr><td>1.</td><td>(0,0.0,False)</td><td>objects.kind</td><td>8. (0,0.0,False)</td><td>objects.kind</td></tr><tr><td>2.</td><td>(0,0.0,False)</td><td>entity.kind</td><td>9. (1, 0.0,False)</td><td>entity.kind</td></tr><tr><td>3.</td><td>(1,0.0,False)</td><td>line.is_constr</td><td>10. (0, 0.0,False)</td><td>Point point.is_const</td></tr><tr><td>4.</td><td>(0, 0.0,False)</td><td>line.start.x</td><td>11. (0, 0.0,False)</td><td>point .x</td></tr><tr><td>5.</td><td>(0,0.1,False)</td><td>line.start.y</td><td>12. (0,0.1,False)</td><td>point.y</td></tr><tr><td>6.</td><td>(0,-0.5,False)</td><td>line.end.x</td><td>13. (0, 0.0, True)</td><td>objects.kind</td></tr><tr><td>7.</td><td>(0, 0.2,False)</td><td>line.end.y</td><td></td><td></td></tr></table>",
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+                                    "score": 1.0,
+                                    "content": "then the first object is an entity which means that the second",
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+                                    "content": "token corresponds to entity.kind . The rest of the sequence is associated in a similar fashion.",
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+                                    "score": 1.0,
+                                    "content": "Field identifiers along with their locations within an object form the context of the tokens. We use",
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+                                    "score": 1.0,
+                                    "content": "this contextual information as an additional input for our machine learning models since it makes it",
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+                                    "score": 1.0,
+                                    "content": "In Onshape, constraints can be applied not only to whole entities but also to their subparts (e.g., the",
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+                                    "content": "center of a circle or the end points of a line segment). To handle this, we introduce special referrable",
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+                                    "type": "text"
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+                        {
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+                                    "score": 1.0,
+                                    "content": "and have the same identifier within each entity type. In order to let the model distinguish between",
+                                    "type": "text"
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+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "different subparts, we adjust Equation 3 to use a learnable embedding of a part index instead of",
+                                    "type": "text"
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+                        },
+                        {
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+                                    "bbox": [
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+                                    "score": 0.92,
+                                    "content": "V ^ { \\mathcal { G } } [ t _ { i - 1 } ]",
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+                                    "content": ". As referrable tokens do not need to be predicted the respective terms are removed from",
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+                                    "score": 1.0,
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+                                    "score": 1.0,
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+                                    "score": 1.0,
+                                    "content": "output and not the input. This allows us to avoid having unused Transformer outputs.",
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+                                    "score": 1.0,
+                                    "content": "Finally, we need to specify how we embed pointers as inputs to the Transformer network. Following",
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+                                    "score": 1.0,
+                                    "content": "for tokens that point to",
+                                    "type": "text"
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+                                    "score": 1.0,
+                                    "content": ". Unfortunately, this creates output-to-input",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "connections which are extremely detrimental to the efficiency of the Transformer architecture —",
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+                            "index": 18
+                        },
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+                                    "score": 1.0,
+                                    "content": "different time steps can no longer be processed in parallel during training. Instead, we opt for a",
+                                    "type": "text"
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+                            ],
+                            "index": 19
+                        },
+                        {
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "simpler solution and employ the standard embedding scheme for discrete tokens (Equation 3).",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        }
+                    ],
+                    "index": 18
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+                {
+                    "type": "text",
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "Sampling from the model Sampling from the byte model is identical to sampling from any typical",
+                                    "type": "text"
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+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
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+                                    "score": 1.0,
+                                    "content": "Transformer-based LM. The triplet model, on the other hand, requires slightly more bespoke handling.",
+                                    "type": "text"
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+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
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+                                    "score": 1.0,
+                                    "content": "Figure 2 illustrates the procedure. We start by embedding and feeding a special BOS token into the",
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+                                    "content": "In Onshape, constraints can be applied not only to whole entities but also to their subparts (e.g., the",
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+                                    "content": "center of a circle or the end points of a line segment). To handle this, we introduce special referrable",
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+                                    "score": 1.0,
+                                    "content": "and have the same identifier within each entity type. In order to let the model distinguish between",
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+                                    "type": "text"
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+                                    "score": 0.92,
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+                                    "score": 1.0,
+                                    "content": "Finally, we need to specify how we embed pointers as inputs to the Transformer network. Following",
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+                                    "score": 1.0,
+                                    "content": ". Unfortunately, this creates output-to-input",
+                                    "type": "text"
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+                                    "score": 1.0,
+                                    "content": "connections which are extremely detrimental to the efficiency of the Transformer architecture —",
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+                                    "score": 1.0,
+                                    "content": "different time steps can no longer be processed in parallel during training. Instead, we opt for a",
+                                    "type": "text"
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+                            ],
+                            "index": 19
+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "simpler solution and employ the standard embedding scheme for discrete tokens (Equation 3).",
+                                    "type": "text"
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+                            ],
+                            "index": 20
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+                    ],
+                    "index": 18,
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+                                    "score": 1.0,
+                                    "content": "Sampling from the model Sampling from the byte model is identical to sampling from any typical",
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+                        },
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+                                    "content": "Transformer-based LM. The triplet model, on the other hand, requires slightly more bespoke handling.",
+                                    "type": "text"
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+                            ],
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+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "Figure 2 illustrates the procedure. We start by embedding and feeding a special BOS token into the",
+                                    "type": "text"
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+                            ],
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+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "Transformer. The Transformer then outputs a collection of triplets, one for each possible token group.",
+                                    "type": "text"
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+                            ],
+                            "index": 24
+                        },
+                        {
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+                            "spans": [
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+                                    "score": 1.0,
+                                    "content": "In order to determine which concrete token needs to be emitted, we employ an interpreter (a state",
+                                    "type": "text"
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+                            ],
+                            "index": 25
+                        },
+                        {
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "machine) automatically generated from the data specification. Knowing the current state allows us",
+                                    "type": "text"
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+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
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+                                    "score": 1.0,
+                                    "content": "to choose the right token group and associate the active component of the triplet with a field in the",
+                                    "type": "text"
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+                            ],
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+                        },
+                        {
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "synthesized object. Once the appropriate field is populated the interpreter transitions to the next state",
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+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "and produces an output token which is then fed back into the model. The process stops when the",
+                                    "type": "text"
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+                                    "content": "within both the sequence of entities and the sequence of constraints are taken directly from the",
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+                                    "score": 1.0,
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+                                    "content": "tokens on average with the maximum length of 959 vs. 1987.",
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+                                    "score": 1.0,
+                                    "content": "explanation for this is that at any point in time, the model has more explicit information about the",
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+                            ],
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+                                    "score": 1.0,
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+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        }
+                    ],
+                    "index": 25.5
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+                                    "score": 1.0,
+                                    "content": "In the row 3 of Table 2, we also provide the test log-likelihood for a conventional language modeling",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
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+                                    "score": 1.0,
+                                    "content": "SentencePiece tokenizer [17] with fairly aggressive settings (8000 words in the vocabulary; splitting",
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+                                }
+                            ],
+                            "index": 30
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+                        {
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+                                    "score": 1.0,
+                                    "content": "at whitespaces switched off) to be able to keep the sequences within the budget of 1024 tokens. As",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "can be seen from the table, the resulting Transformer model (of exactly the same architecture as other",
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+                                    "score": 1.0,
+                                    "content": "entries) despite being better than the uniform baselines is still substantially worse than the proposed",
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+                    ],
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+                            ],
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+                        },
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+                                    "score": 1.0,
+                                    "content": "and triplet models and computed distributions of various high-level statistics (Figure 4 and Figure 6",
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+                            ],
+                            "index": 36
+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "in the appendix). We repeated this procedure both with and without using Nucleus Sampling (NS)",
+                                    "type": "text"
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+                            ],
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+                        },
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+                                    "score": 1.0,
+                                    "content": "[15]. Both models follow the data distribution closely when we use samples from the unmodified",
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+                                }
+                            ],
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+                        },
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+                                    "score": 1.0,
+                                    "content": "model output. In this setting, however, a significant fraction of sketches is either malformed (e.g.,",
+                                    "type": "text"
+                                }
+                            ],
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+                        },
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+                                    "score": 1.0,
+                                    "content": "the generated PB message cannot be parsed) or unsolvable:",
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+                                    "score": 0.88,
+                                    "content": "3 6 \\%",
+                                    "type": "inline_equation"
+                                },
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+                                    "bbox": [
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+                                    "score": 1.0,
+                                    "content": "for the byte model and",
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+                                    "score": 0.88,
+                                    "content": "1 4 \\%",
+                                    "type": "inline_equation"
+                                },
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+                                    "score": 1.0,
+                                    "content": "for",
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+                                    "content": "explanation for this is that at any point in time, the model has more explicit information about the",
+                                    "type": "text"
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+                        {
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+                                    "score": 1.0,
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+                                    "score": 1.0,
+                                    "content": "In the row 3 of Table 2, we also provide the test log-likelihood for a conventional language modeling",
+                                    "type": "text"
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+                        {
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+                                    "content": "baseline trained on the text representation of PB messages (see Section 3). Here, we employ the",
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+                        {
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+                                    "score": 1.0,
+                                    "content": "at whitespaces switched off) to be able to keep the sequences within the budget of 1024 tokens. As",
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+                                    "score": 1.0,
+                                    "content": "can be seen from the table, the resulting Transformer model (of exactly the same architecture as other",
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+                                    "score": 1.0,
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+                                    "score": 1.0,
+                                    "content": "and triplet models and computed distributions of various high-level statistics (Figure 4 and Figure 6",
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+                                    "score": 1.0,
+                                    "content": "in the appendix). We repeated this procedure both with and without using Nucleus Sampling (NS)",
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+                                    "content": "[15]. Both models follow the data distribution closely when we use samples from the unmodified",
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+                                    "score": 1.0,
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+                                    "score": 0.88,
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+                                    "type": "inline_equation"
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+                                {
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+                                    "score": 1.0,
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+                                    "score": 0.88,
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+                                    "type": "inline_equation"
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+                                    "score": 1.0,
+                                    "content": "the triplet model. NS with top-",
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+                                    "score": 0.9,
+                                    "content": "p = 0 . 9",
+                                    "type": "inline_equation"
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+                                    "score": 1.0,
+                                    "content": "pronounced negative effect on the byte model. The upside is that the resulting sketches become",
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+                                    "score": 1.0,
+                                    "content": "Figures 3a and 3b show renders of random samples from several proposed models. Overall, generated",
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+                                    "score": 1.0,
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+                                    "score": 1.0,
+                                    "content": "complex samples with fewer open arcs but this could be a side effect of a particular top-",
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+                                    "content": "value. We",
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+                            "index": 11
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+                        {
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+                                    "score": 1.0,
+                                    "content": "also note that the model does not always synthesize sensible sketches — just like any other typical",
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+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "autoregressive model trained with teacher forcing it suffers from not being able to recover from",
+                                    "type": "text"
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+                                    "score": 1.0,
+                                    "content": "mistakes made early on in the sequence [28]. This can potentially be addressed by fine-tuning using,",
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+                                    "content": "for example, reinforcement learning.",
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+                                    "content": "We show a more detailed sample from the triplet model in Figure 5. While not perfect, the inferred",
+                                    "type": "text"
+                                }
+                            ],
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+                        {
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+                                    "content": "constraints are reasonable most of the time. The model does a good job at connecting entities using",
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+                        {
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+                                    "content": "Coincident constraints but also successfully detects more complex relations spanning more than",
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+                                    "content": "two primitives (e.g., Mirror). Having access to constraints gives us opportunity to correct mistakes",
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+                        {
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+                                    "score": 1.0,
+                                    "content": "in entity prediction by applying an external sketch solver (see Figure 3d). Although this aspect of",
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+                        {
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+                                    "score": 1.0,
+                                    "content": "and the CAD software will lead to a significant boost in generation quality.",
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+                                    "score": 1.0,
+                                    "content": "(the last row of Table 2) but at the same time retains a non-trivial amount of uncertainty. The latter is",
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+                                    "content": "image. Image-conditional samples can be found in Figure 3c. The model was able to nearly perfectly",
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+                                    "content": "reconstruct simpler sketches and mostly made mistakes in the presence of a large number of fine",
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+                                    "score": 1.0,
+                                    "content": "details. Additionally, we compared our system against the nearest neighbour baseline in terms of",
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+                                    "score": 1.0,
+                                    "content": "visual reconstruction error as measured by Chamfer distance. We found that the proposed method",
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+                                    "score": 0.89,
+                                    "content": "\\approx 8 0 \\%",
+                                    "type": "inline_equation"
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+                                    "score": 1.0,
+                                    "content": "(see Appendix H). In order to test the out-of-distribution performance,",
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+                                    "score": 1.0,
+                                    "content": "we supply the model with several custom-made drawings. Surprisingly, after minor post-processing",
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+                                    "score": 1.0,
+                                    "content": "to account for the short sequence bias the system manages to produce reasonable reconstructions (see",
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+                                    "score": 1.0,
+                                    "content": "Figures 3a and 3b show renders of random samples from several proposed models. Overall, generated",
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+                                    "content": "complex samples with fewer open arcs but this could be a side effect of a particular top-",
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+                                    "content": "also note that the model does not always synthesize sensible sketches — just like any other typical",
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+                                    "content": "mistakes made early on in the sequence [28]. This can potentially be addressed by fine-tuning using,",
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+                                    "content": "for example, reinforcement learning.",
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+                                    "content": "We show a more detailed sample from the triplet model in Figure 5. While not perfect, the inferred",
+                                    "type": "text"
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+                            ],
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+                                    "content": "constraints are reasonable most of the time. The model does a good job at connecting entities using",
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+                                    "score": 1.0,
+                                    "content": "Coincident constraints but also successfully detects more complex relations spanning more than",
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+                                    "type": "inline_equation"
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+                                    "score": 1.0,
+                                    "content": "(see Appendix H). In order to test the out-of-distribution performance,",
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+                                    "content": "we supply the model with several custom-made drawings. Surprisingly, after minor post-processing",
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+                                    "content": "to account for the short sequence bias the system manages to produce reasonable reconstructions (see",
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+                                    "score": 1.0,
+                                    "content": "the bottom example in Figure 5). We detail this experiment in Appendix I.",
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+                                    "content": "In this work, we have demonstrated how a combination of a general-purpose language modeling",
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+                                    "score": 1.0,
+                                    "content": "generation of complex structured objects. We showcased the proposed system on the domain of",
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+                                    "score": 1.0,
+                                    "content": "between them both unconditionally as well as using a bitmap as a reference. These are only initial",
+                                    "type": "text"
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+                            ],
+                            "index": 5
+                        },
+                        {
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+                                    "score": 1.0,
+                                    "content": "proof-of-concept experiments and we are hoping to see more applications taking advantage of the",
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+                                    "content": "flexibility of the developed interface: conditioning on various sketch properties, inferring constraints",
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+                                    "content": "Thus, most of the ideas from the present work can be taken verbatim to this new setting.",
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+                                    "content": "Acknowledgments and Disclosure of Funding",
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+                                    "content": "with the manuscript preparation as well as Igor Babuschkin, David Choi, Nate Kushman, Andrew",
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+                                    "content": "Kimpton, Jake Rosenfeld, Lana Saksonov, John Rousseau, Greg Guarriello, Andy Brock, Francesco",
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+                                    "content": "Nori, Aäron van den Oord, and Oriol Vinyals for insightful discussions and support.",
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+                        420,
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+                    ],
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+                                419,
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+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        }
+                    ],
+                    "index": 25
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        110,
+                        439,
+                        507,
+                        722
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                110,
+                                439,
+                                506,
+                                452
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        110,
+                                        439,
+                                        506,
+                                        452
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[1] J. Alakuijala, A. Farruggia, P. Ferragina, E. Kliuchnikov, R. Obryk, Z. Szabadka, and L. Vande-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                451,
+                                384,
+                                463
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        451,
+                                        384,
+                                        463
+                                    ],
+                                    "score": 1.0,
+                                    "content": "venne. Brotli: A general-purpose data compressor. TOIS, 2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                110,
+                                468,
+                                439,
+                                482
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        110,
+                                        468,
+                                        439,
+                                        482
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[2] H. K. Ault. Using geometric constraints to capture design intent. JGG, 1999.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                110,
+                                487,
+                                506,
+                                502
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        110,
+                                        487,
+                                        506,
+                                        502
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[3] H. G. Barrow, J. M. Tenenbaum, R. C. Bolles, and H. C. Wolf. Parametric correspondence",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                498,
+                                506,
+                                512
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        498,
+                                        506,
+                                        512
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and chamfer matching: Two new techniques for image matching. Technical report, SRI",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                128,
+                                511,
+                                491,
+                                522
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        128,
+                                        511,
+                                        491,
+                                        522
+                                    ],
+                                    "score": 1.0,
+                                    "content": "INTERNATIONAL MENLO PARK CA ARTIFICIAL INTELLIGENCE CENTER, 1977.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                110,
+                                528,
+                                505,
+                                542
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        110,
+                                        528,
+                                        505,
+                                        542
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[4] R. Bavishi, C. Lemieux, R. Fox, K. Sen, and I. Stoica. AutoPandas: Neural-backed generators",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                540,
+                                299,
+                                554
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        540,
+                                        299,
+                                        554
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for program synthesis. In OOPSLA, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                110,
+                                558,
+                                506,
+                                571
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        110,
+                                        558,
+                                        506,
+                                        571
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[5] Y. Bengio, R. Ducharme, P. Vincent, and C. Janvin. A neural probabilistic language model.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                570,
+                                181,
+                                582
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        570,
+                                        181,
+                                        582
+                                    ],
+                                    "score": 1.0,
+                                    "content": "JMLR, 2003.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                110,
+                                588,
+                                506,
+                                601
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        110,
+                                        588,
+                                        506,
+                                        601
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[6] T. B. Brown, B. Mann, N. Ryder, M. Subbiah, J. Kaplan, P. Dhariwal, A. Neelakantan,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                599,
+                                505,
+                                612
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        599,
+                                        505,
+                                        612
+                                    ],
+                                    "score": 1.0,
+                                    "content": "P. Shyam, G. Sastry, A. Askell, et al. Language models are few-shot learners. arXiv preprint",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                611,
+                                230,
+                                622
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        611,
+                                        230,
+                                        622
+                                    ],
+                                    "score": 1.0,
+                                    "content": "arXiv:2005.14165, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                110,
+                                629,
+                                505,
+                                642
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        110,
+                                        629,
+                                        505,
+                                        642
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[7] A. Carlier, M. Danelljan, A. Alahi, and R. Timofte. DeepSVG: A hierarchical generative",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                640,
+                                448,
+                                654
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        640,
+                                        448,
+                                        654
+                                    ],
+                                    "score": 1.0,
+                                    "content": "network for vector graphics animation. arXiv preprint arXiv:2007.11301, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                110,
+                                657,
+                                505,
+                                673
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        110,
+                                        657,
+                                        505,
+                                        673
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[8] P. Company, F. Naya, M. Contero, and J. Camba. On the role of geometric constraints to support",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                669,
+                                507,
+                                685
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        669,
+                                        507,
+                                        685
+                                    ],
+                                    "score": 1.0,
+                                    "content": "design intent communication and model reusability. Computer-Aided Design and Applications,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                681,
+                                153,
+                                693
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        681,
+                                        153,
+                                        693
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        },
+                        {
+                            "bbox": [
+                                111,
+                                700,
+                                505,
+                                713
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        111,
+                                        700,
+                                        505,
+                                        713
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[9] P. Dhariwal, H. Jun, C. Payne, J. W. Kim, A. Radford, and I. Sutskever. Jukebox: A generative",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                711,
+                                361,
+                                723
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        711,
+                                        361,
+                                        723
+                                    ],
+                                    "score": 1.0,
+                                    "content": "model for music. arXiv preprint arXiv:2005.00341, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 45
+                        }
+                    ],
+                    "index": 35.5
+                }
+            ],
+            "page_idx": 9,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        300,
+                        741,
+                        311,
+                        750
+                    ],
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+                            "bbox": [
+                                299,
+                                740,
+                                313,
+                                754
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+                    ],
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+                                419,
+                                165,
+                                434
+                            ],
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+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        }
+                    ],
+                    "index": 25
+                },
+                {
+                    "type": "list",
+                    "bbox": [
+                        110,
+                        439,
+                        507,
+                        722
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                110,
+                                439,
+                                506,
+                                452
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        110,
+                                        439,
+                                        506,
+                                        452
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[1] J. Alakuijala, A. Farruggia, P. Ferragina, E. Kliuchnikov, R. Obryk, Z. Szabadka, and L. Vande-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                451,
+                                384,
+                                463
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        451,
+                                        384,
+                                        463
+                                    ],
+                                    "score": 1.0,
+                                    "content": "venne. Brotli: A general-purpose data compressor. TOIS, 2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                110,
+                                468,
+                                439,
+                                482
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        110,
+                                        468,
+                                        439,
+                                        482
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[2] H. K. Ault. Using geometric constraints to capture design intent. JGG, 1999.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28,
+                            "is_list_start_line": true,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                110,
+                                487,
+                                506,
+                                502
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        110,
+                                        487,
+                                        506,
+                                        502
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[3] H. G. Barrow, J. M. Tenenbaum, R. C. Bolles, and H. C. Wolf. Parametric correspondence",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                498,
+                                506,
+                                512
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        498,
+                                        506,
+                                        512
+                                    ],
+                                    "score": 1.0,
+                                    "content": "and chamfer matching: Two new techniques for image matching. Technical report, SRI",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                128,
+                                511,
+                                491,
+                                522
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        128,
+                                        511,
+                                        491,
+                                        522
+                                    ],
+                                    "score": 1.0,
+                                    "content": "INTERNATIONAL MENLO PARK CA ARTIFICIAL INTELLIGENCE CENTER, 1977.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                110,
+                                528,
+                                505,
+                                542
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        110,
+                                        528,
+                                        505,
+                                        542
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[4] R. Bavishi, C. Lemieux, R. Fox, K. Sen, and I. Stoica. AutoPandas: Neural-backed generators",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                540,
+                                299,
+                                554
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        540,
+                                        299,
+                                        554
+                                    ],
+                                    "score": 1.0,
+                                    "content": "for program synthesis. In OOPSLA, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                110,
+                                558,
+                                506,
+                                571
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        110,
+                                        558,
+                                        506,
+                                        571
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[5] Y. Bengio, R. Ducharme, P. Vincent, and C. Janvin. A neural probabilistic language model.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                570,
+                                181,
+                                582
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        570,
+                                        181,
+                                        582
+                                    ],
+                                    "score": 1.0,
+                                    "content": "JMLR, 2003.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                110,
+                                588,
+                                506,
+                                601
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        110,
+                                        588,
+                                        506,
+                                        601
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[6] T. B. Brown, B. Mann, N. Ryder, M. Subbiah, J. Kaplan, P. Dhariwal, A. Neelakantan,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                599,
+                                505,
+                                612
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        599,
+                                        505,
+                                        612
+                                    ],
+                                    "score": 1.0,
+                                    "content": "P. Shyam, G. Sastry, A. Askell, et al. Language models are few-shot learners. arXiv preprint",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                611,
+                                230,
+                                622
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        611,
+                                        230,
+                                        622
+                                    ],
+                                    "score": 1.0,
+                                    "content": "arXiv:2005.14165, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                110,
+                                629,
+                                505,
+                                642
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        110,
+                                        629,
+                                        505,
+                                        642
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[7] A. Carlier, M. Danelljan, A. Alahi, and R. Timofte. DeepSVG: A hierarchical generative",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                640,
+                                448,
+                                654
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        640,
+                                        448,
+                                        654
+                                    ],
+                                    "score": 1.0,
+                                    "content": "network for vector graphics animation. arXiv preprint arXiv:2007.11301, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                110,
+                                657,
+                                505,
+                                673
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        110,
+                                        657,
+                                        505,
+                                        673
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[8] P. Company, F. Naya, M. Contero, and J. Camba. On the role of geometric constraints to support",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                669,
+                                507,
+                                685
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        669,
+                                        507,
+                                        685
+                                    ],
+                                    "score": 1.0,
+                                    "content": "design intent communication and model reusability. Computer-Aided Design and Applications,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                681,
+                                153,
+                                693
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        681,
+                                        153,
+                                        693
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                111,
+                                700,
+                                505,
+                                713
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        111,
+                                        700,
+                                        505,
+                                        713
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[9] P. Dhariwal, H. Jun, C. Payne, J. W. Kim, A. Radford, and I. Sutskever. Jukebox: A generative",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 44,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                711,
+                                361,
+                                723
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        711,
+                                        361,
+                                        723
+                                    ],
+                                    "score": 1.0,
+                                    "content": "model for music. arXiv preprint arXiv:2005.00341, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 45,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                72,
+                                507,
+                                86
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        72,
+                                        507,
+                                        86
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[10] D. Dori and K. Tombre. From engineering drawings to 3d CAD models: are we ready now?",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 0,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                83,
+                                255,
+                                97
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        83,
+                                        255,
+                                        97
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Computer-Aided Design, 1995.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 1,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                103,
+                                506,
+                                117
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        103,
+                                        506,
+                                        117
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[11] D. Dori and L. Wenyin. Automated cad conversion with the machine drawing understanding",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 2,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                114,
+                                373,
+                                127
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        114,
+                                        373,
+                                        127
+                                    ],
+                                    "score": 1.0,
+                                    "content": "system: concepts, algorithms, and performance. SMC, 1999.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 3,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                132,
+                                506,
+                                147
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        132,
+                                        506,
+                                        147
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[12] A. Dosovitskiy, L. Beyer, A. Kolesnikov, D. Weissenborn, X. Zhai, T. Unterthiner, M. Dehghani,",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 4,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                145,
+                                506,
+                                156
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        145,
+                                        506,
+                                        156
+                                    ],
+                                    "score": 1.0,
+                                    "content": "M. Minderer, G. Heigold, S. Gelly, et al. An image is worth 16x16 words: Transformers for",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                155,
+                                401,
+                                169
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        155,
+                                        401,
+                                        169
+                                    ],
+                                    "score": 1.0,
+                                    "content": "image recognition at scale. arXiv preprint arXiv:2010.11929, 2020.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 6,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                174,
+                                506,
+                                189
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        174,
+                                        506,
+                                        189
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[13] V. Egiazarian, O. Voynov, A. Artemov, D. Volkhonskiy, A. Safin, M. Taktasheva, D. Zorin, and",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 7,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                185,
+                                414,
+                                199
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        185,
+                                        414,
+                                        199
+                                    ],
+                                    "score": 1.0,
+                                    "content": "E. Burnaev. Deep vectorization of technical drawings. In ECCV, 2020.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 8,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                204,
+                                506,
+                                218
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        204,
+                                        506,
+                                        218
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[14] Y. Ganin, T. Kulkarni, I. Babuschkin, S. A. Eslami, and O. Vinyals. Synthesizing programs for",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 9,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                216,
+                                377,
+                                228
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        216,
+                                        377,
+                                        228
+                                    ],
+                                    "score": 1.0,
+                                    "content": "images using reinforced adversarial learning. In ICML, 2018.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 10,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                235,
+                                506,
+                                248
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        235,
+                                        506,
+                                        248
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[15] A. Holtzman, J. Buys, L. Du, M. Forbes, and Y. Choi. The curious case of neural text",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 11,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                245,
+                                350,
+                                259
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        245,
+                                        350,
+                                        259
+                                    ],
+                                    "score": 1.0,
+                                    "content": "degeneration. arXiv preprint arXiv:1904.09751, 2019.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 12,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                265,
+                                506,
+                                277
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        265,
+                                        506,
+                                        277
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[16] S. Koch, A. Matveev, Z. Jiang, F. Williams, A. Artemov, E. Burnaev, M. Alexa, D. Zorin, and",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 13,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                276,
+                                495,
+                                290
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        276,
+                                        495,
+                                        290
+                                    ],
+                                    "score": 1.0,
+                                    "content": "D. Panozzo. ABC: A big CAD model dataset for geometric deep learning. In CVPR, 2019.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                294,
+                                506,
+                                309
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        294,
+                                        506,
+                                        309
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[17] T. Kudo and J. Richardson. Sentencepiece: A simple and language independent subword",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 15,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                307,
+                                504,
+                                319
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        307,
+                                        504,
+                                        319
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tokenizer and detokenizer for neural text processing. arXiv preprint arXiv:1808.06226, 2018.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                324,
+                                507,
+                                342
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        324,
+                                        507,
+                                        342
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[18] A. Meurer, C. P. Smith, M. Paprocki, O. Certík, S. B. Kirpichev, M. Rocklin, A. Kumar, ˇ",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 17,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                336,
+                                506,
+                                352
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        336,
+                                        506,
+                                        352
+                                    ],
+                                    "score": 1.0,
+                                    "content": "S. Ivanov, J. K. Moore, S. Singh, et al. SymPy: symbolic computing in Python. PeerJ Computer",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                347,
+                                189,
+                                362
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        347,
+                                        189,
+                                        362
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Science, 2017.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 19,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                367,
+                                507,
+                                381
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        367,
+                                        507,
+                                        381
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[19] T. Mikolov, M. Karafiát, L. Burget, J. Cernock ˇ y, and S. Khudanpur. Recurrent neural network `",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 20,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                378,
+                                330,
+                                392
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        378,
+                                        330,
+                                        392
+                                    ],
+                                    "score": 1.0,
+                                    "content": "based language model. In INTERSPEECH, 2010.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 21,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                397,
+                                507,
+                                412
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        397,
+                                        507,
+                                        412
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[20] V. Nagasamy and N. A. Langrana. Engineering drawing processing and vectorization system.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 22,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                408,
+                                187,
+                                422
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        408,
+                                        187,
+                                        422
+                                    ],
+                                    "score": 1.0,
+                                    "content": "CVGIP, 1990.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 23,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                428,
+                                506,
+                                442
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        428,
+                                        506,
+                                        442
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[21] C. Nash, Y. Ganin, S. A. Eslami, and P. Battaglia. PolyGen: An autoregressive generative model",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 24,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                439,
+                                253,
+                                451
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        439,
+                                        253,
+                                        451
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of 3D meshes. In ICML, 2020.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 25,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                458,
+                                507,
+                                472
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        458,
+                                        507,
+                                        472
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[22] Onshape developers. Onshape website. https://www.onshape.com/. Accessed: 2021-03-10.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 26,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                477,
+                                507,
+                                491
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        477,
+                                        507,
+                                        491
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[23] A. v. d. Oord, N. Kalchbrenner, O. Vinyals, L. Espeholt, A. Graves, and K. Kavukcuoglu.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 27,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                487,
+                                507,
+                                503
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        487,
+                                        507,
+                                        503
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Conditional image generation with PixelCNN decoders. arXiv preprint arXiv:1606.05328,",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                498,
+                                155,
+                                513
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        498,
+                                        155,
+                                        513
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2016.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 29,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                518,
+                                507,
+                                533
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        518,
+                                        507,
+                                        533
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[24] W. R. Para, S. F. Bhat, P. Guerrero, T. Kelly, N. Mitra, L. Guibas, and P. Wonka. SketchGen:",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 30,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                529,
+                                449,
+                                543
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        529,
+                                        449,
+                                        543
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Generating constrained CAD sketches. arXiv preprint arXiv:2106.02711, 2021.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 31,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                548,
+                                506,
+                                562
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        548,
+                                        506,
+                                        562
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[25] F. Pezoa, J. L. Reutter, F. Suarez, M. Ugarte, and D. Vrgoc. Foundations of JSON schema. In ˇ",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 32,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                559,
+                                183,
+                                574
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        559,
+                                        183,
+                                        574
+                                    ],
+                                    "score": 1.0,
+                                    "content": "WWW, 2016.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 33,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                579,
+                                506,
+                                593
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        579,
+                                        506,
+                                        593
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[26] A. Radford, J. Wu, R. Child, D. Luan, D. Amodei, and I. Sutskever. Language models are",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 34,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                590,
+                                342,
+                                603
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        590,
+                                        342,
+                                        603
+                                    ],
+                                    "score": 1.0,
+                                    "content": "unsupervised multitask learners. OpenAI blog, 2019.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 35,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                609,
+                                507,
+                                623
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        609,
+                                        507,
+                                        623
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[27] A. Ramesh, M. Pavlov, G. Goh, S. Gray, C. Voss, A. Radford, M. Chen, and I. Sutskever.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 36,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                620,
+                                435,
+                                634
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        620,
+                                        435,
+                                        634
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Zero-shot text-to-image generation. arXiv preprint arXiv:2102.12092, 2021.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 37,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                639,
+                                506,
+                                653
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        639,
+                                        506,
+                                        653
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[28] M. Ranzato, S. Chopra, M. Auli, and W. Zaremba. Sequence level training with recurrent neural",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 38,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                650,
+                                335,
+                                664
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        650,
+                                        335,
+                                        664
+                                    ],
+                                    "score": 1.0,
+                                    "content": "networks. arXiv preprint arXiv:1511.06732, 2015.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 39,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                669,
+                                507,
+                                683
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        669,
+                                        507,
+                                        683
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[29] A. Razavi, A. v. d. Oord, and O. Vinyals. Generating diverse high-fidelity images with VQ-",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 40,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                680,
+                                324,
+                                694
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        680,
+                                        324,
+                                        694
+                                    ],
+                                    "score": 1.0,
+                                    "content": "VAE-2. arXiv preprint arXiv:1906.00446, 2019.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 41,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                700,
+                                506,
+                                714
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        700,
+                                        506,
+                                        714
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[30] P. Reddy, M. Gharbi, M. Lukac, and N. J. Mitra. Im2Vec: Synthesizing vector graphics without",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 42,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                711,
+                                370,
+                                725
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        711,
+                                        370,
+                                        725
+                                    ],
+                                    "score": 1.0,
+                                    "content": "vector supervision. arXiv preprint arXiv:2102.02798, 2021.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 43,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                72,
+                                505,
+                                87
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        72,
+                                        505,
+                                        87
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[31] A. Seff, Y. Ovadia, W. Zhou, and R. P. Adams. Sketchgraphs: A large-scale dataset for modeling",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 0,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                84,
+                                477,
+                                97
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        84,
+                                        477,
+                                        97
+                                    ],
+                                    "score": 1.0,
+                                    "content": "relational geometry in computer-aided design. arXiv preprint arXiv:2007.08506, 2020.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 1,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                102,
+                                505,
+                                117
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        102,
+                                        505,
+                                        117
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[32] K. Varda. Google protocol buffers: Google’s data interchange format. Technical report, 2008.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 2,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                121,
+                                505,
+                                134
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        121,
+                                        505,
+                                        134
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[33] A. Vaswani, N. Shazeer, N. Parmar, J. Uszkoreit, L. Jones, A. N. Gomez, L. Kaiser, and",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 3,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                133,
+                                454,
+                                146
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        133,
+                                        454,
+                                        146
+                                    ],
+                                    "score": 1.0,
+                                    "content": "I. Polosukhin. Attention is all you need. arXiv preprint arXiv:1706.03762, 2017.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 4,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                150,
+                                507,
+                                166
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        150,
+                                        507,
+                                        166
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[34] P. Vaxiviere and K. Tombre. Celesstin: CAD conversion of mechanical drawings. Computer,",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 5,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                163,
+                                153,
+                                174
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        163,
+                                        153,
+                                        174
+                                    ],
+                                    "score": 1.0,
+                                    "content": "1992.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 6,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                181,
+                                438,
+                                194
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        181,
+                                        438,
+                                        194
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[35] O. Vinyals, M. Fortunato, and N. Jaitly. Pointer networks. In NeurIPS, 2015.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 7,
+                            "is_list_start_line": true,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                200,
+                                505,
+                                213
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        200,
+                                        505,
+                                        213
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[36] K. D. Willis, Y. Pu, J. Luo, H. Chu, T. Du, J. G. Lambourne, A. Solar-Lezama, and W. Matusik.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 8,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                211,
+                                506,
+                                225
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        211,
+                                        506,
+                                        225
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Fusion 360 gallery: A dataset and environment for programmatic CAD reconstruction. arXiv",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                223,
+                                266,
+                                235
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        223,
+                                        266,
+                                        235
+                                    ],
+                                    "score": 1.0,
+                                    "content": "preprint arXiv:2010.02392, 2020.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 10,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                241,
+                                505,
+                                254
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        241,
+                                        505,
+                                        254
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[37] K. D. Willis, P. K. Jayaraman, J. G. Lambourne, H. Chu, and Y. Pu. Engineering sketch",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 11,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                252,
+                                447,
+                                266
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        252,
+                                        447,
+                                        266
+                                    ],
+                                    "score": 1.0,
+                                    "content": "generation for computer-aided design. arXiv preprint arXiv:2104.09621, 2021.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 12,
+                            "is_list_end_line": true
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                271,
+                                505,
+                                285
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        271,
+                                        505,
+                                        285
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[38] R. Wu, C. Xiao, and C. Zheng. DeepCAD: A deep generative network for computer-aided",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 13,
+                            "is_list_start_line": true
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                282,
+                                256,
+                                296
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        282,
+                                        256,
+                                        296
+                                    ],
+                                    "score": 1.0,
+                                    "content": "design models. In ICCV, 2021.",
+                                    "type": "text",
+                                    "cross_page": true
+                                }
+                            ],
+                            "index": 14,
+                            "is_list_end_line": true
+                        }
+                    ],
+                    "index": 35.5,
+                    "bbox_fs": [
+                        110,
+                        439,
+                        507,
+                        723
+                    ]
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        44,
+                        507,
+                        724
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                72,
+                                507,
+                                86
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        72,
+                                        507,
+                                        86
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[10] D. Dori and K. Tombre. From engineering drawings to 3d CAD models: are we ready now?",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                83,
+                                255,
+                                97
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        83,
+                                        255,
+                                        97
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Computer-Aided Design, 1995.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                103,
+                                506,
+                                117
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        103,
+                                        506,
+                                        117
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[11] D. Dori and L. Wenyin. Automated cad conversion with the machine drawing understanding",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                114,
+                                373,
+                                127
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        114,
+                                        373,
+                                        127
+                                    ],
+                                    "score": 1.0,
+                                    "content": "system: concepts, algorithms, and performance. SMC, 1999.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                132,
+                                506,
+                                147
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        132,
+                                        506,
+                                        147
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[12] A. Dosovitskiy, L. Beyer, A. Kolesnikov, D. Weissenborn, X. Zhai, T. Unterthiner, M. Dehghani,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                145,
+                                506,
+                                156
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        145,
+                                        506,
+                                        156
+                                    ],
+                                    "score": 1.0,
+                                    "content": "M. Minderer, G. Heigold, S. Gelly, et al. An image is worth 16x16 words: Transformers for",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                155,
+                                401,
+                                169
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        155,
+                                        401,
+                                        169
+                                    ],
+                                    "score": 1.0,
+                                    "content": "image recognition at scale. arXiv preprint arXiv:2010.11929, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                174,
+                                506,
+                                189
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        174,
+                                        506,
+                                        189
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[13] V. Egiazarian, O. Voynov, A. Artemov, D. Volkhonskiy, A. Safin, M. Taktasheva, D. Zorin, and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                185,
+                                414,
+                                199
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        185,
+                                        414,
+                                        199
+                                    ],
+                                    "score": 1.0,
+                                    "content": "E. Burnaev. Deep vectorization of technical drawings. In ECCV, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                204,
+                                506,
+                                218
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        204,
+                                        506,
+                                        218
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[14] Y. Ganin, T. Kulkarni, I. Babuschkin, S. A. Eslami, and O. Vinyals. Synthesizing programs for",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                216,
+                                377,
+                                228
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        216,
+                                        377,
+                                        228
+                                    ],
+                                    "score": 1.0,
+                                    "content": "images using reinforced adversarial learning. In ICML, 2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                235,
+                                506,
+                                248
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        235,
+                                        506,
+                                        248
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[15] A. Holtzman, J. Buys, L. Du, M. Forbes, and Y. Choi. The curious case of neural text",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                245,
+                                350,
+                                259
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        245,
+                                        350,
+                                        259
+                                    ],
+                                    "score": 1.0,
+                                    "content": "degeneration. arXiv preprint arXiv:1904.09751, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                265,
+                                506,
+                                277
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        265,
+                                        506,
+                                        277
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[16] S. Koch, A. Matveev, Z. Jiang, F. Williams, A. Artemov, E. Burnaev, M. Alexa, D. Zorin, and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                276,
+                                495,
+                                290
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        276,
+                                        495,
+                                        290
+                                    ],
+                                    "score": 1.0,
+                                    "content": "D. Panozzo. ABC: A big CAD model dataset for geometric deep learning. In CVPR, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                294,
+                                506,
+                                309
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        294,
+                                        506,
+                                        309
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[17] T. Kudo and J. Richardson. Sentencepiece: A simple and language independent subword",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                307,
+                                504,
+                                319
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        307,
+                                        504,
+                                        319
+                                    ],
+                                    "score": 1.0,
+                                    "content": "tokenizer and detokenizer for neural text processing. arXiv preprint arXiv:1808.06226, 2018.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                104,
+                                324,
+                                507,
+                                342
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        324,
+                                        507,
+                                        342
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[18] A. Meurer, C. P. Smith, M. Paprocki, O. Certík, S. B. Kirpichev, M. Rocklin, A. Kumar, ˇ",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                336,
+                                506,
+                                352
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        336,
+                                        506,
+                                        352
+                                    ],
+                                    "score": 1.0,
+                                    "content": "S. Ivanov, J. K. Moore, S. Singh, et al. SymPy: symbolic computing in Python. PeerJ Computer",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                347,
+                                189,
+                                362
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        347,
+                                        189,
+                                        362
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Science, 2017.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                367,
+                                507,
+                                381
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        367,
+                                        507,
+                                        381
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[19] T. Mikolov, M. Karafiát, L. Burget, J. Cernock ˇ y, and S. Khudanpur. Recurrent neural network `",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                378,
+                                330,
+                                392
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        378,
+                                        330,
+                                        392
+                                    ],
+                                    "score": 1.0,
+                                    "content": "based language model. In INTERSPEECH, 2010.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                397,
+                                507,
+                                412
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        397,
+                                        507,
+                                        412
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[20] V. Nagasamy and N. A. Langrana. Engineering drawing processing and vectorization system.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                408,
+                                187,
+                                422
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        408,
+                                        187,
+                                        422
+                                    ],
+                                    "score": 1.0,
+                                    "content": "CVGIP, 1990.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                428,
+                                506,
+                                442
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        428,
+                                        506,
+                                        442
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[21] C. Nash, Y. Ganin, S. A. Eslami, and P. Battaglia. PolyGen: An autoregressive generative model",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                439,
+                                253,
+                                451
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        439,
+                                        253,
+                                        451
+                                    ],
+                                    "score": 1.0,
+                                    "content": "of 3D meshes. In ICML, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                458,
+                                507,
+                                472
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        458,
+                                        507,
+                                        472
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[22] Onshape developers. Onshape website. https://www.onshape.com/. Accessed: 2021-03-10.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                477,
+                                507,
+                                491
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        477,
+                                        507,
+                                        491
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[23] A. v. d. Oord, N. Kalchbrenner, O. Vinyals, L. Espeholt, A. Graves, and K. Kavukcuoglu.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                487,
+                                507,
+                                503
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        487,
+                                        507,
+                                        503
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Conditional image generation with PixelCNN decoders. arXiv preprint arXiv:1606.05328,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                498,
+                                155,
+                                513
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        498,
+                                        155,
+                                        513
+                                    ],
+                                    "score": 1.0,
+                                    "content": "2016.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 29
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                518,
+                                507,
+                                533
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        518,
+                                        507,
+                                        533
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[24] W. R. Para, S. F. Bhat, P. Guerrero, T. Kelly, N. Mitra, L. Guibas, and P. Wonka. SketchGen:",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                529,
+                                449,
+                                543
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        529,
+                                        449,
+                                        543
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Generating constrained CAD sketches. arXiv preprint arXiv:2106.02711, 2021.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                548,
+                                506,
+                                562
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        548,
+                                        506,
+                                        562
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[25] F. Pezoa, J. L. Reutter, F. Suarez, M. Ugarte, and D. Vrgoc. Foundations of JSON schema. In ˇ",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                559,
+                                183,
+                                574
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        559,
+                                        183,
+                                        574
+                                    ],
+                                    "score": 1.0,
+                                    "content": "WWW, 2016.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                579,
+                                506,
+                                593
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        579,
+                                        506,
+                                        593
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[26] A. Radford, J. Wu, R. Child, D. Luan, D. Amodei, and I. Sutskever. Language models are",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                590,
+                                342,
+                                603
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        590,
+                                        342,
+                                        603
+                                    ],
+                                    "score": 1.0,
+                                    "content": "unsupervised multitask learners. OpenAI blog, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                609,
+                                507,
+                                623
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        609,
+                                        507,
+                                        623
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[27] A. Ramesh, M. Pavlov, G. Goh, S. Gray, C. Voss, A. Radford, M. Chen, and I. Sutskever.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                620,
+                                435,
+                                634
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        620,
+                                        435,
+                                        634
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Zero-shot text-to-image generation. arXiv preprint arXiv:2102.12092, 2021.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                639,
+                                506,
+                                653
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        639,
+                                        506,
+                                        653
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[28] M. Ranzato, S. Chopra, M. Auli, and W. Zaremba. Sequence level training with recurrent neural",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 38
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                650,
+                                335,
+                                664
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        650,
+                                        335,
+                                        664
+                                    ],
+                                    "score": 1.0,
+                                    "content": "networks. arXiv preprint arXiv:1511.06732, 2015.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 39
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                669,
+                                507,
+                                683
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        669,
+                                        507,
+                                        683
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[29] A. Razavi, A. v. d. Oord, and O. Vinyals. Generating diverse high-fidelity images with VQ-",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 40
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                680,
+                                324,
+                                694
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        680,
+                                        324,
+                                        694
+                                    ],
+                                    "score": 1.0,
+                                    "content": "VAE-2. arXiv preprint arXiv:1906.00446, 2019.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 41
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                700,
+                                506,
+                                714
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        700,
+                                        506,
+                                        714
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[30] P. Reddy, M. Gharbi, M. Lukac, and N. J. Mitra. Im2Vec: Synthesizing vector graphics without",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 42
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                711,
+                                370,
+                                725
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        711,
+                                        370,
+                                        725
+                                    ],
+                                    "score": 1.0,
+                                    "content": "vector supervision. arXiv preprint arXiv:2102.02798, 2021.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 43
+                        }
+                    ],
+                    "index": 21.5
+                }
+            ],
+            "page_idx": 10,
+            "page_size": [
+                612,
+                792
+            ],
+            "discarded_blocks": [
+                {
+                    "type": "discarded",
+                    "bbox": [
+                        300,
+                        741,
+                        311,
+                        751
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                299,
+                                740,
+                                312,
+                                754
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        299,
+                                        740,
+                                        312,
+                                        754
+                                    ],
+                                    "score": 1.0,
+                                    "content": "11",
+                                    "type": "text"
+                                }
+                            ]
+                        }
+                    ]
+                }
+            ],
+            "para_blocks": [
+                {
+                    "type": "list",
+                    "bbox": [
+                        105,
+                        44,
+                        507,
+                        724
+                    ],
+                    "lines": [],
+                    "index": 21.5,
+                    "bbox_fs": [
+                        104,
+                        72,
+                        507,
+                        725
+                    ],
+                    "lines_deleted": true
+                }
+            ]
+        },
+        {
+            "preproc_blocks": [
+                {
+                    "type": "text",
+                    "bbox": [
+                        105,
+                        72,
+                        507,
+                        294
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                105,
+                                72,
+                                505,
+                                87
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        72,
+                                        505,
+                                        87
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[31] A. Seff, Y. Ovadia, W. Zhou, and R. P. Adams. Sketchgraphs: A large-scale dataset for modeling",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                84,
+                                477,
+                                97
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        84,
+                                        477,
+                                        97
+                                    ],
+                                    "score": 1.0,
+                                    "content": "relational geometry in computer-aided design. arXiv preprint arXiv:2007.08506, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                102,
+                                505,
+                                117
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        102,
+                                        505,
+                                        117
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[32] K. Varda. Google protocol buffers: Google’s data interchange format. Technical report, 2008.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                121,
+                                505,
+                                134
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        121,
+                                        505,
+                                        134
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[33] A. Vaswani, N. Shazeer, N. Parmar, J. Uszkoreit, L. Jones, A. N. Gomez, L. Kaiser, and",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                133,
+                                454,
+                                146
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        133,
+                                        454,
+                                        146
+                                    ],
+                                    "score": 1.0,
+                                    "content": "I. Polosukhin. Attention is all you need. arXiv preprint arXiv:1706.03762, 2017.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                150,
+                                507,
+                                166
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        150,
+                                        507,
+                                        166
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[34] P. Vaxiviere and K. Tombre. Celesstin: CAD conversion of mechanical drawings. Computer,",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                163,
+                                153,
+                                174
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        163,
+                                        153,
+                                        174
+                                    ],
+                                    "score": 1.0,
+                                    "content": "1992.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                105,
+                                181,
+                                438,
+                                194
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        105,
+                                        181,
+                                        438,
+                                        194
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[35] O. Vinyals, M. Fortunato, and N. Jaitly. Pointer networks. In NeurIPS, 2015.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                200,
+                                505,
+                                213
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        200,
+                                        505,
+                                        213
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[36] K. D. Willis, Y. Pu, J. Luo, H. Chu, T. Du, J. G. Lambourne, A. Solar-Lezama, and W. Matusik.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                211,
+                                506,
+                                225
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        211,
+                                        506,
+                                        225
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Fusion 360 gallery: A dataset and environment for programmatic CAD reconstruction. arXiv",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                223,
+                                266,
+                                235
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        223,
+                                        266,
+                                        235
+                                    ],
+                                    "score": 1.0,
+                                    "content": "preprint arXiv:2010.02392, 2020.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                241,
+                                505,
+                                254
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        241,
+                                        505,
+                                        254
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[37] K. D. Willis, P. K. Jayaraman, J. G. Lambourne, H. Chu, and Y. Pu. Engineering sketch",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                126,
+                                252,
+                                447,
+                                266
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        126,
+                                        252,
+                                        447,
+                                        266
+                                    ],
+                                    "score": 1.0,
+                                    "content": "generation for computer-aided design. arXiv preprint arXiv:2104.09621, 2021.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                106,
+                                271,
+                                505,
+                                285
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        271,
+                                        505,
+                                        285
+                                    ],
+                                    "score": 1.0,
+                                    "content": "[38] R. Wu, C. Xiao, and C. Zheng. DeepCAD: A deep generative network for computer-aided",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                127,
+                                282,
+                                256,
+                                296
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        127,
+                                        282,
+                                        256,
+                                        296
+                                    ],
+                                    "score": 1.0,
+                                    "content": "design models. In ICCV, 2021.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 14
+                        }
+                    ],
+                    "index": 7
+                },
+                {
+                    "type": "title",
+                    "bbox": [
+                        107,
+                        314,
+                        156,
+                        327
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                106,
+                                313,
+                                158,
+                                328
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        106,
+                                        313,
+                                        158,
+                                        328
+                                    ],
+                                    "score": 1.0,
+                                    "content": "Checklist",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 15
+                        }
+                    ],
+                    "index": 15
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        131,
+                        335,
+                        208,
+                        346
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                129,
+                                334,
+                                210,
+                                347
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        129,
+                                        334,
+                                        210,
+                                        347
+                                    ],
+                                    "score": 1.0,
+                                    "content": "1. For all authors...",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 16
+                        }
+                    ],
+                    "index": 16
+                },
+                {
+                    "type": "text",
+                    "bbox": [
+                        146,
+                        350,
+                        505,
+                        444
+                    ],
+                    "lines": [
+                        {
+                            "bbox": [
+                                146,
+                                350,
+                                505,
+                                362
+                            ],
+                            "spans": [
+                                {
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+                                        146,
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+                                        505,
+                                        362
+                                    ],
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+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                162,
+                                361,
+                                288,
+                                374
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        162,
+                                        361,
+                                        288,
+                                        374
+                                    ],
+                                    "score": 1.0,
+                                    "content": "contributions and scope? [Yes]",
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+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                144,
+                                372,
+                                376,
+                                387
+                            ],
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+                                        144,
+                                        372,
+                                        376,
+                                        387
+                                    ],
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+                                    "content": "(b) Did you describe the limitations of your work? [Yes]",
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+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                145,
+                                386,
+                                506,
+                                400
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        145,
+                                        386,
+                                        506,
+                                        400
+                                    ],
+                                    "score": 1.0,
+                                    "content": "(c) Did you discuss any potential negative societal impacts of your work? [No] The",
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+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                161,
+                                398,
+                                506,
+                                410
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        161,
+                                        398,
+                                        506,
+                                        410
+                                    ],
+                                    "score": 1.0,
+                                    "content": "method presented in this work is a general machine learning framework and it is not",
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+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                161,
+                                408,
+                                420,
+                                422
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        161,
+                                        408,
+                                        420,
+                                        422
+                                    ],
+                                    "score": 1.0,
+                                    "content": "immediately obvious how it could negatively impact the society.",
+                                    "type": "text"
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                144,
+                                420,
+                                505,
+                                435
+                            ],
+                            "spans": [
+                                {
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diff --git a/parse/train/z-X_PpwaroO/z-X_PpwaroO_model.json b/parse/train/z-X_PpwaroO/z-X_PpwaroO_model.json
new file mode 100644
index 0000000000000000000000000000000000000000..c5ef4fc20a8d90b10ad6bcd366a8b91a76c5610e
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