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+# HIGH-LIKELIHOOD AREA MATTERS — REWARDING CORRECT, RARE CLASS PREDICTIONS UNDER IMBALANCED DISTRIBUTIONS
+
+Anonymous authors Paper under double-blind review
+
+# ABSTRACT
+
+Learning from natural datasets poses significant challenges for traditional classification methods based on the cross-entropy objective due to imbalanced class distributions. It is intuitive to assume that the examples from rare classes are harder to learn so that the classifier is uncertain of the prediction, which establishes the low-likelihood area. Based on this, existing approaches drive the classifier actively to correctly predict those incorrect, rare examples. However, this assumption is one-sided and could be misleading. We find in practice that the high-likelihood area contains correct predictions for rare class examples and it plays a vital role in learning imbalanced class distributions. In light of this finding, we propose the Eureka Loss, which rewards the classifier when examples belong to rare classes in the high-likelihood area are correctly predicted. Experiments on the large-scale long-tailed iNaturalist 2018 classification dataset and the ImageNet-LT benchmark both validate the proposed approach. We further analyze the influence of the Eureka Loss in detail on diverse data distributions.
+
+# 1 INTRODUCTION
+
+Existing classification methods usually struggle in real-world applications, where the class distributions are inherently imbalanced and long-tailed (Van Horn & Perona, 2017; Buda et al., 2018; Liu et al., 2019; Gupta et al., 2019), in which a few head classes occupy a large probability mass while most tail (or rare) classes only possess a few examples. The language generation task is a vivid example of the long-tailed classification. In this case, word types are considered as the classes and the model predicts probabilities over the vocabulary. Common words such as the, of, and and are the head classes, while tailed classes are rare words like Gobbledygook, Scrumptious, and Agastopia. Conventional classifiers based on deep neural networks require a large number of training examples to generalize and have been found to under-perform on rare classes with a few training examples in downstream applications (Van Horn & Perona, 2017; Buda et al., 2018; Cao et al., 2019).
+
+It is proposed that the traditional cross-entropy objective is unsuitable for learning imbalanced distributions since it treats each instance and each class equivalently (Lin et al., 2017; Tan et al., 2020). In contrast, the instances from tail classes should be paid more attention, indicated by two main approaches that have been recently investigated for class-imbalanced classification: the frequencybased methods and the likelihood-based methods. The former (Cui et al., 2019; Cao et al., 2019) directly adjust the weights of the instances in terms of their class frequencies, so that the instances from the tail classes are learned with a higher priority no matter whether they are correctly predicted or not. The latter (Lin et al., 2017; Zhu et al., 2018) instead penalize the inaccurate predictions more heavily, assuming that the well-classified instances, i.e., the instances in the high-likelihood area, factor inconsequentially in learning imbalanced distributions.
+
+However, neither of these two approaches realistically depicts the likelihood landscape. In particular, the high-likelihood area, where the classifier makes the correct predictions for both common class examples and rare class ones, contributes significantly to generalization. However, this area is not well-shaped, as illustrated in Figure 1. Specifically, the frequency-based methods imply an impaired learning of common class examples that are the principle part of the natural data, while the likelihoodbased methods ignore the correctly-predicted rare class examples that can provide crucial insights into the underlying mechanism for predicting such examples.
+
+![](images/4a77a3007324713ae2f486ac47167ea60bca25def88b2de62bb08f9fd4d8e76d.jpg)  
+Figure 1: Conceptual illustration of approaches to learning unbalanced class distributions. For an instance in the training data, the frequency-based methods either sharpen or soften the loss for all likelihoods according to its class frequency, while the likelihood-based methods adjust the loss in the low- or high-likelihood area, respectively. The high-likelihood area is relatively deprioritized in both cases. The proposed Eureka Loss progressively rewards the systems with higher bonus for higher-likelihood.
+
+In this paper, we first demonstrate that existing practice of neglecting predictions in the high-likelihood area is harmful to learning imbalanced class distributions. Furthermore, we find that simply mixing the cross-entropy loss and the Focal Loss (Lin et al., 2017) can induce substantially superior performance, which validates our motivation. In turn, we propose to elevate the importance of high-likelihood predictions even further and design a novel objective called Eureka Loss. It progressively rewards the classifiers according to both the likelihood and the class frequency of an example such that the system is encouraged to be more confident in the correct prediction of examples from rare classes. Experimental results on the image classification and the language generation tasks demonstrate that the Eureka Loss outperforms strong baselines in learning imbalanced class distributions.
+
+Our contributions are twofold:
+
+• We challenge the common belief that learning for examples in low-likelihood area is more important for learning tail classes and reveal that the correctly-predicted rare class examples make important contribution to learning long-tailed class distributions. • We explore a new direction for learning imbalanced classification that focuses on rewarding correct predictions for tail classes examples, rather than penalizing incorrect ones. The proposed Eureka Loss rewards the classifier for its high-likelihood predictions progressively to the rarity of their class and achieves substantial improvements on various problems with long-tailed distributions.
+
+# 2 RELATED WORK
+
+Frequency-based Data and Loss Re-balancing Previous literature on learning with long-tailed distribution mainly focusing on re-balancing the data distribution and re-weighting the loss function.
+
+The former is based on a straightforward idea to manually create a pseudo-balanced data distribution to ease the learning problem, including up-sampling for rare class examples (Chawla et al., 2002), down-sampling for head class examples (Drummond & Holte, 2003) and a more concrete sampling strategy based on class frequency (Shen et al., 2016).
+
+As for the latter, recent studies propose to assign different weights to different classes, and the weights can be calculated according to the class distribution. For example, Khan et al. (2018) design a cost-sensitive loss for major and minor class examples. An intuitive method is to down-weight the loss of frequent classes, while up-weight the contribution of rare class examples. However, frequency is not suitable to be directly treated as the the weight since there exists overlap among samples. An advancing alternative loss CB (Cui et al., 2019) proposes to calculate the effective number to substitute the frequency for loss re-weighting. However, since it assigns lower weight to head classes in the maximum likelihood training (Cross Entropy objective), it seriously impairs the learning of head classes. Moreover, CB requires a delicate hyper-parameter tuning for every imbalanced distribution, leading to a lot of manul efforts. From the perspective of max-margin, a recent study LDAM (Cao et al., 2019) proposes to up-weight the loss of tail classes by a class-distribution based margin. Compared to the above methods, we choose to decrease the loss of tail classes by rewarding correct predictions rather than increasing the loss of tail classes through aggravated penalization.
+
+Deferring the Frequency-based Class-balanced Training Recent studies find that deferring the class-balanced training helps learn high-quality representations (Liu et al., 2019), and propose deferred Class-balanced training (deferred CB) (Cao et al., 2019), which chooses to adopt Cross Entropy objective at the beginning of training. Similarly, the Decoupling method (Kang et al., 2020) shows that the re-balancing strategies impair the quality of learned feature representations and demonstrate an improved performance learned with original data distribution, by training the model with Cross Entropy in the first phase and adopting class-balanced training in the second phase. This decoupling strategy can also be found in BBN (Zhou et al., 2019), which includes both class imbalanced and balanced training, and the transition from the former to the latter is achieved through a curriculum learning schedule. These methods achieve state-of-the-art performance in long-tailed classification. To be comparable with these methods and to analyse whether Eureka Loss is complementary to this technique, we propose deferred Eureka Loss, in which rewarding for rare class prediction is introduced to encourage the model to learn rare patterns when learning is stalled.
+
+Likelihood-based Loss Another dominant method for imbalanced classification is the likelihoodbased method Focal Loss (FL) (Lin et al., 2017), which proposes to down-weight the contribution of examples in the high-likelihood area. However, we argue that it is harmful for learning tail classes and choose an opposite direction by highlighting the high-likelihood area with a steeper loss.
+
+Transferring Representations Techniques for transferring information from sufficient head classes examples to under-represented rare classes examples belong to a parallel successful direction in this field. They include MBJ (Liu et al., 2020), which utilizes external semantic feature memory and FSA (Chu et al., 2020), which decomposes feature in to class-specific and class-generic components. These latest transfer learning based studies are less related to our paper but they also obtain good improvements in long-tailed classification, so we add them into comparison in the experiments.
+
+# 3 ROLE OF THE HIGH-LIKELIHOOD AREA
+
+The existing approaches to the long-tailed classification independently consider the class frequency and the example likelihood. However, we show that this one-sided reflection is problematic when dealing with the tail class examples that can be confidently classified. The tail class examples can be easily classified by the classifier, and the head class examples can also be hard for the classifier to recognize. The difficulty of classification depends on the inherent characteristic of the classes, rather than the sample size of the class. For example, in species classification, the Portuguese man o’war may be a rare class but can be easily classified due to its distinct features, compared to various kinds of moths which are common classes yet are hard to distinguish. However, the frequency-based methods continuously drive the classifier to fit the rare class examples, especially when they are difficult to predict, which may lead to overfitting. On the other hand, the likelihood-based methods relax the concentration in the high-likelihood area, which contains the tail class examples that are not hard to predict and provide insights to generalization.
+
+To verify our point of view, we analyze the problem by dissecting the influence of the high-likelihood area with respect to the class frequency and demonstrate that properly encouraging the learning of well-classified tail class examples induce substantial improvements, before which we first give a brief introduction of classification with long-tailed class distributions.
+
+# 3.1 PREPARATION: CLASSIFICATION WITH LONG-TAILED CLASS DISTRIBUTIONS
+
+Let’s consider the multi-class classification problem with the long-tailed class distribution. Given a class set $\mathbb { C }$ , $n$ denotes the number of different classes in $\mathbb { C }$ and $m _ { i }$ is the number of examples of the class $C _ { i }$ . For simplicity, we sort the class set $\mathbb { C }$ according to cardinal $m _ { i }$ for $C _ { i }$ such that $C _ { 0 }$ is the class with the most examples and $C _ { n - 1 }$ is the rarest class. Let $\pmb { p }$ be a $n$ -dim probability vector predicted by a classifier model $f ( \pmb { x } ; \pmb { \theta } )$ based on the input $_ { \textbf { \em x } }$ , where each element $p _ { i }$ denotes the probability of the class $C _ { i }$ and $\textbf {  { y } }$ is a $n$ -dim one-hot label vector with $y$ being the ground-truth class.
+
+The probability vector can be calculated as
+
+$$
+\begin{array} { r } { \pmb { p } = \sigma ( f ( \pmb { x } ; \pmb { \theta } ) ) , } \end{array}
+$$
+
+where $\sigma$ is the normalizing function, e.g., softmax for multi-class classification. Typically, the parameters are estimated using maximum likelihood estimation (MLE), which is equivalent to using the Cross-Entropy Loss (CE) function, where the scalar $y \cdot \log p$ can be regarded as the (log)-likelihood:
+
+$$
+\mathcal { L } = - \mathbb { E } _ { ( \pmb { x } , \pmb { y } ) \in \mathcal { D } } \log p _ { \mathrm { m o d e l } } ( \pmb { y } | \pmb { x } ) = - \frac { 1 } { | \mathcal { D } | } \sum _ { ( \pmb { x } , \pmb { y } ) \in \mathcal { D } } \pmb { y } \cdot \log p .
+$$
+
+For deep neural network–based classifiers, due to the non-linearity of the loss function, the problem is typically solved by stochastic gradient descent, which requires the calculation of the gradient with respect to the parameters using the chain-rule, the process of which is called back-propagation:
+
+$$
+\frac { \partial \mathcal { L } } { \partial \pmb { \theta } } = \frac { \partial \mathcal { L } } { \partial \pmb { p } } \frac { \partial \pmb { p } } { \partial \pmb { \theta } } = \frac { \partial \mathcal { L } } { \partial \pmb { p } } \frac { \partial \sigma ( f ( \pmb { x } ; \pmb { \theta } ) ) } { \partial \pmb { \theta } } .
+$$
+
+We introduce the term likelihood gradient to denote $\partial \mathcal { L } / \partial \mathbf { \boldsymbol { p } }$ , which modulates how the probability mass should be shifted and is a characteristic of the loss function instead of the classifier. For learning imbalanced class distributions, the common methods aim to shape the likelihood gradient so the rare classes are learned with priority, i.e., embodying a sharper loss and a larger likelihood gradient.
+
+Frequency-Based Methods Frequency-based methods alter the likelihood gradient according to the class frequencies, which are irrelevant to how well individual examples are classified. A simple form is using a $n$ -dim weight vector $\textbf { \em w }$ composed of the class weights based on their frequencies in the dataset to determine the importance of examples from each class:
+
+$$
+\mathcal { L } = - w _ { y } \cdot ( { \pmb y } \cdot \log { \pmb p } ) .
+$$
+
+Note that when ${ \pmb w } = { \bf 1 }$ , it is identical to the cross-entropy objective. The weight vector is typically calculated as $w _ { i } = \bar { m } / m _ { i }$ , where $\bar { m }$ is the average of $m _ { i }$ . As we can see, the standard weight is taken as the average of the class size, so that the classes with more examples are down-weighted and the classes with fewer examples are up-weighted. For a natural long-tailed distribution, the average is larger than the median, which suggests more classes are up-weighted. Advanced frequency-based methods try to obtain a more meaningful measurement of the class size, e.g., the Class-Balanced Loss (CB) proposed by Cui et al. (2019) utilizes an effective number $\left. 1 - \beta ^ { m _ { i } } \right/ 1 - \beta$ for each class, where $\beta \in [ 0 . 9 , 1 )$ is a tunable class-balanced term.
+
+Likelihood-Based Methods Different from the frequency-based methods, likelihood-based methods adjust the likelihood gradient based on the instance-level difficulty as predicted by the classifier such that the examples in the low-likelihood area are more focused in training. For example, the well-known Focal Loss (FL) with a balanced factor $\alpha$ proposed by Lin et al. (2017) takes the following form:
+
+$$
+\mathcal { L } = - \alpha ( 1 - p _ { y } ) ^ { \gamma _ { f } } \cdot ( { \pmb y } \cdot \log { \pmb p } ) ,
+$$
+
+where $\gamma _ { f } > 0$ , which controls the convexness of the loss and higher $\gamma _ { f }$ indicates adjustment that are more significant. Note that when $\alpha = 1$ and $\gamma _ { f } = 0$ , it is identical to the cross-entropy objective. Following previous works (Cao et al., 2019; Liu et al., 2019; Cui et al., 2019), the $\alpha$ is set to 1 in multi-class classification, and Class-Balanced Focal Loss $\mathrm { ( F L + C B ) }$ can be viewed Focal Loss with uneven alpha for each class in the multi-class setting. The key idea is to pay less attention to the well-classified examples and pay more attention to the badly-classified examples, because it is natural to assume the tail class examples are harder to learn and thus cannot be well-classified. However, such methods neglect the correctly-predicted tail class examples, the practice of which we show is not constructive to the learning of long-tailed class distributions.
+
+# 3.2 UNDERSTANDING THE INFLUENCE OF THE HIGH-LIKELIHOOD AREA
+
+To understand the influence of the high-likelihood area, we first prepare a variant of the Focal Loss, the Halted Focal Loss (HFL), such that the high-likelihood area is not deprioritized. The Halted Focal Loss reverts the Focal Loss to the Cross-Entropy Loss when the likelihood is high enough:
+
+$$
+\mathcal { L } = \left\{ \begin{array} { l l } { - \alpha ( 1 - p _ { y } ) ^ { \gamma _ { f } } \cdot ( y \cdot \log p ) , } & { \mathrm { i f } \ p _ { y } \leq \varphi } \\ { - \alpha y \cdot [ \log p + b ] , } & { \mathrm { o t h e r w i s e } } \end{array} \right.
+$$
+
+![](images/272a974ef7d496f88181e8c74c4b702c525ed37dbfd8442493f5e20269d26187.jpg)  
+Figure 2: Regaining focus on the high-likelihood area for the rare classes benefits classification. Left: Illustration of HFL which reverts FL to CE in the high-likelihood area. Right: Applying HFL only to the rare classes improves overall performance.
+
+<table><tr><td>Method</td><td>AP</td><td>AP50</td><td>AP75</td></tr><tr><td>CE</td><td>32.8</td><td>52.3</td><td>34.7</td></tr><tr><td>FL</td><td>33.8</td><td>52.5</td><td>35.9</td></tr><tr><td>HFL</td><td>34.0</td><td>52.7</td><td>36.2</td></tr><tr><td>FL (Head) + HFL (Tail)</td><td>34.2</td><td>52.7</td><td>36.3</td></tr></table>
+
+Table 1: Results of HFL on the COCO detection dataset, AP denotes average precision. As we can see, increasing the importance of the high-likelihood area achieves better results, and the main improvements come from the tail class examples.
+
+where $p _ { y }$ is prediction probability of the correct label, $b = \alpha ( 1 - ( 1 - \varphi ) ^ { \gamma _ { f } } ) \log \varphi$ to ensure monotonicity and continuity, and $\varphi$ is the boundary between the low- and the high-likelihood area, which we set as 0.5, i.e., a likelihood higher than which definitely renders a correct prediction. This mixed loss is plotted in left of the Figure 2, which has the same likelihood gradient as the cross-entropy in the high-likelihood area and remains the same as the Focal Loss in the low-likelihood area.
+
+To decouple the effect of class frequency, we further explore to gradually transition from the Focal Loss to the Halted Focal Loss according to the class frequency of an example, e.g., from adopting the Halted Focal Loss only for the rarest class and the Focal Loss to other classes to adopting the Focal Loss only for the most common class and the Halted Focal Loss for the rest. Concretely, we set a proportion $t \in [ 0 , 1 ]$ of classes to receive this loss and the remaining $1 - t$ proportion of classes adopt the original Focal Loss. The classes are ranked by inverse frequencies, such that the first class is the rarest class.
+
+We conduct experiments on long-tailed CIFAR-10 using the aforementioned protocol to examine the effect of the high-likelihood area. The construction of the dataset is provided in Appendix C. We run each configuration 5 times with different random initialization and report the average test performance. The results are shown in the right of Figure 2.
+
+As we can see, compared to the original Focal Loss, the proposed adaptation achieves better performance, indicating regaining focus in the high-likelihood area is beneficial. Nonetheless, the phenomenon can be also attributed to a better learning of the common classes instead of the rare classes. Our analysis based on the class frequency resolves this concern because the Halted Focal Loss brings more improvements if only tailed classes are learned this way, e.g., applying to the top-4 rare classes achieve the best overall performance, which proves that there are rare class examples that reside in the high-likelihood area and have non-negligible effect to generalization.
+
+The importance of the high-likelihood area of the rare examples is further validated on the COCO detection dataset, where the classifier should determine whether the object appears in the image or not. The positive detection is the rare class since there are many false proposals. The experiment setting is in Appendix C. $A P _ { 5 0 }$ and $A P _ { 7 5 }$ measure the precision under different levels of overlap between predictions and ground-truth. As shown in Table 1, strengthening the high-likelihood area of the Focal Loss, especially for the rare class examples, obtains a more accurate and confident prediction.
+
+# 4 EUREKA LOSS
+
+We have shown that the high-likelihood area matters for long-tailed classification and in particular, the rare class examples in the area have pivotal contributions. Inspired by this finding, we propose to further enhance the importance of the high-likelihood area so that the likelihood gradient in the high-likelihood area can match or even surpass that in the low-likelihood area. Moreover, the adjustment is inline with the frequency of the class so the rarer the class, the larger the likelihood gradient. Extending the adjustment term $b$ in Eq. (6), we propose the Eureka Loss (EL):
+
+$$
+\mathcal { L } = - \pmb { y } \mathrm { \cdot } \log \pmb { p } - \mathrm { b o n u s } \mathrm { \cdot } \mathrm { e n c o u r a g e m e n t } ,
+$$
+
+where −bonus·encouragement is intended to reward the well-classified rare examples. The bonus term depends on the example likelihood and the encouragement term depends on the class frequency. Different from the existing approaches that scale the Cross-Entropy Loss, punishing the incorrect predictions selectively, the proposed Eureka Loss deals with long-tailed classification from another perspective, rewarding the correct predictions progressively with their class frequencies.
+
+Bonus indicates how well the system executes the task and is designed to be a function of the probability of the ground-truth class to reward the model when it makes correct prediction. In particular, in light of the findings discussed in Section 3.2, we propose to increase the likelihood gradient in the high-likelihood area and adopt the form of
+
+$$
+{ \mathrm { b o n u s } } = { \pmb y } \cdot \mathrm { l o g } ( 1 - { \pmb p } ) ,
+$$
+
+which ensures that the monotonicity of the likelihood gradient is consistent with that of the CrossEntropy Loss, meaning that the classifier obtains more bonus when making highly-confident correct predictions. The design is against most existing studies in that the high-likelihood area is given more focus than the low-likelihood area.
+
+Encouragement implies the system realizes unusual achievements that should be encouraged. Since the unusual achievements in long-tailed classification should be correctly predicting rare class examples, we propose to reward the system based on the frequency of the example’s class:
+
+$$
+{ \mathrm { e n c o u r a g e m e n t } } = w _ { y } = { \frac { \bar { m } } { m _ { y } } } ,
+$$
+
+where $m _ { y }$ denotes the measurement of the frequency of the class $y$ . The form is flexible and similar to the frequency-based methods, and thus can be further extended based on the related studies. In our experiments, we use the effective number from Cui et al. (2019) as the measurement.
+
+Compared to the existing frequency-based and likelihood-based objective, our Eureka Loss takes the bonus term to calibrate the attention to different likelihood landscapes and the encouragement term to inform the model with the class difficulty, composing a more targeted yet comprehensive loss for learning imbalanced distributions.
+
+# 5 EXPERIMENTS
+
+We validate the proposed Eureka Loss on diverse long-tailed classification problems and analyze the characteristics of the Eureka Loss with insights into the learned models.
+
+# 5.1 TASKS, DATASETS, AND TRAINING SETTINGS
+
+Tasks and Datasets We conduct experiments on two image classification tasks and a dialogue generation task. iNaturalist 2018 is a real-world dataset which embodies a highly imbalanced class distribution of 8,142 classes. Apart from the test performance, we also report the validation performance grouped by the class frequency and categorize the examples into three groups: many (classes with more than 100 examples), medium (classes with 20 to 100 examples), and few (classes with fewer than 20 examples). ImageNet-LT (Liu et al., 2019) is an artificially constructed long-tailed classification dataset based on ILSVRC 2012 of 1000 classes. ConvAI2 is a natural conversation dataset for evaluating dialogue system, where each word type can be treated as a class, i.e., 18,848 words (classes) in total, and have extremely imbalanced training and test datasets.
+
+Evaluation Metric For the image classification tasks, we use the accuracy on ’All’ data and subset of classes with ’Many’, ’Medium’ and ’Few’ examples , i.e., the precision of the top-1 prediction. Since the test set of those tasks are balanced in classes, we further propose to estimate the accuracy on the imbalanced class distribution that reflects natural performance in real-world scenarios. The natural accuracy is the linear interpolation of the accuracy on the balanced test set using the class frequencies from the training set. For the natural language generation task, we adopt the micro and macro F-scores from Zhang et al. (2018) between the generated and the reference sentences to check how well the systems participate in the conversation. We further adopt the 4-gram diversity to examine the rare phrases, since a well-known problem for dialogue tasks is that the model tends to generate common, dull and repetitive responses and thus cannot capture the diversity of natural language distributions. Since the test set of natural language generation task is naturally imbalanced, we do not need to estimate the natural performance.
+
+Table 2: Results on iNaturalist 2018. ∗ denotes results from the corresponding paper and † denotes deferred learning, where the base loss is applied at the beginning of training and the improved method is adopted later. § denotes that it focuses on transferring representations and the method is less related to our work. Best results are shown in bold. The proposed Eureka Loss achieves the best results in learning both common and rare classes.   
+
+<table><tr><td>Method</td><td>All</td><td>Many</td><td>Medium</td><td>Few</td><td>All (Natural)</td></tr><tr><td>CE</td><td>64.3</td><td>74.1</td><td>65.9</td><td>59.8</td><td>71.7</td></tr><tr><td>CB</td><td>58.3</td><td>61.8</td><td>58.6</td><td>56.9</td><td>59.8</td></tr><tr><td>FL</td><td>62.9</td><td>72.9</td><td>64.1</td><td>58.8</td><td>70.7</td></tr><tr><td>FL +CB</td><td>59.6</td><td>45.5</td><td>61.8</td><td>60.5</td><td>46.7</td></tr><tr><td>Eureka Loss</td><td>68.5</td><td>70.8</td><td>69.3</td><td>66.7</td><td>70.6</td></tr><tr><td>CB†</td><td>68.1</td><td>71.0</td><td>68.3</td><td>67.1</td><td>70.4</td></tr><tr><td>FL + CB†</td><td>66.9</td><td>64.4</td><td>67.4</td><td>67.0</td><td>64.9</td></tr><tr><td>LDAM+CB† (Cao et al., 2019)</td><td>63.3</td><td>65.2</td><td>63.0</td><td>63.1</td><td>64.1</td></tr><tr><td>BBN (Zhou et al., 2019)*†</td><td>69.6</td><td>1</td><td>1</td><td>-</td><td>-</td></tr><tr><td>Decoupling-LWs (Kang et al., 2020)*†</td><td>69.5</td><td>71.0</td><td>68.8</td><td>69.5</td><td>-</td></tr><tr><td>Eureka Loss†</td><td>69.9</td><td>73.3</td><td>69.3</td><td>69.6</td><td>73.0</td></tr><tr><td>FSA (Chu et al., 2020)*$</td><td>65.9</td><td>1</td><td>-</td><td>-</td><td></td></tr><tr><td>MBJ (Liu et al., 2020)* §</td><td>68.6</td><td>68.0</td><td>69.8</td><td>68.5</td><td>-</td></tr><tr><td>Eureka Loss + CB†</td><td>70.3</td><td>69.0</td><td>70.1</td><td>70.9</td><td>69.4</td></tr></table>
+
+For the detailed introduction to tasks, datasets, and training settings, please refer to the appendix.
+
+# 5.2 RESULTS
+
+iNaturalist 2018 The results are reported in Table 2. We tune the hyper-parameters for our implemented baselines and report the averaged performance among 3 runs at the best setting.
+
+We compare Eureka Loss with frequency-based method Class-balanced Loss (CB), likelihood-based method Focal Loss (FL) and their combination $\mathrm { F L + C B }$ . As we can see from the first group in the table, neither FL nor CB achieves improvements over Cross Entropy (CE), but Eureka Loss outperforms CE by a large margin in terms of overall accuracy and accuracy for classes with few examples.
+
+In contrary to the first group, considering only the accuracy on the balanced test set, the two-stage version of frequency class-balanced training which adopts the class-balanced training only in the latter training phase includes deferred CB(denotes $\mathrm { C B ^ { \dag } }$ in the table), LDAM $^ +$ deferred CB, BBN and Decoupling-LWS enjoy clear advantage over CE. In order to check whether Eureka Loss is additive with the deferred method and the class-balanced training, we take deferred Eureka Loss and Eureka $\mathbf { L o s s + C B ^ { \dagger } }$ into comparison.
+
+The deferred Eureka Loss is motivated by an intuition that when training enters the bottleneck stage, Eureka Loss is introduced to reward rare classes to encourage the model to learn less common patterns, which may be helpful for learning. Compared with the original method, the deferred encouragement brings improvement on both balanced and imbalanced test distribution $( + 1 . 4$ and $+ 2 . 4$ regarding All and All(Natural), respectively). Moreover, the class-balanced training still impairs the learning for common classes even under the deferred setting, which may cast into unfavorable natural performance in real applications, e.g., the accuracy on the ’Many’ subset for $\mathrm { C B ^ { \dag } }$ and DecouplingLWS is under-performs CE by 3.1, the results is that applying $\mathrm { \dot { C } B ^ { \dagger } }$ reduces the Natural accuracy by 1.3. But deferred Eureka Loss largely outperforms CE and these methods on both balanced and imbalanced test distributions. The reason may be that we do not impair the CE learning and the additional rewarding for rare classes is less harmful. Since Eureka Loss only introduces an additive term, it is flexible and can be combined with CB, the adoption results in best All accuracy of 70.3.
+
+Table 3: Results on ImageNet-LT. ∗ and † are defined similarly to Table 2. Eureka Loss demonstrates consistent improvements against existing methods.   
+
+<table><tr><td>Method</td><td>All</td><td>All (Natural)</td></tr><tr><td>CE</td><td>44.6</td><td>63.7</td></tr><tr><td>FL</td><td>43.6</td><td>62.4</td></tr><tr><td>CB</td><td>43.9</td><td>58.8</td></tr><tr><td>FL+CB</td><td>31.1</td><td>25.0</td></tr><tr><td>Eureka Loss</td><td>48.4</td><td>63.8</td></tr></table>
+
+<table><tr><td>Method (Deferred)</td><td>All</td><td>All (Natural)</td></tr><tr><td>OLTR (Liu et al., 2019)*</td><td>46.5</td><td>1</td></tr><tr><td>CBt</td><td>49.2</td><td>60.5</td></tr><tr><td>Decoupling-LWs (Kang et al.,2020)*</td><td>49.9</td><td>59.8</td></tr><tr><td>Eureka Loss + CB†</td><td>50.4</td><td>62.2</td></tr></table>
+
+<table><tr><td>Name</td><td>F-Score (Macro)</td><td>F-Score (Micro)</td><td>Diversity (4-gram)</td></tr><tr><td>Cross Entropy</td><td>1.17</td><td>16.9</td><td>36.5</td></tr><tr><td>Focal Loss (γ = 1)</td><td>1.17</td><td>16.8</td><td>36.6</td></tr><tr><td>Focal Loss (γ = 2)</td><td>1.13</td><td>16.7</td><td>37.3</td></tr><tr><td>Eureka Loss</td><td>1.32</td><td>17.2</td><td>40.4</td></tr></table>
+
+Table 4: F-scores and 4-gram diversity on ConvAI2. The proposed Eureka Loss achieves better performance than baseline methods and generates responses that are more diverse.
+
+In all, adopting the Eureka Loss achieves a balanced performance on both common and rare classes. Besides, we also outperform the latest representation transferring based methods including MBJ and FSA.
+
+ImageNet-LT Table 3 demonstrates the results on ImageNet-LT of various methods. For this artificial dataset, we first compare with the representative frequency-based method CB and likelihoodbased method Focal Loss (FL). As we can see, the proposed method obtains a significant improvement in the balanced test set and also maintains the lead position in the virtual natural test set. For comparison with methods that defer the class-balanced training including deferred CB and DecoupingLWS, the Eureka Loss of corresponding modification also enjoys a comfortable margin and arguably excels in balancing the performance on both of the common and the rare classes.
+
+ConvAI2 Table 4 shows that the proposal helps the prediction of rare words $+ 1 0 \%$ macro F-score) and thus improves the diversity of language generation $( + 1 0 \%$ 4-gram diversity). Since this dataset is extremely imbalanced, e.g., the imbalance ratio is over 200,000, the frequency-based methods require extensive tuning to work, which we thus omit from the comparison as we are not able to reproduce favorable results. Compared with the likelihood-based method Focal Loss, which is marginally better that the original cross-entropy loss, the Eureka Loss still obtains substantial improvements.
+
+# 5.3 ANALYSIS
+
+Effect on Distributions of Different Imbalance Degrees To analyze the effect on imbalanced distributions of different degrees, we construct several artificial datasets based on CIFAR-100 and control the size of the rarest class. The imbalance degree stands for the ratio of the class size of the most common class to that of the rarest class. Hence, the larger the degree, the more imbalanced the dataset. For example, if imbalance degree is 100 for CIFAR-100, the most common class has 500 examples and the rarest class has 5 examples. As shown in Table 5, the Eureka Loss is consistently better than existing methods, especially for datasets that are more imbalanced. For results on CIFAR-10, please refer to the appendix.
+
+Table 5: Results on long-tailed CIFAR100 of different imbalance degrees (ID). † denotes deferred learning; ♣ and $\spadesuit$ denotes results taken from Zhou et al. (2019) and Cao et al. (2019), respectively.   
+
+<table><tr><td>Method</td><td>ID-100 ID-50 ID-10</td></tr><tr><td>CE+RSt+</td><td>41.61 46.48 58.11</td></tr><tr><td>CE+CB++</td><td>41.51 45.29 58.12</td></tr><tr><td>LDAM+CB† +</td><td>42.04 46.62 58.71</td></tr><tr><td>BBNt+</td><td>42.56 47.02 59.12</td></tr><tr><td>EL + CB+</td><td>43.19 48.48 59.31</td></tr></table>
+
+Varying Strength of Bonus To illustrate the importance of the high-likelihood area in imbalanced classification within Eureka Loss, we compare a
+
+<table><tr><td>Method</td><td>All Many</td><td>Medium</td><td>Few</td></tr><tr><td>EL (β=0.99)</td><td>45.8 67.2</td><td>38.4</td><td>11.3</td></tr><tr><td>EL (β=0.999)</td><td>47.8 66.1</td><td>42.0</td><td>16.4</td></tr><tr><td>EL (β=0.9999)</td><td>50.0 67.1</td><td>44.7</td><td>19.8</td></tr></table>
+
+![](images/c254aa492ed8850f2cffddcc0f6a8a4f01007d65394d8f7689e35e27e769de33.jpg)  
+Figure 3: Varying strength of bonus on long-tailed CIFAR-10. Higher power $\gamma _ { b }$ indicates higher strength.
+
+Table 6: Varying strength of encouragement on the dev set of ImageNet-LT. Higher $\beta$ means higher strength.
+
+exponential form bonus called Power Bonus (PB) to the original bonus, which takes the power form of the probability vector of by a factor $\gamma _ { b }$ :
+
+$$
+P B ( \pmb { p } ) = - \pmb { y } \cdot \pmb { p } ^ { \gamma _ { b } } ,
+$$
+
+where $\gamma _ { b }$ is a positive value to ensure the monotonicity and can be tuned for different tasks. Besides, CE achieves a $7 1 . 4 \%$ accuracy and the likelihood bonus with deferred encouragement gets a $7 6 . 1 \%$ accuracy. Figure 3 demonstrates that bigger likelihood gradient in the high-likelihood area brings more improvements, e.g., power-bonus with power of 4 is better than bonuses of small power.
+
+Varying Strength of Encouragement The strength of encouragement is determined by both of the class frequency and the hyper-parameter $\beta$ as we use the effective number of the class. As $\beta$ controls the variance of the the effective number, e.g., when $\beta = 0$ , the variance is 0, meaning all of the classes receive equal encouragement, we control the strength of the encouragement towards tail classes by altering $\beta$ . The results on the validation set of ImageNet-LT are shown in Table 6. As we can see, higher $\beta$ (more encouragement for tail classes), is connected to higher overall accuracy and better tail class performance, which again validates our motivation for encouraging correct rare class predictions.
+
+Effect on Example-Likelihood The Eureka Loss rewards the high-likelihood predictions especially for tail classes. It is interesting to see how the training dynamic is changed due to this preference. In order to understand the effect, we visualize the example likelihood grouped by target class frequencies after training in Figure 4 and Figure 5 (due to space limit, the complete comparison is provided in the Appendix A), which are from the validation set from iNaturalist 2018. As we can see, with the Eureka Loss, the examples in the high-likelihood area are driven to the extreme. For example, considering the medium and the low frequency group, the “hard” examples that may be inherently difficult to classify stand invariant, while for the examples that can be classified correctly, the system now treats them with more confidence. This dynamics translate into better accuracy in unseen examples in the test set, hinting the importance of rare class examples in the high-likelihood area for the generalization of learning imbalanced class distributions.
+
+![](images/10339a658a49a0924ac45107f28f41ecfa87419a92e24bf15789f9a88b3a945e.jpg)  
+Figure 4: The visualization of test likelihood distribution for models trained with the Eureka Loss. The model classifies the rare class examples more decisively, compared to the existing methods.
+
+# 6 CONCLUSIONS
+
+In this paper, we examine the effect of the high-likelihood area on learning imbalanced class distributions. We find that the existing practice of relatively diminishing the contribution of the examples in the high-likelihood area is actually harmful to the learning. We further show that the rare class examples in the high-likelihood area have pivotal contribution to model performance and should be focused on instead of being neglected. Motivated by this, we propose the Eureka Loss, which additionally rewards the well-classified rare class examples. The results of the Eureka Loss in the image classification and natural language generation problems demonstrate the potential of reconsidering the role of the high-likelihood area. In-depth analysis also verifies the effectiveness of the investigated loss form and reveals the learning dynamics of different approaches to long-tailed classification.
+
+# REFERENCES
+
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+
+# A VISUALIZATION OF EXAMPLE LIKELIHOOD
+
+The complete comparison between the likelihood distribution for Eureka Loss, Cross-Entropy Loss, Focal Loss, Class-balanced Loss are shown in Figure 5. We see from the figure that the model trained with Eureka Loss gives high-confidence predictions for gold labels. Compared with the Cross-Entropy Loss, the Focal Loss diminish the contribution of high-likelihood examples, and the resulted model is unsure in the prediction of unseen examples. In particular, for the examples in the Few group, it almost produces no confident correct predictions. The Class-Balanced Loss, on the other hand, improves the confidence for the tail class examples but degrade the performance for the head class examples, which may imply potential issues regrading to natural performance in real-world applications. Besides, it is worth noting that the Decoupling-LWS obtains a likelihood distribution similar to the Class-Balanced Loss.
+
+# B FURTHER RESULTS AND ANALYSIS
+
+# B.1 RESULTS ON INATURALIST 2018 WITH TRAINING FOR 90 EPOCHS
+
+It is found by existing work (Kang et al., 2020) that training much longer for the iNaturalist 2018 dataset can produce better scores and reflect the performance of the models more authentically. However, most previous studies conduct training for a shorter time. To keep consistent with previous research in this field, we also train the models using Eureka Loss for 90 epochs and the results are shown in Table 7. In this setting, eureka loss achieves better accuracy than the two-stage decoupling methods (Decoupling-LWS and BBN), the advantage is more profound under the Natural accuracy, for example, compared to the Decoupling-LWS, the deferred Eureka Loss gains 3.8 Natural accuracy. Compared to the one-state methods including Class-Balanced Loss (CB), Focal Loss (FL), ClassBalanced Focal Loss $\scriptstyle \left( \mathrm { F L + C B } \right)$ , LDAM, the model trained with the Eureka Loss is much more accurate on the test distribution.
+
+# B.2 RESULTS ON LONG-TAILED CIFAR-10
+
+In the main text, we have reported the results of the Eureka Loss varying the class imbalance on the CIFAR-100 dataset. Here we also perform comprehensive experiments on long-tailed CIFAR-10 and report top-1 precision on the balanced test set. The results are shown in the Table 8. When combined with Class-Balanced Loss, Eureka Loss brings higher improvement in terms of accuracy than Cross-Entropy Loss and LDAM.
+
+# B.3 HYPER-PARAMETER OF THE FOCAL LOSS
+
+In the paper, we report results for the Focal Loss with best hyper-parameters. For COCO detection, the hyper-parameter of $\alpha = 0 . 2 5 , \gamma = 2$ is the best setting reported in Table 1.b of the origin paper (Lin et al., 2017). For the other multi-class classification tasks, we tune hyper-parameters of the Focal Loss on it. The accuracy for the Focal Loss with different hyper-parameter $\gamma$ are listed in the Table1. we set $\gamma = 1$ for Focal Loss since it is consistently optimal in long-tailed image classification. For ConvAI2, $\gamma = 0 . 5$ under-performs Cross Entropy, and neither $\gamma = 1$ nor $\gamma = 2$ outperforms each other, so we report the Focal Loss of $\gamma = 1$ and the Focal Loss of $\gamma = 2$ in the Table 4.
+
+![](images/ddebb6e382209f81701a3a28cdcff5f46ad0bee0b5b9d65fc3eb50cfb21766b0.jpg)  
+Figure 5: Example likelihood on the validation set of iNaturalist18 categorized by class frequencies into few, medium, many, and all.
+
+# B.4 COMPLEMENTARY EXPERIMENT TO THE MOTIVATION EXPERIMENT
+
+In Section 3, we propose Halted Focal Loss(HFL) and compare it to Focal Loss(FL) to illustrate the potential of the high-likelihood area. However, its loss is no steeper than Cross Entropy (CE). Moreover, Focal Loss does not beat CE in the setting of multi-class classification. In order to bridge the gap between the possibly weak motivation experiment of Halted Focal Loss and the proposed method Eureka Loss. We propose simplified Eureka Loss:
+
+$$
+\mathcal { L } = \left\{ \begin{array} { l l } { - y \cdot \log p , } & { \mathrm { i f ~ } p _ { y } \leq \varphi } \\ { - y \cdot \log p + y \cdot [ \log ( 1 - p ) - b ] , } & { \mathrm { o t h e r w i s e } } \end{array} \right.
+$$
+
+Table 7: Results on iNaturalist 2018 after training the model for 90 epochs. ∗ denotes results from the corresponding paper and † denotes that we use the base loss at the beginning of training and then adopt the method later. The proposed Eureka Loss achieves good results in learning both common and rare classes.   
+
+<table><tr><td>Method</td><td>All</td><td>Many</td><td>Medium</td><td>Few</td><td>All (Natural)</td></tr><tr><td>CE</td><td>61.8</td><td>72.2</td><td>63.4</td><td>57.2</td><td>69.8</td></tr><tr><td>FL</td><td>60.2</td><td>70.4</td><td>61.5</td><td>56.0</td><td>68.3</td></tr><tr><td>CB</td><td>52.4</td><td>51.9</td><td>53.0</td><td>51.8</td><td>51.2</td></tr><tr><td>RS</td><td>56.7</td><td>59.0</td><td>56.9</td><td>55.9</td><td>56.5</td></tr><tr><td>FL+CB (Cui et al., 2019)*</td><td>61.1</td><td></td><td>-</td><td>-</td><td>-</td></tr><tr><td>CE+CB† (Cao et al., 2019)*</td><td>63.7</td><td>=</td><td>=</td><td></td><td>1</td></tr><tr><td>LDAM (Cao et al., 2019)*</td><td>64.6</td><td></td><td></td><td></td><td></td></tr><tr><td>LDAM+CB† (Cao et al.,2019)*</td><td>68.0</td><td></td><td></td><td></td><td></td></tr><tr><td>LDAM+CB† (Zhou et al., 2019)*</td><td>64.6</td><td>-</td><td>=</td><td>=</td><td></td></tr><tr><td>BBN (Zhou et al.,2019)*</td><td>66.3</td><td>=</td><td>=</td><td>-</td><td>=</td></tr><tr><td>Decoupling-LWs (Kang et al., 2020)*</td><td>65.9</td><td>65.0</td><td>66.3</td><td>65.5</td><td>65.7</td></tr><tr><td>Eureka Loss</td><td>66.4</td><td>67.5</td><td>66.5</td><td>65.9</td><td>67.9</td></tr><tr><td>Eureka Loss†</td><td>67.1</td><td>69.4</td><td>67.3</td><td>66.1</td><td>69.5</td></tr></table>
+
+Table 8: Results on long-tailed CIFAR-10 data with different imbalance degrees. ID is short for imbalance degree. † is defined similarly; $\clubsuit$ denotes Zhou et al. (2019); $\spadesuit$ denotes Cao et al. (2019).   
+
+<table><tr><td>Method</td><td>ID-100</td><td>ID-50</td><td>ID-10</td></tr><tr><td>CE+RSt+</td><td>75.61</td><td>79.81</td><td>87.38</td></tr><tr><td>CE+CB++</td><td>76.34</td><td>79.97</td><td>87.56</td></tr><tr><td>LDAM+CB†+</td><td>77.03</td><td>81.03</td><td>88.16</td></tr><tr><td>BBNt</td><td>79.82</td><td>82.18</td><td>88.32</td></tr><tr><td>EL + CB†</td><td>77.95</td><td>82.00</td><td>88.35</td></tr></table>
+
+where $\varphi$ is set to 0.5, and $b$ is $l o g ( 1 - \varphi )$ . In the simplified Eureka Loss, the encouragement is removed, and to keep the low-likelihood area unchanged, the new bonus term starts rewarding the model from $p = \varphi$ . As is shown in Table $\lvert 0 , \mathrm { H F L } ( { \mathsf { t } } { = } 0 . 5 )$ is also better than HFL and FL in terms accuracy of tail classes on the large scale long-tailed classification dataset iNaturalist 2018, This result once again shows that high-likelihood area matters and near-correct predictions of rare classes play a major role. But HFL is the combination of Focal Loss(in the low likelihood area) and Cross Entropy(in the high-likelihood area) and the performance is constrained. Unlike HFL, the loss of Simplified Eureka Loss is built on CE and the loss is much steeper than Cross Entropy in the high-likelihood area, it outperforms Cross Entropy(CE) and HFL in terms of all metrics, especially on the subset of tail classes. Eureka Loss reported in Table 2 is a continuous version of simplified Eureka Loss with an additional encouragement for rare classes, similar to $\mathrm { H F L } ( \mathrm { t } { = } 0 . 5 )$ , this setting which rewards more for rare classes achieves the best overall performance.
+
+# B.5 EUREKA LOSS MITIGATES OVER-FITTING ON TAIL CLASSES
+
+As shown in Figure 6, compared to Cross-Entropy Loss, Eureka Loss reduce the gap between the training accuracy and test accuracy from 33.0 to 28.6 on tail classes. Moreover, even though Classbalanced Loss achieves the highest training accuracy, its test accuracy is unexpectedly low. The difference of performance between the seen examples and the unseen examples indicates the degree of over-fitting. The results are from the “Few” subset of the iNaturalist 2018 of training 90 epochs.
+
+Table 9: Mean/(standard deviation) test accuracy of the Focal Loss with different hyper-parameter $\gamma$ in long-tailed image classification.   
+
+<table><tr><td>Y</td><td>CIFAR10</td><td>Imagenet-LT</td><td>iNaturalist20182</td></tr><tr><td>0.5</td><td>21.2/10.8</td><td>8.3/7.1</td><td>9.2/3.2</td></tr><tr><td>1</td><td>70.8/0.6</td><td>43.8/0.3</td><td>60.2/0.3</td></tr><tr><td>2</td><td>70.3/0.6</td><td>43.6/7.9</td><td>59.5/0.2</td></tr></table>
+
+Table 10: Comparison between the Halted Focal Loss and the Simplified Eureka Loss on long-tailed Cifar-10 (imbalance ratio is 100) and iNaturalist 2018, the mean standard deviation (Stdev) for results on iNaturalList2018 is about 0.4.   
+
+<table><tr><td rowspan="2">method Mean/Stdev</td><td rowspan="2">CIFAR10</td><td colspan="5">iNaturalList2018</td></tr><tr><td>All</td><td>Many</td><td> Medium</td><td>Few</td><td> All(natural)</td></tr><tr><td>CE</td><td>71.4/0.5</td><td>64.3</td><td>74.1</td><td>65.9</td><td>59.8</td><td>71.7</td></tr><tr><td>FL</td><td>71.3/0.6</td><td>62.9</td><td>72.9</td><td>64.1</td><td>58.8</td><td>70.7</td></tr><tr><td>HFL</td><td>71.4/0.3</td><td>63.6</td><td>73.1</td><td>64.6</td><td>59.7</td><td>70.7</td></tr><tr><td>HFL(t=0.5)</td><td>71.8/0.5</td><td>64.2</td><td>73.3</td><td>64.3</td><td>61.6</td><td>70.8</td></tr><tr><td>Simplified EL</td><td>71.8/0.9(+0.4)</td><td>66.3(+2.0)</td><td>75.1 (+1.0)</td><td>67.4(+1.6)</td><td>62.6(+2.8)</td><td>72.6(+1.1)</td></tr></table>
+
+# C DETAILS OF EXPERIMENTAL SETTINGS
+
+# C.1 DATASETS
+
+There are six datasets used in this paper in total and an overview of the dataset statistics are demontrated in Table 11 and Figure 7. For image classification tasks, the iNaturalist 2018 dataset is the most imbalanced and has the most classes, which is most satisfactory for evaluating long-tailed classifications. For the language generation task, ConvAI2 has an imbalance ratio of 277K, which, however, should be taken cautiously, since most of the tail classes are not covered in evaluation. The common practice to evaluate the learning on the imbalanced language distributions is to investigate the diversity of the generated text. The 4-grams can be regarded as high-ordered classes and a 4-gram of four common words can also be a “rare class”.
+
+# C.2 TRAINING SETTINGS
+
+CIFAR-10 and CIFAR-100 For experiments on long-tailed CIFAR-10 and CIFAR-100, the backbone network is ResNet-32 (He et al., 2016). The model is optimized with SGD with a momentum of 0.9. The learning rate is set to 0.1 and the model is trained for 200 epochs with 128 examples per mini-batch. To stabilize the training, we adopt the warm-up strategy used by Goyal et al. (2017) in the first 5 epochs. Following Cao et al. (2019), we decay the learning rate by 0.01 at the 160th epoch and again at the 180th epoch. For the results in Figure 2 and Figure 3, we conduct experiments on long-tailed CIFAR-10 with an imbalance ratio of 10.
+
+ImageNet-LT For experiments on ImageNet-LT ILSVRC 2012, the base network is ResNext50 (He et al., 2016). The batch size is set to 512 to accelerate training. The initial learning rate is 0.2 and we utilize a cosine learning rate scheduler.
+
+iNaturalist 2018 Same as the experiments on ImageNet-LT, we also follow the default setting in Kang et al. (2020) for experiments on iNaturalist. To be specific, we adopt ResNet-50 model, use SGD with to train the model for 200 epochs with batch size 512 and a cosine learning rate schedule which gradually decays from 0.2 to 0.0. Results on the valid set are also reported on subset of many $( > 1 0 0$ samples), medium $( 2 0 - 1 0 0$ samples), and few $< 2 0$ samples), respectively.
+
+ConvAI2 For the conversation generation task, we utilize a two-layer LSTM (Hochreiter & Schmidhuber, 1997) encoder-encoder architecture as our base network. The hidden size of both encoder and decoder is set to 1024. We optimize the model with SGD optimizer with momentum 0.9, the batch size is 64 and the learning rate is set to 3. The embedding size is 256 and word vectors are initialized with GloVe (Pennington et al., 2014). We select our final model until the performance on the validation is no longer improving after 5 epochs.
+
+![](images/da48883d1b3e68f8fde8391d7c425565e69d162597da6b41e44bcbf648f733a1.jpg)  
+Figure 6: Illustration of the over-fitting phenomenon on tail classes, the number on the top of each bar is the difference between the training accuracy and the test accuracy.
+
+Table 11: Data statistics of long-tailed image classification tasks. Imbalance Ratio denotes the ratio of the size of the most common class to that of the rarest class.   
+
+<table><tr><td>Dataset</td><td># Classes</td><td>Imbalance Ratio</td></tr><tr><td>COCO Detection</td><td>2</td><td>~1000</td></tr><tr><td>Long-tailed CIFAR-10</td><td>10</td><td>10-100</td></tr><tr><td>Long-tailed CIFAR-100</td><td>100</td><td>10-100</td></tr><tr><td>ImageNet-LT</td><td>1000</td><td>256</td></tr><tr><td>iNaturalist 2018</td><td>8142</td><td>500</td></tr></table>
+
+![](images/76a5227aa259e581dbcd6a56fea4a8c78d8433381a26caf960824d7ddb935f1d.jpg)  
+Figure 7: Word frequency distribution of ConvAI2 dataset. For natural language generation tasks, each word type can be regarded as a class and most words appear scarcely in the data. If measured the same with long-tailed image classification tasks, the imbalance ratio is 277K.
+
+COCO Dectection For experiments on COCO detection, we adopt the configuration of “RetinaNetR-50-FPN-1x” from the GitHub repository Detectron2 as our default setting. In this setting, the one-stage detector of RetinaNet with the backbone ResNet50 is trained for $9 0 \mathrm { k }$ updates and the batch size is 8 images per batch.
+
+For the image classification tasks, the default $\beta$ is set to 0.9999 for all datasets. For the deferred version, we defer the adoption of Eureka Loss after training for 160 epochs and 180epochs on CIFAR100 and iNaturalist 2018 respectively. As for the dialog generation task ConvAI2, $\beta$ is set to 0.999 and we start the encouragement after regularly training the model for 5 epochs.
+
+We tune the $\beta \in \{ 0 . 9 , 0 . 9 9 , 0 . 9 9 9 , 0 . 9 9 9 9 \}$ and $\gamma \in \{ 0 . 5 , 1 , 2 \}$ for the Class-Balanced Loss (CB) and the Focal Loss (FL) respectively in multi-class classification, and report the best results of these baselines. Following previous work (Cui et al., 2019), $\alpha$ is set to 1.0 for the Focal Loss(FL), and the Class-Balanced Focal Loss $\mathrm { ( F L + C B ) }$ ) in multi-class classification tasks can be viewed as the origin Focal Loss with class-level weight $\alpha$ in binary classification tasks.
+
+The training costs are summarized in Table 12.
+
+<table><tr><td>Data</td><td>Infrastructure</td><td>Mem/GPU</td><td>Time</td><td>Epochs</td><td>Samples</td><td>Model</td></tr><tr><td>Long-tailed CIFAR-10</td><td>RTX 2080Ti *1</td><td>1.4G</td><td>0.3h</td><td>200</td><td>12.4K</td><td>ResNet32</td></tr><tr><td>Long-tailed CIFAR-100</td><td>RTX 2080Ti *1</td><td>1.4G</td><td>0.3h</td><td>200</td><td>10.8K</td><td>ResNet32</td></tr><tr><td>ImageNet-LT</td><td>TITAN RTX *4</td><td>17G</td><td>8h</td><td>90</td><td>116K</td><td>ResNext50</td></tr><tr><td>iNaturalist 2018</td><td>RTX TITAN *4</td><td>15G</td><td>48h</td><td>200</td><td>438K</td><td>ResNet50</td></tr><tr><td>ConvAI2</td><td>RTX 2080Ti *1</td><td>9G</td><td>4h</td><td>16</td><td>131K</td><td>2-L LSTM</td></tr><tr><td>COCO Detection</td><td>RTX 2080Ti * 4</td><td>9G</td><td>8h</td><td>90K updates</td><td>118K</td><td>ResNet50</td></tr></table>
+
+Table 12: Training costs of each task. Samples are dialogues in ConvAI2 and images in image classification tasks

parse/train/7Yhok3vJpU/7Yhok3vJpU_content_list.json

@@ -0,0 +1,1851 @@
+[
+    {
+        "type": "text",
+        "text": "HIGH-LIKELIHOOD AREA MATTERS — REWARDING CORRECT, RARE CLASS PREDICTIONS UNDER IMBALANCED DISTRIBUTIONS ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Anonymous authors Paper under double-blind review ",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "ABSTRACT ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Learning from natural datasets poses significant challenges for traditional classification methods based on the cross-entropy objective due to imbalanced class distributions. It is intuitive to assume that the examples from rare classes are harder to learn so that the classifier is uncertain of the prediction, which establishes the low-likelihood area. Based on this, existing approaches drive the classifier actively to correctly predict those incorrect, rare examples. However, this assumption is one-sided and could be misleading. We find in practice that the high-likelihood area contains correct predictions for rare class examples and it plays a vital role in learning imbalanced class distributions. In light of this finding, we propose the Eureka Loss, which rewards the classifier when examples belong to rare classes in the high-likelihood area are correctly predicted. Experiments on the large-scale long-tailed iNaturalist 2018 classification dataset and the ImageNet-LT benchmark both validate the proposed approach. We further analyze the influence of the Eureka Loss in detail on diverse data distributions. ",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Existing classification methods usually struggle in real-world applications, where the class distributions are inherently imbalanced and long-tailed (Van Horn & Perona, 2017; Buda et al., 2018; Liu et al., 2019; Gupta et al., 2019), in which a few head classes occupy a large probability mass while most tail (or rare) classes only possess a few examples. The language generation task is a vivid example of the long-tailed classification. In this case, word types are considered as the classes and the model predicts probabilities over the vocabulary. Common words such as the, of, and and are the head classes, while tailed classes are rare words like Gobbledygook, Scrumptious, and Agastopia. Conventional classifiers based on deep neural networks require a large number of training examples to generalize and have been found to under-perform on rare classes with a few training examples in downstream applications (Van Horn & Perona, 2017; Buda et al., 2018; Cao et al., 2019). ",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "It is proposed that the traditional cross-entropy objective is unsuitable for learning imbalanced distributions since it treats each instance and each class equivalently (Lin et al., 2017; Tan et al., 2020). In contrast, the instances from tail classes should be paid more attention, indicated by two main approaches that have been recently investigated for class-imbalanced classification: the frequencybased methods and the likelihood-based methods. The former (Cui et al., 2019; Cao et al., 2019) directly adjust the weights of the instances in terms of their class frequencies, so that the instances from the tail classes are learned with a higher priority no matter whether they are correctly predicted or not. The latter (Lin et al., 2017; Zhu et al., 2018) instead penalize the inaccurate predictions more heavily, assuming that the well-classified instances, i.e., the instances in the high-likelihood area, factor inconsequentially in learning imbalanced distributions. ",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "However, neither of these two approaches realistically depicts the likelihood landscape. In particular, the high-likelihood area, where the classifier makes the correct predictions for both common class examples and rare class ones, contributes significantly to generalization. However, this area is not well-shaped, as illustrated in Figure 1. Specifically, the frequency-based methods imply an impaired learning of common class examples that are the principle part of the natural data, while the likelihoodbased methods ignore the correctly-predicted rare class examples that can provide crucial insights into the underlying mechanism for predicting such examples. ",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/4a77a3007324713ae2f486ac47167ea60bca25def88b2de62bb08f9fd4d8e76d.jpg",
+        "image_caption": [
+            "Figure 1: Conceptual illustration of approaches to learning unbalanced class distributions. For an instance in the training data, the frequency-based methods either sharpen or soften the loss for all likelihoods according to its class frequency, while the likelihood-based methods adjust the loss in the low- or high-likelihood area, respectively. The high-likelihood area is relatively deprioritized in both cases. The proposed Eureka Loss progressively rewards the systems with higher bonus for higher-likelihood. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 1
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+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In this paper, we first demonstrate that existing practice of neglecting predictions in the high-likelihood area is harmful to learning imbalanced class distributions. Furthermore, we find that simply mixing the cross-entropy loss and the Focal Loss (Lin et al., 2017) can induce substantially superior performance, which validates our motivation. In turn, we propose to elevate the importance of high-likelihood predictions even further and design a novel objective called Eureka Loss. It progressively rewards the classifiers according to both the likelihood and the class frequency of an example such that the system is encouraged to be more confident in the correct prediction of examples from rare classes. Experimental results on the image classification and the language generation tasks demonstrate that the Eureka Loss outperforms strong baselines in learning imbalanced class distributions. ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Our contributions are twofold: ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "• We challenge the common belief that learning for examples in low-likelihood area is more important for learning tail classes and reveal that the correctly-predicted rare class examples make important contribution to learning long-tailed class distributions. • We explore a new direction for learning imbalanced classification that focuses on rewarding correct predictions for tail classes examples, rather than penalizing incorrect ones. The proposed Eureka Loss rewards the classifier for its high-likelihood predictions progressively to the rarity of their class and achieves substantial improvements on various problems with long-tailed distributions. ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2 RELATED WORK ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Frequency-based Data and Loss Re-balancing Previous literature on learning with long-tailed distribution mainly focusing on re-balancing the data distribution and re-weighting the loss function. ",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "The former is based on a straightforward idea to manually create a pseudo-balanced data distribution to ease the learning problem, including up-sampling for rare class examples (Chawla et al., 2002), down-sampling for head class examples (Drummond & Holte, 2003) and a more concrete sampling strategy based on class frequency (Shen et al., 2016). ",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "As for the latter, recent studies propose to assign different weights to different classes, and the weights can be calculated according to the class distribution. For example, Khan et al. (2018) design a cost-sensitive loss for major and minor class examples. An intuitive method is to down-weight the loss of frequent classes, while up-weight the contribution of rare class examples. However, frequency is not suitable to be directly treated as the the weight since there exists overlap among samples. An advancing alternative loss CB (Cui et al., 2019) proposes to calculate the effective number to substitute the frequency for loss re-weighting. However, since it assigns lower weight to head classes in the maximum likelihood training (Cross Entropy objective), it seriously impairs the learning of head classes. Moreover, CB requires a delicate hyper-parameter tuning for every imbalanced distribution, leading to a lot of manul efforts. From the perspective of max-margin, a recent study LDAM (Cao et al., 2019) proposes to up-weight the loss of tail classes by a class-distribution based margin. Compared to the above methods, we choose to decrease the loss of tail classes by rewarding correct predictions rather than increasing the loss of tail classes through aggravated penalization. ",
+        "bbox": [
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+        "page_idx": 1
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+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Deferring the Frequency-based Class-balanced Training Recent studies find that deferring the class-balanced training helps learn high-quality representations (Liu et al., 2019), and propose deferred Class-balanced training (deferred CB) (Cao et al., 2019), which chooses to adopt Cross Entropy objective at the beginning of training. Similarly, the Decoupling method (Kang et al., 2020) shows that the re-balancing strategies impair the quality of learned feature representations and demonstrate an improved performance learned with original data distribution, by training the model with Cross Entropy in the first phase and adopting class-balanced training in the second phase. This decoupling strategy can also be found in BBN (Zhou et al., 2019), which includes both class imbalanced and balanced training, and the transition from the former to the latter is achieved through a curriculum learning schedule. These methods achieve state-of-the-art performance in long-tailed classification. To be comparable with these methods and to analyse whether Eureka Loss is complementary to this technique, we propose deferred Eureka Loss, in which rewarding for rare class prediction is introduced to encourage the model to learn rare patterns when learning is stalled. ",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Likelihood-based Loss Another dominant method for imbalanced classification is the likelihoodbased method Focal Loss (FL) (Lin et al., 2017), which proposes to down-weight the contribution of examples in the high-likelihood area. However, we argue that it is harmful for learning tail classes and choose an opposite direction by highlighting the high-likelihood area with a steeper loss. ",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Transferring Representations Techniques for transferring information from sufficient head classes examples to under-represented rare classes examples belong to a parallel successful direction in this field. They include MBJ (Liu et al., 2020), which utilizes external semantic feature memory and FSA (Chu et al., 2020), which decomposes feature in to class-specific and class-generic components. These latest transfer learning based studies are less related to our paper but they also obtain good improvements in long-tailed classification, so we add them into comparison in the experiments. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3 ROLE OF THE HIGH-LIKELIHOOD AREA ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The existing approaches to the long-tailed classification independently consider the class frequency and the example likelihood. However, we show that this one-sided reflection is problematic when dealing with the tail class examples that can be confidently classified. The tail class examples can be easily classified by the classifier, and the head class examples can also be hard for the classifier to recognize. The difficulty of classification depends on the inherent characteristic of the classes, rather than the sample size of the class. For example, in species classification, the Portuguese man o’war may be a rare class but can be easily classified due to its distinct features, compared to various kinds of moths which are common classes yet are hard to distinguish. However, the frequency-based methods continuously drive the classifier to fit the rare class examples, especially when they are difficult to predict, which may lead to overfitting. On the other hand, the likelihood-based methods relax the concentration in the high-likelihood area, which contains the tail class examples that are not hard to predict and provide insights to generalization. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "To verify our point of view, we analyze the problem by dissecting the influence of the high-likelihood area with respect to the class frequency and demonstrate that properly encouraging the learning of well-classified tail class examples induce substantial improvements, before which we first give a brief introduction of classification with long-tailed class distributions. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1 PREPARATION: CLASSIFICATION WITH LONG-TAILED CLASS DISTRIBUTIONS ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Let’s consider the multi-class classification problem with the long-tailed class distribution. Given a class set $\\mathbb { C }$ , $n$ denotes the number of different classes in $\\mathbb { C }$ and $m _ { i }$ is the number of examples of the class $C _ { i }$ . For simplicity, we sort the class set $\\mathbb { C }$ according to cardinal $m _ { i }$ for $C _ { i }$ such that $C _ { 0 }$ is the class with the most examples and $C _ { n - 1 }$ is the rarest class. Let $\\pmb { p }$ be a $n$ -dim probability vector predicted by a classifier model $f ( \\pmb { x } ; \\pmb { \\theta } )$ based on the input $_ { \\textbf { \\em x } }$ , where each element $p _ { i }$ denotes the probability of the class $C _ { i }$ and $\\textbf {  { y } }$ is a $n$ -dim one-hot label vector with $y$ being the ground-truth class. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "The probability vector can be calculated as ",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/ef206f2119cac6929dfa3268358d5a9ecc44537a7bab01534645c218b4a726d4.jpg",
+        "text": "$$\n\\begin{array} { r } { \\pmb { p } = \\sigma ( f ( \\pmb { x } ; \\pmb { \\theta } ) ) , } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where $\\sigma$ is the normalizing function, e.g., softmax for multi-class classification. Typically, the parameters are estimated using maximum likelihood estimation (MLE), which is equivalent to using the Cross-Entropy Loss (CE) function, where the scalar $y \\cdot \\log p$ can be regarded as the (log)-likelihood: ",
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+        "page_idx": 3
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+    {
+        "type": "equation",
+        "img_path": "images/797234188419c8764cfd4a209fbe87211a7806af6cbfe1909e4a4e4c65545a86.jpg",
+        "text": "$$\n\\mathcal { L } = - \\mathbb { E } _ { ( \\pmb { x } , \\pmb { y } ) \\in \\mathcal { D } } \\log p _ { \\mathrm { m o d e l } } ( \\pmb { y } | \\pmb { x } ) = - \\frac { 1 } { | \\mathcal { D } | } \\sum _ { ( \\pmb { x } , \\pmb { y } ) \\in \\mathcal { D } } \\pmb { y } \\cdot \\log p .\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "For deep neural network–based classifiers, due to the non-linearity of the loss function, the problem is typically solved by stochastic gradient descent, which requires the calculation of the gradient with respect to the parameters using the chain-rule, the process of which is called back-propagation: ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/487ccf3e40b2099b5b62af271309a2ef2570fe174e4874859dcacee9f27940d9.jpg",
+        "text": "$$\n\\frac { \\partial \\mathcal { L } } { \\partial \\pmb { \\theta } } = \\frac { \\partial \\mathcal { L } } { \\partial \\pmb { p } } \\frac { \\partial \\pmb { p } } { \\partial \\pmb { \\theta } } = \\frac { \\partial \\mathcal { L } } { \\partial \\pmb { p } } \\frac { \\partial \\sigma ( f ( \\pmb { x } ; \\pmb { \\theta } ) ) } { \\partial \\pmb { \\theta } } .\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We introduce the term likelihood gradient to denote $\\partial \\mathcal { L } / \\partial \\mathbf { \\boldsymbol { p } }$ , which modulates how the probability mass should be shifted and is a characteristic of the loss function instead of the classifier. For learning imbalanced class distributions, the common methods aim to shape the likelihood gradient so the rare classes are learned with priority, i.e., embodying a sharper loss and a larger likelihood gradient. ",
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+    {
+        "type": "text",
+        "text": "Frequency-Based Methods Frequency-based methods alter the likelihood gradient according to the class frequencies, which are irrelevant to how well individual examples are classified. A simple form is using a $n$ -dim weight vector $\\textbf { \\em w }$ composed of the class weights based on their frequencies in the dataset to determine the importance of examples from each class: ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/1547d31d312b4846653cad9c1ed96718f659643a6c01358ed503036e8a724ea8.jpg",
+        "text": "$$\n\\mathcal { L } = - w _ { y } \\cdot ( { \\pmb y } \\cdot \\log { \\pmb p } ) .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            421,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Note that when ${ \\pmb w } = { \\bf 1 }$ , it is identical to the cross-entropy objective. The weight vector is typically calculated as $w _ { i } = \\bar { m } / m _ { i }$ , where $\\bar { m }$ is the average of $m _ { i }$ . As we can see, the standard weight is taken as the average of the class size, so that the classes with more examples are down-weighted and the classes with fewer examples are up-weighted. For a natural long-tailed distribution, the average is larger than the median, which suggests more classes are up-weighted. Advanced frequency-based methods try to obtain a more meaningful measurement of the class size, e.g., the Class-Balanced Loss (CB) proposed by Cui et al. (2019) utilizes an effective number $\\left. 1 - \\beta ^ { m _ { i } } \\right/ 1 - \\beta$ for each class, where $\\beta \\in [ 0 . 9 , 1 )$ is a tunable class-balanced term. ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Likelihood-Based Methods Different from the frequency-based methods, likelihood-based methods adjust the likelihood gradient based on the instance-level difficulty as predicted by the classifier such that the examples in the low-likelihood area are more focused in training. For example, the well-known Focal Loss (FL) with a balanced factor $\\alpha$ proposed by Lin et al. (2017) takes the following form: ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/1ec4995fc9dbae2463a0ef5c51f676e86d31860224bce44cd7c84c9422234019.jpg",
+        "text": "$$\n\\mathcal { L } = - \\alpha ( 1 - p _ { y } ) ^ { \\gamma _ { f } } \\cdot ( { \\pmb y } \\cdot \\log { \\pmb p } ) ,\n$$",
+        "text_format": "latex",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "where $\\gamma _ { f } > 0$ , which controls the convexness of the loss and higher $\\gamma _ { f }$ indicates adjustment that are more significant. Note that when $\\alpha = 1$ and $\\gamma _ { f } = 0$ , it is identical to the cross-entropy objective. Following previous works (Cao et al., 2019; Liu et al., 2019; Cui et al., 2019), the $\\alpha$ is set to 1 in multi-class classification, and Class-Balanced Focal Loss $\\mathrm { ( F L + C B ) }$ can be viewed Focal Loss with uneven alpha for each class in the multi-class setting. The key idea is to pay less attention to the well-classified examples and pay more attention to the badly-classified examples, because it is natural to assume the tail class examples are harder to learn and thus cannot be well-classified. However, such methods neglect the correctly-predicted tail class examples, the practice of which we show is not constructive to the learning of long-tailed class distributions. ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.2 UNDERSTANDING THE INFLUENCE OF THE HIGH-LIKELIHOOD AREA ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "To understand the influence of the high-likelihood area, we first prepare a variant of the Focal Loss, the Halted Focal Loss (HFL), such that the high-likelihood area is not deprioritized. The Halted Focal Loss reverts the Focal Loss to the Cross-Entropy Loss when the likelihood is high enough: ",
+        "bbox": [
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+    },
+    {
+        "type": "equation",
+        "img_path": "images/f8c5d2e85a0b3af334273456a91f9cdd7c9d4a0a5f8f4ec8b83e8e7cd3b1181a.jpg",
+        "text": "$$\n\\mathcal { L } = \\left\\{ \\begin{array} { l l } { - \\alpha ( 1 - p _ { y } ) ^ { \\gamma _ { f } } \\cdot ( y \\cdot \\log p ) , } & { \\mathrm { i f } \\ p _ { y } \\leq \\varphi } \\\\ { - \\alpha y \\cdot [ \\log p + b ] , } & { \\mathrm { o t h e r w i s e } } \\end{array} \\right.\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/272a974ef7d496f88181e8c74c4b702c525ed37dbfd8442493f5e20269d26187.jpg",
+        "image_caption": [
+            "Figure 2: Regaining focus on the high-likelihood area for the rare classes benefits classification. Left: Illustration of HFL which reverts FL to CE in the high-likelihood area. Right: Applying HFL only to the rare classes improves overall performance. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/7fda920ffbc46747ea8419d691aacf07bee68040fb14f703107bfde96624ecad.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>AP</td><td>AP50</td><td>AP75</td></tr><tr><td>CE</td><td>32.8</td><td>52.3</td><td>34.7</td></tr><tr><td>FL</td><td>33.8</td><td>52.5</td><td>35.9</td></tr><tr><td>HFL</td><td>34.0</td><td>52.7</td><td>36.2</td></tr><tr><td>FL (Head) + HFL (Tail)</td><td>34.2</td><td>52.7</td><td>36.3</td></tr></table>",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Table 1: Results of HFL on the COCO detection dataset, AP denotes average precision. As we can see, increasing the importance of the high-likelihood area achieves better results, and the main improvements come from the tail class examples. ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where $p _ { y }$ is prediction probability of the correct label, $b = \\alpha ( 1 - ( 1 - \\varphi ) ^ { \\gamma _ { f } } ) \\log \\varphi$ to ensure monotonicity and continuity, and $\\varphi$ is the boundary between the low- and the high-likelihood area, which we set as 0.5, i.e., a likelihood higher than which definitely renders a correct prediction. This mixed loss is plotted in left of the Figure 2, which has the same likelihood gradient as the cross-entropy in the high-likelihood area and remains the same as the Focal Loss in the low-likelihood area. ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "To decouple the effect of class frequency, we further explore to gradually transition from the Focal Loss to the Halted Focal Loss according to the class frequency of an example, e.g., from adopting the Halted Focal Loss only for the rarest class and the Focal Loss to other classes to adopting the Focal Loss only for the most common class and the Halted Focal Loss for the rest. Concretely, we set a proportion $t \\in [ 0 , 1 ]$ of classes to receive this loss and the remaining $1 - t$ proportion of classes adopt the original Focal Loss. The classes are ranked by inverse frequencies, such that the first class is the rarest class. ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We conduct experiments on long-tailed CIFAR-10 using the aforementioned protocol to examine the effect of the high-likelihood area. The construction of the dataset is provided in Appendix C. We run each configuration 5 times with different random initialization and report the average test performance. The results are shown in the right of Figure 2. ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "As we can see, compared to the original Focal Loss, the proposed adaptation achieves better performance, indicating regaining focus in the high-likelihood area is beneficial. Nonetheless, the phenomenon can be also attributed to a better learning of the common classes instead of the rare classes. Our analysis based on the class frequency resolves this concern because the Halted Focal Loss brings more improvements if only tailed classes are learned this way, e.g., applying to the top-4 rare classes achieve the best overall performance, which proves that there are rare class examples that reside in the high-likelihood area and have non-negligible effect to generalization. ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The importance of the high-likelihood area of the rare examples is further validated on the COCO detection dataset, where the classifier should determine whether the object appears in the image or not. The positive detection is the rare class since there are many false proposals. The experiment setting is in Appendix C. $A P _ { 5 0 }$ and $A P _ { 7 5 }$ measure the precision under different levels of overlap between predictions and ground-truth. As shown in Table 1, strengthening the high-likelihood area of the Focal Loss, especially for the rare class examples, obtains a more accurate and confident prediction. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "4 EUREKA LOSS ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We have shown that the high-likelihood area matters for long-tailed classification and in particular, the rare class examples in the area have pivotal contributions. Inspired by this finding, we propose to further enhance the importance of the high-likelihood area so that the likelihood gradient in the high-likelihood area can match or even surpass that in the low-likelihood area. Moreover, the adjustment is inline with the frequency of the class so the rarer the class, the larger the likelihood gradient. Extending the adjustment term $b$ in Eq. (6), we propose the Eureka Loss (EL): ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/a2903558b11fe401e2b357241657e05b379ee53b2dac927a774fe8d9332a9677.jpg",
+        "text": "$$\n\\mathcal { L } = - \\pmb { y } \\mathrm { \\cdot } \\log \\pmb { p } - \\mathrm { b o n u s } \\mathrm { \\cdot } \\mathrm { e n c o u r a g e m e n t } ,\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where −bonus·encouragement is intended to reward the well-classified rare examples. The bonus term depends on the example likelihood and the encouragement term depends on the class frequency. Different from the existing approaches that scale the Cross-Entropy Loss, punishing the incorrect predictions selectively, the proposed Eureka Loss deals with long-tailed classification from another perspective, rewarding the correct predictions progressively with their class frequencies. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Bonus indicates how well the system executes the task and is designed to be a function of the probability of the ground-truth class to reward the model when it makes correct prediction. In particular, in light of the findings discussed in Section 3.2, we propose to increase the likelihood gradient in the high-likelihood area and adopt the form of ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "img_path": "images/ba34f6a1fa07659aa2dd260834c793fb1bf46d6926d18dfb7931ba102f44f467.jpg",
+        "text": "$$\n{ \\mathrm { b o n u s } } = { \\pmb y } \\cdot \\mathrm { l o g } ( 1 - { \\pmb p } ) ,\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "which ensures that the monotonicity of the likelihood gradient is consistent with that of the CrossEntropy Loss, meaning that the classifier obtains more bonus when making highly-confident correct predictions. The design is against most existing studies in that the high-likelihood area is given more focus than the low-likelihood area. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Encouragement implies the system realizes unusual achievements that should be encouraged. Since the unusual achievements in long-tailed classification should be correctly predicting rare class examples, we propose to reward the system based on the frequency of the example’s class: ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "img_path": "images/bb373d7f711155c47cca77973226284aacdfea6d1937f758b0d61c5480f4f15c.jpg",
+        "text": "$$\n{ \\mathrm { e n c o u r a g e m e n t } } = w _ { y } = { \\frac { \\bar { m } } { m _ { y } } } ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            400,
+            381,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where $m _ { y }$ denotes the measurement of the frequency of the class $y$ . The form is flexible and similar to the frequency-based methods, and thus can be further extended based on the related studies. In our experiments, we use the effective number from Cui et al. (2019) as the measurement. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Compared to the existing frequency-based and likelihood-based objective, our Eureka Loss takes the bonus term to calibrate the attention to different likelihood landscapes and the encouragement term to inform the model with the class difficulty, composing a more targeted yet comprehensive loss for learning imbalanced distributions. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5 EXPERIMENTS ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We validate the proposed Eureka Loss on diverse long-tailed classification problems and analyze the characteristics of the Eureka Loss with insights into the learned models. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5.1 TASKS, DATASETS, AND TRAINING SETTINGS ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Tasks and Datasets We conduct experiments on two image classification tasks and a dialogue generation task. iNaturalist 2018 is a real-world dataset which embodies a highly imbalanced class distribution of 8,142 classes. Apart from the test performance, we also report the validation performance grouped by the class frequency and categorize the examples into three groups: many (classes with more than 100 examples), medium (classes with 20 to 100 examples), and few (classes with fewer than 20 examples). ImageNet-LT (Liu et al., 2019) is an artificially constructed long-tailed classification dataset based on ILSVRC 2012 of 1000 classes. ConvAI2 is a natural conversation dataset for evaluating dialogue system, where each word type can be treated as a class, i.e., 18,848 words (classes) in total, and have extremely imbalanced training and test datasets. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Evaluation Metric For the image classification tasks, we use the accuracy on ’All’ data and subset of classes with ’Many’, ’Medium’ and ’Few’ examples , i.e., the precision of the top-1 prediction. Since the test set of those tasks are balanced in classes, we further propose to estimate the accuracy on the imbalanced class distribution that reflects natural performance in real-world scenarios. The natural accuracy is the linear interpolation of the accuracy on the balanced test set using the class frequencies from the training set. For the natural language generation task, we adopt the micro and macro F-scores from Zhang et al. (2018) between the generated and the reference sentences to check how well the systems participate in the conversation. We further adopt the 4-gram diversity to examine the rare phrases, since a well-known problem for dialogue tasks is that the model tends to generate common, dull and repetitive responses and thus cannot capture the diversity of natural language distributions. Since the test set of natural language generation task is naturally imbalanced, we do not need to estimate the natural performance. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/1b58e85c1b453f87737e889cd7142fed7390780fc0f0c1756bd6f62f3560126b.jpg",
+        "table_caption": [
+            "Table 2: Results on iNaturalist 2018. ∗ denotes results from the corresponding paper and † denotes deferred learning, where the base loss is applied at the beginning of training and the improved method is adopted later. § denotes that it focuses on transferring representations and the method is less related to our work. Best results are shown in bold. The proposed Eureka Loss achieves the best results in learning both common and rare classes. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>All</td><td>Many</td><td>Medium</td><td>Few</td><td>All (Natural)</td></tr><tr><td>CE</td><td>64.3</td><td>74.1</td><td>65.9</td><td>59.8</td><td>71.7</td></tr><tr><td>CB</td><td>58.3</td><td>61.8</td><td>58.6</td><td>56.9</td><td>59.8</td></tr><tr><td>FL</td><td>62.9</td><td>72.9</td><td>64.1</td><td>58.8</td><td>70.7</td></tr><tr><td>FL +CB</td><td>59.6</td><td>45.5</td><td>61.8</td><td>60.5</td><td>46.7</td></tr><tr><td>Eureka Loss</td><td>68.5</td><td>70.8</td><td>69.3</td><td>66.7</td><td>70.6</td></tr><tr><td>CB†</td><td>68.1</td><td>71.0</td><td>68.3</td><td>67.1</td><td>70.4</td></tr><tr><td>FL + CB†</td><td>66.9</td><td>64.4</td><td>67.4</td><td>67.0</td><td>64.9</td></tr><tr><td>LDAM+CB† (Cao et al., 2019)</td><td>63.3</td><td>65.2</td><td>63.0</td><td>63.1</td><td>64.1</td></tr><tr><td>BBN (Zhou et al., 2019)*†</td><td>69.6</td><td>1</td><td>1</td><td>-</td><td>-</td></tr><tr><td>Decoupling-LWs (Kang et al., 2020)*†</td><td>69.5</td><td>71.0</td><td>68.8</td><td>69.5</td><td>-</td></tr><tr><td>Eureka Loss†</td><td>69.9</td><td>73.3</td><td>69.3</td><td>69.6</td><td>73.0</td></tr><tr><td>FSA (Chu et al., 2020)*$</td><td>65.9</td><td>1</td><td>-</td><td>-</td><td></td></tr><tr><td>MBJ (Liu et al., 2020)* §</td><td>68.6</td><td>68.0</td><td>69.8</td><td>68.5</td><td>-</td></tr><tr><td>Eureka Loss + CB†</td><td>70.3</td><td>69.0</td><td>70.1</td><td>70.9</td><td>69.4</td></tr></table>",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "For the detailed introduction to tasks, datasets, and training settings, please refer to the appendix. ",
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "5.2 RESULTS ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "iNaturalist 2018 The results are reported in Table 2. We tune the hyper-parameters for our implemented baselines and report the averaged performance among 3 runs at the best setting. ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "We compare Eureka Loss with frequency-based method Class-balanced Loss (CB), likelihood-based method Focal Loss (FL) and their combination $\\mathrm { F L + C B }$ . As we can see from the first group in the table, neither FL nor CB achieves improvements over Cross Entropy (CE), but Eureka Loss outperforms CE by a large margin in terms of overall accuracy and accuracy for classes with few examples. ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "In contrary to the first group, considering only the accuracy on the balanced test set, the two-stage version of frequency class-balanced training which adopts the class-balanced training only in the latter training phase includes deferred CB(denotes $\\mathrm { C B ^ { \\dag } }$ in the table), LDAM $^ +$ deferred CB, BBN and Decoupling-LWS enjoy clear advantage over CE. In order to check whether Eureka Loss is additive with the deferred method and the class-balanced training, we take deferred Eureka Loss and Eureka $\\mathbf { L o s s + C B ^ { \\dagger } }$ into comparison. ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "The deferred Eureka Loss is motivated by an intuition that when training enters the bottleneck stage, Eureka Loss is introduced to reward rare classes to encourage the model to learn less common patterns, which may be helpful for learning. Compared with the original method, the deferred encouragement brings improvement on both balanced and imbalanced test distribution $( + 1 . 4$ and $+ 2 . 4$ regarding All and All(Natural), respectively). Moreover, the class-balanced training still impairs the learning for common classes even under the deferred setting, which may cast into unfavorable natural performance in real applications, e.g., the accuracy on the ’Many’ subset for $\\mathrm { C B ^ { \\dag } }$ and DecouplingLWS is under-performs CE by 3.1, the results is that applying $\\mathrm { \\dot { C } B ^ { \\dagger } }$ reduces the Natural accuracy by 1.3. But deferred Eureka Loss largely outperforms CE and these methods on both balanced and imbalanced test distributions. The reason may be that we do not impair the CE learning and the additional rewarding for rare classes is less harmful. Since Eureka Loss only introduces an additive term, it is flexible and can be combined with CB, the adoption results in best All accuracy of 70.3. ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/d45aa662d4712d72985dd3f41578b8e4a2bd3a9681382face1f1cf211e4c3a33.jpg",
+        "table_caption": [
+            "Table 3: Results on ImageNet-LT. ∗ and † are defined similarly to Table 2. Eureka Loss demonstrates consistent improvements against existing methods. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>All</td><td>All (Natural)</td></tr><tr><td>CE</td><td>44.6</td><td>63.7</td></tr><tr><td>FL</td><td>43.6</td><td>62.4</td></tr><tr><td>CB</td><td>43.9</td><td>58.8</td></tr><tr><td>FL+CB</td><td>31.1</td><td>25.0</td></tr><tr><td>Eureka Loss</td><td>48.4</td><td>63.8</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/c880b2a87bcd6562b13a165093a948bb108d08b26a692590b9d8fcd0fb2aaf0b.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method (Deferred)</td><td>All</td><td>All (Natural)</td></tr><tr><td>OLTR (Liu et al., 2019)*</td><td>46.5</td><td>1</td></tr><tr><td>CBt</td><td>49.2</td><td>60.5</td></tr><tr><td>Decoupling-LWs (Kang et al.,2020)*</td><td>49.9</td><td>59.8</td></tr><tr><td>Eureka Loss + CB†</td><td>50.4</td><td>62.2</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/32f660214c7ad25d07c3d5ae87cd4dc650f693ba3dabb563f1766660eeae83d8.jpg",
+        "table_caption": [],
+        "table_footnote": [
+            "Table 4: F-scores and 4-gram diversity on ConvAI2. The proposed Eureka Loss achieves better performance than baseline methods and generates responses that are more diverse. "
+        ],
+        "table_body": "<table><tr><td>Name</td><td>F-Score (Macro)</td><td>F-Score (Micro)</td><td>Diversity (4-gram)</td></tr><tr><td>Cross Entropy</td><td>1.17</td><td>16.9</td><td>36.5</td></tr><tr><td>Focal Loss (γ = 1)</td><td>1.17</td><td>16.8</td><td>36.6</td></tr><tr><td>Focal Loss (γ = 2)</td><td>1.13</td><td>16.7</td><td>37.3</td></tr><tr><td>Eureka Loss</td><td>1.32</td><td>17.2</td><td>40.4</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "In all, adopting the Eureka Loss achieves a balanced performance on both common and rare classes. Besides, we also outperform the latest representation transferring based methods including MBJ and FSA. ",
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+    {
+        "type": "text",
+        "text": "ImageNet-LT Table 3 demonstrates the results on ImageNet-LT of various methods. For this artificial dataset, we first compare with the representative frequency-based method CB and likelihoodbased method Focal Loss (FL). As we can see, the proposed method obtains a significant improvement in the balanced test set and also maintains the lead position in the virtual natural test set. For comparison with methods that defer the class-balanced training including deferred CB and DecoupingLWS, the Eureka Loss of corresponding modification also enjoys a comfortable margin and arguably excels in balancing the performance on both of the common and the rare classes. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "ConvAI2 Table 4 shows that the proposal helps the prediction of rare words $+ 1 0 \\%$ macro F-score) and thus improves the diversity of language generation $( + 1 0 \\%$ 4-gram diversity). Since this dataset is extremely imbalanced, e.g., the imbalance ratio is over 200,000, the frequency-based methods require extensive tuning to work, which we thus omit from the comparison as we are not able to reproduce favorable results. Compared with the likelihood-based method Focal Loss, which is marginally better that the original cross-entropy loss, the Eureka Loss still obtains substantial improvements. ",
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+    {
+        "type": "text",
+        "text": "5.3 ANALYSIS ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Effect on Distributions of Different Imbalance Degrees To analyze the effect on imbalanced distributions of different degrees, we construct several artificial datasets based on CIFAR-100 and control the size of the rarest class. The imbalance degree stands for the ratio of the class size of the most common class to that of the rarest class. Hence, the larger the degree, the more imbalanced the dataset. For example, if imbalance degree is 100 for CIFAR-100, the most common class has 500 examples and the rarest class has 5 examples. As shown in Table 5, the Eureka Loss is consistently better than existing methods, especially for datasets that are more imbalanced. For results on CIFAR-10, please refer to the appendix. ",
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+    {
+        "type": "table",
+        "img_path": "images/97baf5a47a6cf2838bc6648bbb2bcfb21f0c886170251ff52ef795866c21ab57.jpg",
+        "table_caption": [
+            "Table 5: Results on long-tailed CIFAR100 of different imbalance degrees (ID). † denotes deferred learning; ♣ and $\\spadesuit$ denotes results taken from Zhou et al. (2019) and Cao et al. (2019), respectively. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>ID-100 ID-50 ID-10</td></tr><tr><td>CE+RSt+</td><td>41.61 46.48 58.11</td></tr><tr><td>CE+CB++</td><td>41.51 45.29 58.12</td></tr><tr><td>LDAM+CB† +</td><td>42.04 46.62 58.71</td></tr><tr><td>BBNt+</td><td>42.56 47.02 59.12</td></tr><tr><td>EL + CB+</td><td>43.19 48.48 59.31</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Varying Strength of Bonus To illustrate the importance of the high-likelihood area in imbalanced classification within Eureka Loss, we compare a ",
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+    {
+        "type": "table",
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+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>All Many</td><td>Medium</td><td>Few</td></tr><tr><td>EL (β=0.99)</td><td>45.8 67.2</td><td>38.4</td><td>11.3</td></tr><tr><td>EL (β=0.999)</td><td>47.8 66.1</td><td>42.0</td><td>16.4</td></tr><tr><td>EL (β=0.9999)</td><td>50.0 67.1</td><td>44.7</td><td>19.8</td></tr></table>",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "image",
+        "img_path": "images/c254aa492ed8850f2cffddcc0f6a8a4f01007d65394d8f7689e35e27e769de33.jpg",
+        "image_caption": [
+            "Figure 3: Varying strength of bonus on long-tailed CIFAR-10. Higher power $\\gamma _ { b }$ indicates higher strength. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Table 6: Varying strength of encouragement on the dev set of ImageNet-LT. Higher $\\beta$ means higher strength. ",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "exponential form bonus called Power Bonus (PB) to the original bonus, which takes the power form of the probability vector of by a factor $\\gamma _ { b }$ : ",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "equation",
+        "img_path": "images/c0580e2f94f8e959e0556e1525feeb88f7612e50ace567b789cd3abcf5ad1e51.jpg",
+        "text": "$$\nP B ( \\pmb { p } ) = - \\pmb { y } \\cdot \\pmb { p } ^ { \\gamma _ { b } } ,\n$$",
+        "text_format": "latex",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "where $\\gamma _ { b }$ is a positive value to ensure the monotonicity and can be tuned for different tasks. Besides, CE achieves a $7 1 . 4 \\%$ accuracy and the likelihood bonus with deferred encouragement gets a $7 6 . 1 \\%$ accuracy. Figure 3 demonstrates that bigger likelihood gradient in the high-likelihood area brings more improvements, e.g., power-bonus with power of 4 is better than bonuses of small power. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Varying Strength of Encouragement The strength of encouragement is determined by both of the class frequency and the hyper-parameter $\\beta$ as we use the effective number of the class. As $\\beta$ controls the variance of the the effective number, e.g., when $\\beta = 0$ , the variance is 0, meaning all of the classes receive equal encouragement, we control the strength of the encouragement towards tail classes by altering $\\beta$ . The results on the validation set of ImageNet-LT are shown in Table 6. As we can see, higher $\\beta$ (more encouragement for tail classes), is connected to higher overall accuracy and better tail class performance, which again validates our motivation for encouraging correct rare class predictions. ",
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+    },
+    {
+        "type": "text",
+        "text": "Effect on Example-Likelihood The Eureka Loss rewards the high-likelihood predictions especially for tail classes. It is interesting to see how the training dynamic is changed due to this preference. In order to understand the effect, we visualize the example likelihood grouped by target class frequencies after training in Figure 4 and Figure 5 (due to space limit, the complete comparison is provided in the Appendix A), which are from the validation set from iNaturalist 2018. As we can see, with the Eureka Loss, the examples in the high-likelihood area are driven to the extreme. For example, considering the medium and the low frequency group, the “hard” examples that may be inherently difficult to classify stand invariant, while for the examples that can be classified correctly, the system now treats them with more confidence. This dynamics translate into better accuracy in unseen examples in the test set, hinting the importance of rare class examples in the high-likelihood area for the generalization of learning imbalanced class distributions. ",
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+    },
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+        "type": "image",
+        "img_path": "images/10339a658a49a0924ac45107f28f41ecfa87419a92e24bf15789f9a88b3a945e.jpg",
+        "image_caption": [
+            "Figure 4: The visualization of test likelihood distribution for models trained with the Eureka Loss. The model classifies the rare class examples more decisively, compared to the existing methods. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "6 CONCLUSIONS ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "In this paper, we examine the effect of the high-likelihood area on learning imbalanced class distributions. We find that the existing practice of relatively diminishing the contribution of the examples in the high-likelihood area is actually harmful to the learning. We further show that the rare class examples in the high-likelihood area have pivotal contribution to model performance and should be focused on instead of being neglected. Motivated by this, we propose the Eureka Loss, which additionally rewards the well-classified rare class examples. The results of the Eureka Loss in the image classification and natural language generation problems demonstrate the potential of reconsidering the role of the high-likelihood area. In-depth analysis also verifies the effectiveness of the investigated loss form and reveals the learning dynamics of different approaches to long-tailed classification. ",
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+    {
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+    {
+        "type": "text",
+        "text": "A VISUALIZATION OF EXAMPLE LIKELIHOOD ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            352,
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+    {
+        "type": "text",
+        "text": "The complete comparison between the likelihood distribution for Eureka Loss, Cross-Entropy Loss, Focal Loss, Class-balanced Loss are shown in Figure 5. We see from the figure that the model trained with Eureka Loss gives high-confidence predictions for gold labels. Compared with the Cross-Entropy Loss, the Focal Loss diminish the contribution of high-likelihood examples, and the resulted model is unsure in the prediction of unseen examples. In particular, for the examples in the Few group, it almost produces no confident correct predictions. The Class-Balanced Loss, on the other hand, improves the confidence for the tail class examples but degrade the performance for the head class examples, which may imply potential issues regrading to natural performance in real-world applications. Besides, it is worth noting that the Decoupling-LWS obtains a likelihood distribution similar to the Class-Balanced Loss. ",
+        "bbox": [
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+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "B FURTHER RESULTS AND ANALYSIS ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "B.1 RESULTS ON INATURALIST 2018 WITH TRAINING FOR 90 EPOCHS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            574,
+            676,
+            588
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "It is found by existing work (Kang et al., 2020) that training much longer for the iNaturalist 2018 dataset can produce better scores and reflect the performance of the models more authentically. However, most previous studies conduct training for a shorter time. To keep consistent with previous research in this field, we also train the models using Eureka Loss for 90 epochs and the results are shown in Table 7. In this setting, eureka loss achieves better accuracy than the two-stage decoupling methods (Decoupling-LWS and BBN), the advantage is more profound under the Natural accuracy, for example, compared to the Decoupling-LWS, the deferred Eureka Loss gains 3.8 Natural accuracy. Compared to the one-state methods including Class-Balanced Loss (CB), Focal Loss (FL), ClassBalanced Focal Loss $\\scriptstyle \\left( \\mathrm { F L + C B } \\right)$ , LDAM, the model trained with the Eureka Loss is much more accurate on the test distribution. ",
+        "bbox": [
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+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "B.2 RESULTS ON LONG-TAILED CIFAR-10",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "In the main text, we have reported the results of the Eureka Loss varying the class imbalance on the CIFAR-100 dataset. Here we also perform comprehensive experiments on long-tailed CIFAR-10 and report top-1 precision on the balanced test set. The results are shown in the Table 8. When combined with Class-Balanced Loss, Eureka Loss brings higher improvement in terms of accuracy than Cross-Entropy Loss and LDAM. ",
+        "bbox": [
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+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "B.3 HYPER-PARAMETER OF THE FOCAL LOSS ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In the paper, we report results for the Focal Loss with best hyper-parameters. For COCO detection, the hyper-parameter of $\\alpha = 0 . 2 5 , \\gamma = 2$ is the best setting reported in Table 1.b of the origin paper (Lin et al., 2017). For the other multi-class classification tasks, we tune hyper-parameters of the Focal Loss on it. The accuracy for the Focal Loss with different hyper-parameter $\\gamma$ are listed in the Table1. we set $\\gamma = 1$ for Focal Loss since it is consistently optimal in long-tailed image classification. For ConvAI2, $\\gamma = 0 . 5$ under-performs Cross Entropy, and neither $\\gamma = 1$ nor $\\gamma = 2$ outperforms each other, so we report the Focal Loss of $\\gamma = 1$ and the Focal Loss of $\\gamma = 2$ in the Table 4. ",
+        "bbox": [
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+        "page_idx": 10
+    },
+    {
+        "type": "image",
+        "img_path": "images/ddebb6e382209f81701a3a28cdcff5f46ad0bee0b5b9d65fc3eb50cfb21766b0.jpg",
+        "image_caption": [
+            "Figure 5: Example likelihood on the validation set of iNaturalist18 categorized by class frequencies into few, medium, many, and all. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            178,
+            97,
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+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "B.4 COMPLEMENTARY EXPERIMENT TO THE MOTIVATION EXPERIMENT ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            727,
+            686,
+            741
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+    },
+    {
+        "type": "text",
+        "text": "In Section 3, we propose Halted Focal Loss(HFL) and compare it to Focal Loss(FL) to illustrate the potential of the high-likelihood area. However, its loss is no steeper than Cross Entropy (CE). Moreover, Focal Loss does not beat CE in the setting of multi-class classification. In order to bridge the gap between the possibly weak motivation experiment of Halted Focal Loss and the proposed method Eureka Loss. We propose simplified Eureka Loss: ",
+        "bbox": [
+            173,
+            753,
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+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "equation",
+        "img_path": "images/227fc9a287f5e1eda38168112ec867444e874973f478b5bea85208831d0a5625.jpg",
+        "text": "$$\n\\mathcal { L } = \\left\\{ \\begin{array} { l l } { - y \\cdot \\log p , } & { \\mathrm { i f ~ } p _ { y } \\leq \\varphi } \\\\ { - y \\cdot \\log p + y \\cdot [ \\log ( 1 - p ) - b ] , } & { \\mathrm { o t h e r w i s e } } \\end{array} \\right.\n$$",
+        "text_format": "latex",
+        "bbox": [
+            320,
+            833,
+            671,
+            869
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "table",
+        "img_path": "images/1b862724a1351b53818185d4f52db5796e72b3c622f507dca402c28189dfc6a7.jpg",
+        "table_caption": [
+            "Table 7: Results on iNaturalist 2018 after training the model for 90 epochs. ∗ denotes results from the corresponding paper and † denotes that we use the base loss at the beginning of training and then adopt the method later. The proposed Eureka Loss achieves good results in learning both common and rare classes. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>All</td><td>Many</td><td>Medium</td><td>Few</td><td>All (Natural)</td></tr><tr><td>CE</td><td>61.8</td><td>72.2</td><td>63.4</td><td>57.2</td><td>69.8</td></tr><tr><td>FL</td><td>60.2</td><td>70.4</td><td>61.5</td><td>56.0</td><td>68.3</td></tr><tr><td>CB</td><td>52.4</td><td>51.9</td><td>53.0</td><td>51.8</td><td>51.2</td></tr><tr><td>RS</td><td>56.7</td><td>59.0</td><td>56.9</td><td>55.9</td><td>56.5</td></tr><tr><td>FL+CB (Cui et al., 2019)*</td><td>61.1</td><td></td><td>-</td><td>-</td><td>-</td></tr><tr><td>CE+CB† (Cao et al., 2019)*</td><td>63.7</td><td>=</td><td>=</td><td></td><td>1</td></tr><tr><td>LDAM (Cao et al., 2019)*</td><td>64.6</td><td></td><td></td><td></td><td></td></tr><tr><td>LDAM+CB† (Cao et al.,2019)*</td><td>68.0</td><td></td><td></td><td></td><td></td></tr><tr><td>LDAM+CB† (Zhou et al., 2019)*</td><td>64.6</td><td>-</td><td>=</td><td>=</td><td></td></tr><tr><td>BBN (Zhou et al.,2019)*</td><td>66.3</td><td>=</td><td>=</td><td>-</td><td>=</td></tr><tr><td>Decoupling-LWs (Kang et al., 2020)*</td><td>65.9</td><td>65.0</td><td>66.3</td><td>65.5</td><td>65.7</td></tr><tr><td>Eureka Loss</td><td>66.4</td><td>67.5</td><td>66.5</td><td>65.9</td><td>67.9</td></tr><tr><td>Eureka Loss†</td><td>67.1</td><td>69.4</td><td>67.3</td><td>66.1</td><td>69.5</td></tr></table>",
+        "bbox": [
+            230,
+            101,
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+            304
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "table",
+        "img_path": "images/5cb06c2121d1c46113fbd532d4eae33bc4a4a3ff286676c34cc07525332f354b.jpg",
+        "table_caption": [
+            "Table 8: Results on long-tailed CIFAR-10 data with different imbalance degrees. ID is short for imbalance degree. † is defined similarly; $\\clubsuit$ denotes Zhou et al. (2019); $\\spadesuit$ denotes Cao et al. (2019). "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>ID-100</td><td>ID-50</td><td>ID-10</td></tr><tr><td>CE+RSt+</td><td>75.61</td><td>79.81</td><td>87.38</td></tr><tr><td>CE+CB++</td><td>76.34</td><td>79.97</td><td>87.56</td></tr><tr><td>LDAM+CB†+</td><td>77.03</td><td>81.03</td><td>88.16</td></tr><tr><td>BBNt</td><td>79.82</td><td>82.18</td><td>88.32</td></tr><tr><td>EL + CB†</td><td>77.95</td><td>82.00</td><td>88.35</td></tr></table>",
+        "bbox": [
+            367,
+            410,
+            630,
+            515
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "where $\\varphi$ is set to 0.5, and $b$ is $l o g ( 1 - \\varphi )$ . In the simplified Eureka Loss, the encouragement is removed, and to keep the low-likelihood area unchanged, the new bonus term starts rewarding the model from $p = \\varphi$ . As is shown in Table $\\lvert 0 , \\mathrm { H F L } ( { \\mathsf { t } } { = } 0 . 5 )$ is also better than HFL and FL in terms accuracy of tail classes on the large scale long-tailed classification dataset iNaturalist 2018, This result once again shows that high-likelihood area matters and near-correct predictions of rare classes play a major role. But HFL is the combination of Focal Loss(in the low likelihood area) and Cross Entropy(in the high-likelihood area) and the performance is constrained. Unlike HFL, the loss of Simplified Eureka Loss is built on CE and the loss is much steeper than Cross Entropy in the high-likelihood area, it outperforms Cross Entropy(CE) and HFL in terms of all metrics, especially on the subset of tail classes. Eureka Loss reported in Table 2 is a continuous version of simplified Eureka Loss with an additional encouragement for rare classes, similar to $\\mathrm { H F L } ( \\mathrm { t } { = } 0 . 5 )$ , this setting which rewards more for rare classes achieves the best overall performance. ",
+        "bbox": [
+            174,
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+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "B.5 EUREKA LOSS MITIGATES OVER-FITTING ON TAIL CLASSES ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            815,
+            637,
+            832
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "As shown in Figure 6, compared to Cross-Entropy Loss, Eureka Loss reduce the gap between the training accuracy and test accuracy from 33.0 to 28.6 on tail classes. Moreover, even though Classbalanced Loss achieves the highest training accuracy, its test accuracy is unexpectedly low. The difference of performance between the seen examples and the unseen examples indicates the degree of over-fitting. The results are from the “Few” subset of the iNaturalist 2018 of training 90 epochs. ",
+        "bbox": [
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+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "table",
+        "img_path": "images/03ece730eef5feb9b8dbfb55c1bbe5689e720b027f75544f852b23e525f594a7.jpg",
+        "table_caption": [
+            "Table 9: Mean/(standard deviation) test accuracy of the Focal Loss with different hyper-parameter $\\gamma$ in long-tailed image classification. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Y</td><td>CIFAR10</td><td>Imagenet-LT</td><td>iNaturalist20182</td></tr><tr><td>0.5</td><td>21.2/10.8</td><td>8.3/7.1</td><td>9.2/3.2</td></tr><tr><td>1</td><td>70.8/0.6</td><td>43.8/0.3</td><td>60.2/0.3</td></tr><tr><td>2</td><td>70.3/0.6</td><td>43.6/7.9</td><td>59.5/0.2</td></tr></table>",
+        "bbox": [
+            341,
+            101,
+            653,
+            169
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "table",
+        "img_path": "images/b3239d0f44064e3f1b8190689f36fef09633f4df0b4f663268326b386b2a54b0.jpg",
+        "table_caption": [
+            "Table 10: Comparison between the Halted Focal Loss and the Simplified Eureka Loss on long-tailed Cifar-10 (imbalance ratio is 100) and iNaturalist 2018, the mean standard deviation (Stdev) for results on iNaturalList2018 is about 0.4. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">method Mean/Stdev</td><td rowspan=\"2\">CIFAR10</td><td colspan=\"5\">iNaturalList2018</td></tr><tr><td>All</td><td>Many</td><td> Medium</td><td>Few</td><td> All(natural)</td></tr><tr><td>CE</td><td>71.4/0.5</td><td>64.3</td><td>74.1</td><td>65.9</td><td>59.8</td><td>71.7</td></tr><tr><td>FL</td><td>71.3/0.6</td><td>62.9</td><td>72.9</td><td>64.1</td><td>58.8</td><td>70.7</td></tr><tr><td>HFL</td><td>71.4/0.3</td><td>63.6</td><td>73.1</td><td>64.6</td><td>59.7</td><td>70.7</td></tr><tr><td>HFL(t=0.5)</td><td>71.8/0.5</td><td>64.2</td><td>73.3</td><td>64.3</td><td>61.6</td><td>70.8</td></tr><tr><td>Simplified EL</td><td>71.8/0.9(+0.4)</td><td>66.3(+2.0)</td><td>75.1 (+1.0)</td><td>67.4(+1.6)</td><td>62.6(+2.8)</td><td>72.6(+1.1)</td></tr></table>",
+        "bbox": [
+            173,
+            220,
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+            361
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "C DETAILS OF EXPERIMENTAL SETTINGS ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            439,
+            535,
+            455
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "C.1 DATASETS ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            470,
+            290,
+            486
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "There are six datasets used in this paper in total and an overview of the dataset statistics are demontrated in Table 11 and Figure 7. For image classification tasks, the iNaturalist 2018 dataset is the most imbalanced and has the most classes, which is most satisfactory for evaluating long-tailed classifications. For the language generation task, ConvAI2 has an imbalance ratio of 277K, which, however, should be taken cautiously, since most of the tail classes are not covered in evaluation. The common practice to evaluate the learning on the imbalanced language distributions is to investigate the diversity of the generated text. The 4-grams can be regarded as high-ordered classes and a 4-gram of four common words can also be a “rare class”. ",
+        "bbox": [
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+            496,
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+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "C.2 TRAINING SETTINGS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            625,
+            362,
+            640
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "CIFAR-10 and CIFAR-100 For experiments on long-tailed CIFAR-10 and CIFAR-100, the backbone network is ResNet-32 (He et al., 2016). The model is optimized with SGD with a momentum of 0.9. The learning rate is set to 0.1 and the model is trained for 200 epochs with 128 examples per mini-batch. To stabilize the training, we adopt the warm-up strategy used by Goyal et al. (2017) in the first 5 epochs. Following Cao et al. (2019), we decay the learning rate by 0.01 at the 160th epoch and again at the 180th epoch. For the results in Figure 2 and Figure 3, we conduct experiments on long-tailed CIFAR-10 with an imbalance ratio of 10. ",
+        "bbox": [
+            173,
+            650,
+            825,
+            750
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "ImageNet-LT For experiments on ImageNet-LT ILSVRC 2012, the base network is ResNext50 (He et al., 2016). The batch size is set to 512 to accelerate training. The initial learning rate is 0.2 and we utilize a cosine learning rate scheduler. ",
+        "bbox": [
+            174,
+            756,
+            825,
+            797
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "iNaturalist 2018 Same as the experiments on ImageNet-LT, we also follow the default setting in Kang et al. (2020) for experiments on iNaturalist. To be specific, we adopt ResNet-50 model, use SGD with to train the model for 200 epochs with batch size 512 and a cosine learning rate schedule which gradually decays from 0.2 to 0.0. Results on the valid set are also reported on subset of many $( > 1 0 0$ samples), medium $( 2 0 - 1 0 0$ samples), and few $< 2 0$ samples), respectively. ",
+        "bbox": [
+            174,
+            804,
+            825,
+            875
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "ConvAI2 For the conversation generation task, we utilize a two-layer LSTM (Hochreiter & Schmidhuber, 1997) encoder-encoder architecture as our base network. The hidden size of both encoder and decoder is set to 1024. We optimize the model with SGD optimizer with momentum 0.9, the batch size is 64 and the learning rate is set to 3. The embedding size is 256 and word vectors are initialized with GloVe (Pennington et al., 2014). We select our final model until the performance on the validation is no longer improving after 5 epochs. ",
+        "bbox": [
+            176,
+            882,
+            823,
+            924
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "image",
+        "img_path": "images/da48883d1b3e68f8fde8391d7c425565e69d162597da6b41e44bcbf648f733a1.jpg",
+        "image_caption": [
+            "Figure 6: Illustration of the over-fitting phenomenon on tail classes, the number on the top of each bar is the difference between the training accuracy and the test accuracy. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            348,
+            114,
+            642,
+            286
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "table",
+        "img_path": "images/ee34b59cd30d4f57c6ceda7f9a1a8d5f13bcd857a0568a13edf6962d9ea09583.jpg",
+        "table_caption": [
+            "Table 11: Data statistics of long-tailed image classification tasks. Imbalance Ratio denotes the ratio of the size of the most common class to that of the rarest class. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Dataset</td><td># Classes</td><td>Imbalance Ratio</td></tr><tr><td>COCO Detection</td><td>2</td><td>~1000</td></tr><tr><td>Long-tailed CIFAR-10</td><td>10</td><td>10-100</td></tr><tr><td>Long-tailed CIFAR-100</td><td>100</td><td>10-100</td></tr><tr><td>ImageNet-LT</td><td>1000</td><td>256</td></tr><tr><td>iNaturalist 2018</td><td>8142</td><td>500</td></tr></table>",
+        "bbox": [
+            196,
+            368,
+            516,
+            460
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "image",
+        "img_path": "images/76a5227aa259e581dbcd6a56fea4a8c78d8433381a26caf960824d7ddb935f1d.jpg",
+        "image_caption": [
+            "Figure 7: Word frequency distribution of ConvAI2 dataset. For natural language generation tasks, each word type can be regarded as a class and most words appear scarcely in the data. If measured the same with long-tailed image classification tasks, the imbalance ratio is 277K. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            573,
+            345,
+            790,
+            430
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            176,
+            564,
+            821,
+            607
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "COCO Dectection For experiments on COCO detection, we adopt the configuration of “RetinaNetR-50-FPN-1x” from the GitHub repository Detectron2 as our default setting. In this setting, the one-stage detector of RetinaNet with the backbone ResNet50 is trained for $9 0 \\mathrm { k }$ updates and the batch size is 8 images per batch. ",
+        "bbox": [
+            174,
+            613,
+            825,
+            670
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "For the image classification tasks, the default $\\beta$ is set to 0.9999 for all datasets. For the deferred version, we defer the adoption of Eureka Loss after training for 160 epochs and 180epochs on CIFAR100 and iNaturalist 2018 respectively. As for the dialog generation task ConvAI2, $\\beta$ is set to 0.999 and we start the encouragement after regularly training the model for 5 epochs. ",
+        "bbox": [
+            173,
+            676,
+            825,
+            733
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "We tune the $\\beta \\in \\{ 0 . 9 , 0 . 9 9 , 0 . 9 9 9 , 0 . 9 9 9 9 \\}$ and $\\gamma \\in \\{ 0 . 5 , 1 , 2 \\}$ for the Class-Balanced Loss (CB) and the Focal Loss (FL) respectively in multi-class classification, and report the best results of these baselines. Following previous work (Cui et al., 2019), $\\alpha$ is set to 1.0 for the Focal Loss(FL), and the Class-Balanced Focal Loss $\\mathrm { ( F L + C B ) }$ ) in multi-class classification tasks can be viewed as the origin Focal Loss with class-level weight $\\alpha$ in binary classification tasks. ",
+        "bbox": [
+            174,
+            738,
+            825,
+            809
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "The training costs are summarized in Table 12. ",
+        "bbox": [
+            174,
+            816,
+            480,
+            830
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "table",
+        "img_path": "images/cd0e70e58a94f4fcbf8c3fcf6c53a6795fa4f76eaf2bcc99f9da9c7d998655ff.jpg",
+        "table_caption": [],
+        "table_footnote": [
+            "Table 12: Training costs of each task. Samples are dialogues in ConvAI2 and images in image classification tasks "
+        ],
+        "table_body": "<table><tr><td>Data</td><td>Infrastructure</td><td>Mem/GPU</td><td>Time</td><td>Epochs</td><td>Samples</td><td>Model</td></tr><tr><td>Long-tailed CIFAR-10</td><td>RTX 2080Ti *1</td><td>1.4G</td><td>0.3h</td><td>200</td><td>12.4K</td><td>ResNet32</td></tr><tr><td>Long-tailed CIFAR-100</td><td>RTX 2080Ti *1</td><td>1.4G</td><td>0.3h</td><td>200</td><td>10.8K</td><td>ResNet32</td></tr><tr><td>ImageNet-LT</td><td>TITAN RTX *4</td><td>17G</td><td>8h</td><td>90</td><td>116K</td><td>ResNext50</td></tr><tr><td>iNaturalist 2018</td><td>RTX TITAN *4</td><td>15G</td><td>48h</td><td>200</td><td>438K</td><td>ResNet50</td></tr><tr><td>ConvAI2</td><td>RTX 2080Ti *1</td><td>9G</td><td>4h</td><td>16</td><td>131K</td><td>2-L LSTM</td></tr><tr><td>COCO Detection</td><td>RTX 2080Ti * 4</td><td>9G</td><td>8h</td><td>90K updates</td><td>118K</td><td>ResNet50</td></tr></table>",
+        "bbox": [
+            178,
+            439,
+            821,
+            544
+        ],
+        "page_idx": 15
+    }
+]

parse/train/B1G9tvcgx/B1G9tvcgx.md

@@ -0,0 +1,404 @@
+# NEURAL MACHINE TRANSLATION WITH LATENT SEMANTIC OF IMAGE AND TEXT
+
+Joji Toyama∗, Masanori Misono∗†, Masahiro Suzuki, Kotaro Nakayama & Yutaka Matsuo   
+Graduate School of Engineering, †Graduate School of Information Science and Technology   
+The University of Tokyo   
+Hongo, Tokyo, Japan   
+{toyama,misono,masa,k-nakayama,matsuo}@weblab.t.u-tokyo.ac.jp
+
+# ABSTRACT
+
+Although attention-based Neural Machine Translation have achieved great success, attention-mechanism cannot capture the entire meaning of the source sentence because the attention mechanism generates a target word depending heavily on the relevant parts of the source sentence. The report of earlier studies has introduced a latent variable to capture the entire meaning of sentence and achieved improvement on attention-based Neural Machine Translation. We follow this approach and we believe that the capturing meaning of sentence benefits from image information because human beings understand the meaning of language not only from textual information but also from perceptual information such as that gained from vision. As described herein, we propose a neural machine translation model that introduces a continuous latent variable containing an underlying semantic extracted from texts and images. Our model, which can be trained endto-end, requires image information only when training. Experiments conducted with an English–German translation task show that our model outperforms over the baseline.
+
+# 1 INTRODUCTION
+
+Neural machine translation (NMT) has achieved great success in recent years (Sutskever et al., 2014; Bahdanau et al., 2015). In contrast to statistical machine translation, which requires huge phrase and rule tables, NMT requires much less memory. However, the most standard model, NMT with attention (Bahdanau et al., 2015) entails the shortcoming that the attention mechanism cannot capture the entire meaning of a sentence because it generates a target word while depending heavily on the relevant parts of the source sentence (Tu et al., 2016). To overcome this problem, Variational Neural Machine Translation (VNMT), which outperforms NMT with attention introduces a latent variable to capture the underlying semantic from source and target (Zhang et al., 2016). We follow the motivation of VNMT, which is to capture underlying semantic of a source.
+
+Image information is related to language. For example, we human beings understand the meaning of language by linking perceptual information given by the surrounding environment and language (Barsalou, 1999). Although it is natural and easy for humans, it is difficult for computers to understand different domain’s information integrally. Solving this difficult task might, however, bring great improvements in natural language processing. Several researchers have attempted to link language and images such as image captioning by Xu et al. (2015) or image generation from sentences by Reed et al. (2016). They described the possibility of integral understanding of images and text. In machine translation, we can expect an improvement using not only text information but also image information because image information can bridge two languages.
+
+As described herein, we propose the neural machine translation model which introduces a latent variable containing an underlying semantic extracted from texts and images. Our model includes an explicit latent variable z, which has underlying semantics extracted from text and images by introducing a Variational Autoencoder (VAE) (Kingma et al., 2014; Rezende et al., 2014). Our model, which can be trained end-to-end, requires image information only when training. As described herein, we tackle the task with which one uses a parallel corpus and images in training, while using a source corpus in translating. It is important to define the task in this manner because we rarely have a corresponding image when we want to translate a sentence. During translation, our model generates a semantic variable z from a source, integrates variable z into a decoder of neural machine translation system, and then finally generates the translation. The difference between our model and VNMT is that we use image information in addition to text information.
+
+![](images/7d59f4e9d8e0d16dcda6d9fe5f00e4043acaa4825994a380abfab9cb596829ee.jpg)  
+Figure 1: Architecture of Proposed Model. Green dotted lines denote that $\pi$ and encoded y are used only when training.
+
+For experiments, we used Multi30k (Elliott et al., 2016), which includes images and the corresponding parallel corpora of English and German. Our model outperforms the baseline with two evaluation metrics: METEOR (Denkowski & Lavie, 2014) and BLEU (Papineni et al., 2002). Moreover, we obtain some knowledge related to our model and Multi30k. Finally, we present some examples in which our model either improved, or worsened, the result.
+
+Our paper contributes to the neural machine translation research community in three ways.
+
+• We present the first neural machine translation model to introduce a latent variable inferred from image and text information. We also present the first translation task with which one uses a parallel corpus and images in training, while using a source corpus in translating.   
+• Our translation model can generate more accurate translation by training with images, especially for short sentences.   
+• We present how the translation of source is changed by adding image information compared to VNMT which does not use image information.
+
+# 2 BACKGROUND
+
+Our model is the extension of Variational Neural Machine Translation (VNMT) (Zhang et al., 2016). Our model is also viewed as one of the multimodal translation models. In our model, VAE is used to introduce a latent variable. We describe the background of our model in this section.
+
+# 2.1 VARIATIONAL NEURAL MACHINE TRANSLATION
+
+The VNMT translation model introduces a latent variable. This model’s architecture shown in Figure 1 excludes the arrow from $\pi$ . This model involves three parts: encoder, inferrer, and decoder. In the encoder, both the source and target are encoded by bidirectional-Recurrent Neural Networks (bidirectional-RNN) and a semantic representation is generated. In the inferrer, a latent variable $\mathbf { z }$ is modeled from a semantic representation by introducing VAE. In the decoder, a latent variable $\mathbf { z }$ is integrated in the Gated Recurrent Unit (GRU) decoder; also, a translation is generated.
+
+Our model is followed by architecture, except that the image is also encoded to obtain a latent variable z.
+
+# 2.2 MULTIMODAL TRANSLATION
+
+Multimodal Translation is the task with which one might one can use a parallel corpus and images. The first papers to study multimodal translation are Elliott et al. (2015) and Hitschler & Riezler (2016). It was selected as a shared task in Workshop of Machine Translation 2016 (WMT161). Although several studies have been conducted (Caglayan et al., 2016; Huang et al., 2016; Calixto et al., 2016; Libovicky et al. ´ , 2016; Rodr´ıguez Guasch & Costa-jussa\`, 2016; Shah et al., 2016), they do not show great improvement, especially in neural machine translation (Specia et al., 2016). Here, we introduce end-to-end neural network translation models like our model.
+
+Caglayan et al. (2016) integrate an image into an NMT decoder. They simply put source context vectors and image feature vectors extracted from ResNet-50’s ‘res4f relu’ layer (He et al., 2016) into the decoder called multimodal conditional GRU. They demonstrate that their method does not surpass the text-only baseline: NMT with attention.
+
+Huang et al. (2016) integrate an image into a head of source words sequence. They extract prominent objects from the image by Region-based Convolutional Neural Networks (R-CNN) (Girshick, 2015). Objects are then converted to feature vectors by VGG-19 (Simonyan & Zisserman, 2014) and are put into a head of source words sequence. They demonstrate that object extraction by R-CNN contributes greatly to the improvement. This model achieved the highest METEOR score in NMTbased models in WMT16, which we compare to our model in the experiment. We designate this model as CMU.
+
+Caglayan et al. (2016) argue that their proposed model did not achieve improvement because they failed to benefit from both text and images. We assume that they failed to integrate text and images because they simply put images and text into neural machine translation despite huge gap exists between image information and text information. Our model, however, presents the possibility of benefitting from images and text because text and images are projected to their common semantic space so that the gap of images and text would be filled.
+
+# 2.3 VARIATIONAL AUTO ENCODER
+
+VAE was proposed in an earlier report of the literature Kingma et al. (2014); Rezende et al. (2014). Given an observed variable $\mathbf { x }$ , VAE introduces a continuous latent variable $\mathbf { z }$ , with the assumption that $\mathbf { x }$ is generated from $\mathbf { z }$ . VAE incorporates $p _ { \boldsymbol { \theta } } ( \mathbf { x } | \mathbf { z } )$ and $q _ { \phi } ( { \bf z } | { \bf x } )$ into an end-to-end neural network. The lower bound is shown below.
+
+$$
+\mathcal { L } _ { \mathrm { V A E } } = - \mathrm { D } _ { \mathrm { K L } } \left[ q _ { \phi } ( \mathbf { z } | \mathbf { x } ) | | p _ { \theta } ( \mathbf { z } ) \right] + \mathbb { E } _ { q _ { \phi } ( \mathbf { z } | \mathbf { x } ) } \left[ \log p _ { \theta } ( \mathbf { x } | \mathbf { z } ) \right] \leq \log p _ { \theta } ( \mathbf { x } )
+$$
+
+# 3 NEURAL MACHINE TRANSLATION WITH LATENT SEMANTIC OF IMAGE AND TEXT
+
+We propose a neural machine translation model which explicitly has a latent variable containing an underlying semantic extracted from both text and image. This model can be seen as an extension of VNMT by adding image information.
+
+Our model can be drawn as a graphical model in Figure 3. Its lower bound is
+
+$$
+\mathcal { L } = - \mathrm { D } _ { \mathrm { K L } } \left[ q _ { \phi } ( \mathbf { z } | \mathbf { x } , \mathbf { y } , \pi ) | | p _ { \theta } ( \mathbf { z } | \mathbf { x } ) \right] + \mathbb { E } _ { q _ { \phi } ( \mathbf { z } | \mathbf { x } , \mathbf { y } , \pi ) } \left[ \log p _ { \theta } ( \mathbf { y } | \mathbf { z } , \mathbf { x } ) \right] ,
+$$
+
+where ${ \mathbf { x } } , { \mathbf { y } } , \pi , { \mathbf { z } }$ respectively denote the source, target, image and latent variable, and $p _ { \theta }$ and $q _ { \phi }$ respectively denote the prior distribution and the approximate posterior distribution. It is noteworthy in Eq. (2) that we want to model $p ( \mathbf { z } | \mathbf { x } , \mathbf { y } , \pi )$ , which is intractable. Therefore we model $q _ { \phi } ( \mathbf { z } | \mathbf { x } , \mathbf { y } , \pmb { \pi } )$
+
+![](images/be44e2eca20e772743f6f2e21e2702d4272dad150589e6eca8ea1113b2c8c7d9.jpg)  
+Figure 2: VNMT
+
+![](images/c7a23d3386179254d992cf59a6bfb4684fdde8b205007edc2ffd3f3352dbb994.jpg)  
+Figure 3: Our model
+
+instead, and also model prior $p _ { \theta } ( \mathbf { z } | \mathbf { x } )$ so that we can generate a translation from the source in testing.   
+Derivation of the formula is presented in the appendix.
+
+We model all distributions in Eq. (2) by neural networks. Our model architecture is divisible into three parts: 1) encoder, 2) inferrer, and 3) decoder.
+
+# 3.1 ENCODER
+
+In the encoder, the semantic representation $\mathbf { h _ { e } }$ is obtained from the image, source, and target. We propose several methods to encode an image. We show how these methods affect the translation result in the Experiment section. This representation is used in the inferrer. This section links to the green part of Figure 1.
+
+# 3.1.1 TEXT ENCODING
+
+The source and target are encoded in the same way as Bahdanau et al. (2015). The source is converted to a sequence of 1-of- $\mathbf { \nabla } _ { k }$ vector and is embedded to $d _ { e m b }$ dimensions. We designate it as the source sequence. Then, a source sequence is put into bidirectional RNN. Representation $\mathbf { h } _ { i }$ is obtained by concatenating $\vec { \mathbf { h } } _ { i }$ and $\bar { \mathbf { h } } _ { i } : \bar { \vec { \mathbf { h } } } _ { i } = \mathrm { R N N } ( \vec { \mathbf { h } } _ { i - 1 } , E _ { w _ { i } } ) , \bar { \mathbf { h } } _ { i } = \mathrm { R N N } ( \bar { \mathbf { h } } _ { i + 1 } , E _ { w _ { i } } ) , \mathbf { h } _ { i } = [ \vec { \mathbf { h } } _ { i } ; \bar { \mathbf { h } } _ { i } ]$ , where $E _ { w _ { i } }$ is the embedded word in a source sentence, $\mathbf { h } _ { i } \in \mathbb { R } ^ { d _ { h } }$ , and $\vec { \bf h } _ { i } , \bar { \bf h } _ { i } \in \mathbb { R } ^ { \frac { d _ { h } } { 2 } }$ . It is conducted through $i = 0$ to $i = T _ { f }$ , where $T _ { f }$ is the sequence length. GRU is implemented in bidirectional RNN so that it can attain long-term dependence. Finally, we conduct mean-pooling to $\mathbf { h } _ { i }$ and obtain the source representation vector as $\begin{array} { r } { \mathbf { h } _ { f } = \frac { 1 } { T _ { f } } \sum _ { i } ^ { T _ { f } } \mathbf { h } _ { i } } \end{array}$ . The exact same process is applied to target to obtain target representation $\mathbf { h } _ { g }$ .
+
+# 3.1.2 IMAGE ENCODING AND SEMANTIC REPRESENTATION
+
+We use Convolutional Neural Networks (CNN) to extract feature vectors from images. We propose several ways of extracting image features.
+
+Global (G) The image feature vector is extracted from the image using a CNN. With this method, we use a feature vector in the certain layer as $\pi$ . Then $\pi$ is encoded to the image representation vector $\mathbf { h } _ { \pi }$ simply by affine transformation as
+
+$$
+\mathbf { h } _ { \pi } = W _ { \pi } \pi + b _ { \pi } \quad \mathrm { w h e r e } ~ W _ { \pi } \in \mathbb { R } ^ { d _ { \pi } \times d _ { f c 7 } } , b _ { \pi } \in \mathbb { R } ^ { d _ { \pi } } .
+$$
+
+Global and Objects $\mathbf { ( G { + } 0 ) }$ First we extract some prominent objects from images in some way. Then, we obtain fc7 image feature vectors $\pi$ from the original image and extracted objects using a CNN. Therefore $\pi$ takes a variable length. We handle $\pi$ in two ways: average and RNN encoder.
+
+In average $\mathbf { G { + } O { - } A V G }$ , we first obtain intermediate image representation vector ${ \bf h } _ { \pi } ^ { \prime }$ by affine transformation in Eq. (3). Then, the average of ${ \bf h } _ { \pi } ^ { \prime }$ becomes the image representation vector: $\begin{array} { r } { \mathbf { h } _ { \pi } = \frac { \sum _ { i } ^ { l } \mathbf { h } _ { \pi _ { i } } ^ { \prime } } { l } } \end{array}$ , where $l$ is the length of ${ \bf h } _ { \pi } ^ { \prime }$ .
+
+In RNN encoder $\mathbf { G } { + } \mathbf { O } { \mathbf { - } } \mathbf { R } \mathbf { N } \mathbf { N }$ ), we first obtain ${ \bf h } _ { \pi } ^ { \prime }$ by affine transformation in Eq. (3). Then, we encode ${ \bf h } _ { \pi } ^ { \prime }$ in the same way as we encode text in Section 3.1.1 to obtain $\mathbf { h } _ { \pi }$ .
+
+Global and Objects into source and target $\mathbf { \left( G { + } O { - } T X T \right) }$ ) Thereby, we first obtain ${ \bf h } _ { \pi } ^ { \prime }$ by affine transformation in Eq. (3). Then, we put sequential vector ${ \bf h } _ { \pi } ^ { \prime }$ into the head of the source sequence and target sequence. In this case, we set $d _ { \pi }$ to be the same dimension as $d _ { e m b }$ . In fact, the source sequence including ${ \bf h } _ { \pi } ^ { \prime }$ is only used to model $q _ { \phi } ( \mathbf { z } | \mathbf { x } , \mathbf { y } , \pmb { \pi } )$ . Context vector c (Eq. (15)) and $p _ { \theta } ( \mathbf { z } | \mathbf { x } )$ are computed by a source sequence that does not include ${ \bf h } _ { \pi } ^ { \prime }$ . We encode the source sequence including ${ \bf h } _ { \pi } ^ { \prime }$ as Section 3.1.1 to obtain $\mathbf { h } _ { f }$ and $\mathbf { h } _ { g }$ . In this case, $\mathbf { h } _ { \pi }$ is not obtained. Image information is contained in $\mathbf { h } _ { f }$ and $\mathbf { h } _ { g }$ .
+
+All representation vectors $\mathbf { h } _ { f } , \mathbf { h } _ { g }$ and $\mathbf { h } _ { \pi }$ are concatenated to obtain a semantic representation vector as $\mathbf h _ { e } \ = \ [ \mathbf h _ { f } ; \mathbf h _ { g } ; \mathbf h _ { \pi } ]$ , where $\bar { \mathbf { h } } _ { e } \in \mathbb { R } ^ { d _ { e } = 2 \times d _ { h } + d _ { \pi } }$ (in $\mathrm { G } { + } \mathrm { O } \mathrm { \mathrm { \Omega } }$ -TXT: ${ \bf h } _ { e } ~ = ~ [ { \bf h } _ { f } ; { \bf h } _ { g } ]$ , where $\mathbf { h } _ { e } \in$ $\mathbb { R } ^ { d _ { e } = 2 \times d _ { h } }$ ). It is an input of the multimodal variational neural inferrer.
+
+# 3.2 INFERRER
+
+We model the posterior $q _ { \phi } ( \mathbf { z } | \mathbf { x } , \mathbf { y } , \pmb { \pi } )$ using a neural network and also the prior $p _ { \theta } ( \mathbf { z } | \mathbf { x } )$ by neural network. This section links to the black and grey part of Figure 1.
+
+# 3.2.1 NEURAL POSTERIOR APPROXIMATOR
+
+Modeling the true posterior $p _ { \theta } ( \mathbf { z } | \mathbf { x } , \mathbf { y } , \pi )$ is usually intractable. Therefore, we consider modeling of an approximate posterior $q _ { \phi } ( \mathbf { z } | \mathbf { x } , \mathbf { y } , \pmb { \pi } )$ by introducing VAE. We assume that the posterior $q _ { \phi } ( \mathbf { z } | \mathbf { x } , \mathbf { y } , \boldsymbol { \pi } )$ has the following form:
+
+$$
+\begin{array} { r } { q _ { \phi } ( \mathbf { z } | \mathbf { x } , \mathbf { y } , \pi ) = \mathcal { N } ( \mathbf { z } ; \mu ( \mathbf { x } , \mathbf { y } , \pi ) , \pmb { \sigma } ( \mathbf { x } , \mathbf { y } , \pi ) ^ { 2 } \mathbf { I } ) . } \end{array}
+$$
+
+The mean $\pmb { \mu }$ and standard deviation $\sigma$ of the approximate posterior are the outputs of neural networks.
+
+Starting from the variational neural encoder, a semantic representation vector $\mathbf { h } _ { e }$ is projected to latent semantic space as
+
+$$
+{ \bf h } _ { z } = g ( W _ { z } ^ { ( 1 ) } { \bf h } _ { e } + { \bf b } _ { z } ^ { ( 1 ) } ) ,
+$$
+
+where $W _ { z } ^ { ( 1 ) } \in \mathbb { R } ^ { d _ { z } \times ( d _ { e } ) } \mathbf { b } _ { z } ^ { ( 1 ) } \in \mathbb { R } ^ { d _ { z } }$ . $g ( \cdot )$ is an element-wise activation function, which we set as $\operatorname { t a n h } ( { \cdot } )$ . Gaussian parameters of Eq. (4) are obtained through linear regression as
+
+$$
+\pmb { \mu } = W _ { \mu } \mathbf { h } _ { z } + \mathbf { b } _ { \mu } , \log \pmb { \sigma } ^ { 2 } = W _ { \sigma } \mathbf { h } _ { z } + \mathbf { b } _ { \sigma } ,
+$$
+
+where $\mu , \log \sigma ^ { 2 } \in \mathbb { R } ^ { d _ { z } }$ .
+
+# 3.2.2 NEURAL PRIOR MODEL
+
+We model the prior distribution $p _ { \theta } ( \mathbf { z } | \mathbf { x } )$ as follows:
+
+$$
+\begin{array} { r l r } { p _ { \boldsymbol \theta } ( \mathbf { z } | \mathbf { x } ) } & { = } & { \mathcal { N } ( \mathbf { z } ; \mu ^ { \prime } ( \mathbf { x } ) , \pmb \sigma ^ { \prime } ( \mathbf { x } ) ^ { 2 } \mathbf { I } ) . } \end{array}
+$$
+
+$\mu ^ { \prime }$ and $\pmb { \sigma } ^ { \prime }$ are generated in the same way as that presented in Section 3.2.1, except for the absence of $\mathbf { y }$ and $\pi$ as inputs. Because of the absence of representation vectors, the dimensions of weight in equation (5) for prior model are W ′(1)z $W _ { z } ^ { ' ( 1 ) } \in \mathbb { R } ^ { d _ { z } \times d _ { h } }$ , $\mathbf { b } _ { z } ^ { ' ( 1 ) } \in \mathbb { R } ^ { d _ { z } }$ . We use a reparameterization trick to obtain a representation of latent variable $\mathbf { z }$ : $\mathbf h _ { z } ^ { \prime } = \pmb { \mu } + \pmb { \sigma } \pmb { \epsilon }$ , $\epsilon \sim \mathcal { N } ( 0 , I )$ . During translation, $\mathbf { h } _ { z } ^ { \prime }$ is set as the mean of $p _ { \theta } ( \mathbf { z } | \mathbf { x } )$ . Then, $\mathbf { h } _ { z } ^ { \prime }$ is projected onto the target space as
+
+$$
+\mathbf { h } _ { e } ^ { \prime } = g ( W _ { z } ^ { ( 2 ) } \mathbf { h } _ { z } ^ { \prime } + \mathbf { b } _ { z } ^ { ( 2 ) } ) \quad \mathrm { w h e r e ~ } \mathbf { h } _ { e } ^ { \prime } \in \mathbb { R } ^ { d _ { e } } .
+$$
+
+${ \bf h } _ { e } ^ { \prime }$ is then integrated into the neural machine translation’s decoder.
+
+# 3.3 DECODER
+
+This section links to the orange part of Figure 1. Given the source sentence $\mathbf { x }$ and the latent variable $\mathbf { z }$ , decoder defines the probability over translation $\mathbf { y }$ as
+
+$$
+p ( \mathbf { y } | \mathbf { z } , \mathbf { x } ) = \prod _ { j = 1 } ^ { T } p ( \mathbf { y } _ { j } | \mathbf { y } _ { < j } , \mathbf { z } , \mathbf { x } ) .
+$$
+
+How we define the probability over translation $\mathbf { y }$ is fundamentally the same as VNMT, except for using conditional GRU instead of GRU. Conditional GRU involves two GRUs and an attention mechanism. We integrate a latent variable $\mathbf { z }$ into the second GRU. We describe it in the appendix.
+
+# 3.4 MODEL TRAINING
+
+Monte Carlo sampling method is used to approximate the expectation over the posterior Eq. (2), $\begin{array} { r } { \mathbb { E } _ { q _ { \phi } ( \mathbf { z } | \mathbf { x } , \mathbf { y } , \pi ) } \approx \frac { 1 } { L } \sum _ { l = 1 } ^ { L } \log p _ { \theta } ( \mathbf { y } | \mathbf { x } , \mathbf { h } _ { z } ^ { ( l ) } ) } \end{array}$ , where $L$ is the number of samplings. The training objective is defined as
+
+$$
+\mathcal { L } ( \boldsymbol { \theta } , \boldsymbol { \phi } ) = - \mathrm { D } _ { \mathrm { K L } } \left[ q _ { \phi } ( \mathbf { z } | \mathbf { x } , \mathbf { y } , \boldsymbol { \pi } ) | | p _ { \theta } ( \mathbf { z } | \mathbf { x } ) \right] + \frac { 1 } { L } \sum _ { l = 1 } ^ { L } \sum _ { j = 1 } ^ { T } \log p _ { \theta } ( \mathbf { y } _ { j } | \mathbf { y } _ { < j } , \mathbf { x } , \mathbf { h } _ { z } ^ { ( l ) } ) ,
+$$
+
+where $\mathbf { h } _ { z } = \pmb { \mu } + \pmb { \sigma } \cdot \pmb { \epsilon } , \pmb { \epsilon } \sim \mathcal { N } ( 0 , I )$ . The first term, KL divergence, can be computed analytically and is differentiable because both distributions are Gaussian. The second term is also differentiable. We set $L$ as 1. Overall, the objective $\mathcal { L }$ is differentiable. Therefore, we can optimize the parameter $\theta$ and variational parameter $\phi$ using gradient ascent techniques.
+
+# 4 EXPERIMENTS
+
+# 4.1 EXPERIMENTAL SETUP
+
+We used Multi30k (Elliott et al., 2016) as the dataset. Multi30k have an English description and a German description for each corresponding image. We handle 29,000 pairs as training data, 1,014 pairs as validation data, and 1,000 pairs as test data.
+
+Before training, punctuation normalization and lowercase are applied to both English and German sentences by Moses (Koehn et al., 2007) scripts2. Compound-word splitting is conducted only to German sentences using Sennrich et al. $( 2 0 1 \dot { 6 } ) ^ { 3 }$ . Then we tokenize sentences2 and use them as training data. We produce vocabulary dictionaries from training data. The vocabulary becomes 10,211 words for English and 13,180 words for German after compound-word splitting.
+
+Image features are extracted using VGG-19 CNN (Simonyan & Zisserman, 2014). We use 4096- dimensional fc7 features. To extract the object’s region, we use Fast R-CNN (Girshick, 2015). Fast R-CNN is trained on ImageNet and MSCOCO dataset 4.
+
+All weights are initialized by $\mathcal { N } ( 0 , 0 . 0 1 \mathbf { I } )$ . We use the adadelta algorithm as an optimization method. The hyperparameters used in the experiment are presented in the Appendix. All models are trained with early stopping. When training, VNMT is fine-tuned by NMT model and our models are finetuned using VNMT. When translating, we use beam-search. The beam-size is set as 12. Before evaluation, we restore split words to the original state and de-tokenize2 generated sentences.
+
+We implemented proposed models based on $d l 4 m t ^ { 5 }$ . Actually, dl4mt is fundamentally the same model as Bahdanau et al. (2015), except that its decoder employs conditional GRU6. We implemented VNMT also with conditional GRU so small difference exists between our implementation and originally proposed VNMT which employs normal GRU as a decoder. We evaluated results based on METEOR and BLUE using MultEval 7.
+
+# 4.2 RESULT
+
+Table 1 presents experiment results. It shows that our models outperforms the baseline in both METEOR and BLEU. Figure 4 shows the plot of METEOR score of baselines and our models models in validation. Figure 5 shows the plot of METEOR score and the source sentence length.
+
+Table 1: Evaluation Result on Multi30k dataset (English–German). The scores in parentheses are computed with ‘-norm’ parameter. NMT is dl4mt’s NMT (in the session3 directory). The score of the CMU is from (Huang et al., 2016).   
+
+<table><tr><td colspan="2"></td><td colspan="2">METEOR↑</td><td colspan="2">BLEU↑</td></tr><tr><td colspan="2"></td><td>val</td><td>test</td><td>val</td><td>test</td></tr><tr><td rowspan="3"></td><td>NMT</td><td>51.5 (55.8)</td><td>50.5 (54.9)</td><td>35.8</td><td>33.1</td></tr><tr><td>VNMT</td><td>52.2 (56.3)</td><td>51.1 (55.3)</td><td>37.0</td><td>34.9</td></tr><tr><td>CMU</td><td>（）</td><td>1 (54.1)</td><td>1</td><td>1</td></tr><tr><td rowspan="4">Our Model</td><td>G</td><td>50.6 (54.8)</td><td>52.4 (56.0)</td><td>34.5</td><td>36.5</td></tr><tr><td>G+O-AVG</td><td>51.8 (55.8)</td><td>51.8 (55.8)</td><td>35.7</td><td>35.8</td></tr><tr><td>G+O-RNN</td><td>51.8 (56.1)</td><td>51.0 (55.4)</td><td>35.9</td><td>34.9</td></tr><tr><td>G+O-TXT</td><td>52.6 (56.8)</td><td>51.7 (56.0)</td><td>36.6</td><td>35.1</td></tr></table>
+
+# 4.3 QUANTITATIVE ANALYSIS
+
+Table 1 shows that G scores the best in proposed models. In G, we simply put the feature of the original image. Actually, proposed model does not benefit from R-CNN, presumably because we can not handle sequences of image features very well. For example, $\mathrm { G } { + } \mathrm { O }$ -AVG uses the average of multiple image features, but it only makes the original image information unnecessarily confusing.
+
+Figure 4 shows that G and $\mathrm { G } { + } \mathrm { O } { } \mathrm { \cdot }$ -AVG outperforms VNMT almost every time, but all model scores increase suddenly in the 17,000 iteration validation. We have no explanation for this behavior. Figure 4 also shows that G and $\mathrm { G } { + } \mathrm { O } { } \mathrm { \mathrm { \Omega } }$ -AVG scores fluctuate more moderately than others. We state that G and $_ \mathrm { G + O }$ -AVG gain stability by adding image information. When one observes the difference between the test score and the validation score for each model, baseline scores decrease more than proposed model scores. Especially, the G score increases in the test, simply because proposed models produce a better METEOR score on average, as shown in Figure 4.
+
+Figure 5 shows that G and $\mathrm { G } { + } \mathrm { O }$ -AVG make more improvements on baselines in short sentences than in long sentences, presumably because $q _ { \phi } ( \mathbf { z } | \mathbf { x } , \mathbf { y } , \boldsymbol { \pi } )$ can model $\mathbf { z }$ well when a sentence is short. Image features always have the same dimension, but underlying semantics of the image and text differ. We infer that when the sentence is short, image feature representation can afford to approximate the underlying semantic, but when a sentence is long, image feature representation can not approximate the underlying semantic.
+
+Multi30k easily becomes overfitted, as shown in Figure 8 and 9 in the appendix. This is presumably because 1) Multi30k is the descriptions of image, making the sentences short and simple, and 2) Multi30k has 29,000 sentences, which could be insufficient. In the appendix, we show how the parameter setting affects the score. One can see that decay-c has a strong effect. Huang et al. (2016) states that their proposed model outperforms the baseline (NMT), but we do not have that observation. It can be assumed that their baseline parameters are not well tuned.
+
+# 4.4 QUALITATIVE ANALYSIS
+
+We presented the top 30 sentences, which make the largest METEOR score difference between G and VNMT, to native speakers of German and get the overall comments. They were not informed of our model training with image in addition to text. These comments are summarized into two general remarks. One is that G translates the meaning of the source material more accurately than VNMT. The other is that our model has more grammatical errors as prepositions’ mistakes or missing verbs compared to VNMT. We assume these two remarks are reasonable because G is trained with images which mainly have a representation of noun rather than verb, therefore can capture the meaning of materials in sentence.
+
+![](images/336f0b01b64b29847f26f5ecff9a7f50cb3d156bfae6b39739bff0d875544a49.jpg)  
+Figure 4: METEOR score to the validation data which are calculated for each 1000 iterations.
+
+![](images/5cbe81cb72340f2ba8e4f579766d3dc674988f34d481a805fadc437a74525605.jpg)  
+Figure 5: METEOR score on different groups of the source sentence length.
+
+Figure 6 presents the translation results and the corresponding image which G translates more accurately than VNMT in METEOR. Figure 7 presents the translation results and the corresponding image which G translates less accurately than VNMT in METEOR. Again, we note that our model does not use image during translating. In Figure 6, G translates ”a white and black dog” correctly while VNMT translates it incorrectly implying ”a white dog and a black dog”. We assume that G correctly translates the source because G captures the meaning of material in the source. In Figure 7, G incorrectly translates the source. Its translation result is missing the preposition meaning ”at”, which is hardly represented in image.We present more translation examples in appendix.
+
+![](images/3e6e262a2cb9ed0521cc90b099233c2907e3bb10cdea3ffc73cf509db5803456.jpg)
+
+![](images/f5285ea63366850a021ab9f7f8e2cac294f6d2bbde53ffb04b34c0156f44619e.jpg)  
+Figure 6: Translation 1
+
+![](images/b9aa0f94d1e754dd559290e8983f30176de9651a391cc7a962dce590875455c5.jpg)
+
+![](images/b0308383548bfd1bdb406863a7474d490fee0deafc740e5feabcee5ef1f7bab4.jpg)  
+Figure 7: Translation 2
+
+# 5 CONCLUSION
+
+As described herein, we proposed the neural machine translation model that explicitly has a latent variable that includes underlying semantics extracted from both text and images. Our model outperforms the baseline in both METEOR and BLEU scores. Experiments and analysis present that our model can generate more accurate translation for short sentences. In qualitative analysis, we present that our model can translate nouns accurately while our model make grammatical errors.
+
+# REFERENCES
+
+Dzmitry Bahdanau, Kyunghyun Cho, and Yoshua Bengio. Neural machine translation by jointly learning to align and translate. In ICLR, 2015.
+
+Lawrence W. Barsalou. Perceptual symbol Systems. Behavioral and Brain Sciences, 22:577–609, 1999.
+
+Ozan Caglayan, Walid Aransa, Yaxing Wang, Marc Masana, Mercedes Garc´ıa-Mart´ınez, Fethi Bougares, Lo¨ıc Barrault, and Joost van de Weijer. Does Multimodality Help Human and Machine for Translation and Image Captioning? In WMT, 2016.
+
+Iacer Calixto, Desmond Elliott, and Stella Frank. DCU-UvA Multimodal MT System Report. In Proceedings of the First Conference on Machine Translation, pp. 634–638. Association for Computational Linguistics, 2016.
+
+Michael Denkowski and Alon Lavie. Meteor Universal: Language Specific Translation Evaluation for Any Target Language. In Proceedings of the EACL 2014 Workshop on Statistical Machine Translation, 2014.
+
+D. Elliott, S. Frank, and E. Hasler. Multilingual Image Description with Neural Sequence Models. ArXiv e-prints, 2015.
+
+Desmond Elliott, Stella Frank, Khalil Sima’an, and Lucia Specia. Multi30K: Multilingual EnglishGerman Image Descriptions. CoRR, abs/1605.00459, 2016.
+
+Ross Girshick. Fast R-CNN. In ICCV, 2015.
+
+Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep Residual Learning for Image Recognition. In CVPR, 2016.
+
+Julian Hitschler and Stefan Riezler. Multimodal Pivots for Image Caption Translation. arXiv preprint arXiv:1601.03916, 2016.
+
+Po-Yao Huang, Frederick Liu, Sz-Rung Shiang, Jean Oh, and Chris Dyer. Attention-based Multimodal Neural Machine Translation. In WMT, 2016.
+
+Diederik P Kingma, Shakir Mohamed, Danilo Jimenez Rezende, and Max Welling. Semi-supervised Learning with Deep Generative Models. In NIPS, 2014.
+
+Philipp Koehn, Hieu Hoang, Alexandra Birch, Chris Callison-Burch, Marcello Federico, Nicola Bertoldi, Brooke Cowan, Wade Shen, Christine Moran, Richard Zens, Chris Dyer, Ondˇrej Bojar, Alexandra Constantin, and Evan Herbst. Moses: Open Source Toolkit for Statistical Machine Translation. In ACL, 2007.
+
+Jindˇrich Libovicky, Jind ´ ˇrich Helcl, Marek Tlusty, Ond ´ ˇrej Bojar, and Pavel Pecina. CUNI System for WMT16 Automatic Post-Editing and Multimodal Translation Tasks. In Proceedings of the First Conference on Machine Translation, pp. 646–654. Association for Computational Linguistics, 2016.
+
+Kishore Papineni, Salim Roukos, Todd Ward, and Wei-Jing Zhu. BLEU: A Method for Automatic Evaluation of Machine Translation. In ACL, 2002.
+
+Scott Reed, Zeynep Akata, Xinchen Yan, Lajanugen Logeswaran, Bernt Schiele, and Honglak Lee. Generative Adversarial Text to Image Synthesis. In ICML, 2016.
+
+Danilo J. Rezende, Shakir Mohamed, and Daan Wierstra. Stochastic Backpropagation and Approximate Inference in Deep Generative Models. In ICML, 2014.
+
+Sergio Rodr´ıguez Guasch and Marta R. Costa-jussa. WMT 2016 Multimodal Translation System \` Description based on Bidirectional Recurrent Neural Networks with Double-Embeddings. In Proceedings of the First Conference on Machine Translation, pp. 655–659. Association for Computational Linguistics, 2016.
+
+Rico Sennrich, Barry Haddow, and Alexandra Birch. Neural Machine Translation of Rare Words with Subword Units. In ACL, 2016.
+
+Kashif Shah, Josiah Wang, and Lucia Specia. SHEF-Multimodal: Grounding Machine Translation on Images. In Proceedings of the First Conference on Machine Translation, pp. 660–665. Association for Computational Linguistics, 2016.
+
+Karen Simonyan and Andrew Zisserman. Very Deep Convolutional Networks for Large-Scale Image Recognition. CoRR, abs/1409.1556, 2014.
+
+Lucia Specia, Stella Frank, Khalil Sima ’an, and Desmond Elliott. A shared Task on Multimodal Machine Translation and Crosslingual Image Description. In Proceedings of the First Conference on Machine Translation, Berlin, Germany. Association for Computational Linguistics, 2016.
+
+Ilya Sutskever, Oriol Vinyals, and Quoc V Le. Sequence to Sequence Learning with Neural Networks. In NIPS, 2014.
+
+Zhaopeng Tu, Zhengdong Lu, Yang Liu, Xiaohua Liu, and Hang Li. Modeling Coverage for Neural Machine Translation. In ACL, 2016.
+
+Kelvin Xu, Jimmy Ba, Ryan Kiros, Kyunghyun Cho, Aaron Courville, Ruslan Salakhutdinov, Richard S Zemel, and Yoshua Bengio. Show, Attend and Tell: Neural Image Caption Generation with Visual Attention. In CVPR, 2015.
+
+Biao Zhang, Deyi Xiong, and Jinsong Su. Variational Neural Machine Translation. In EMNLP, 2016.
+
+# A DERIVATION OF LOWER BOUNDS
+
+The lower bound of our model can be derived as follows:
+
+$$
+\begin{array} { l l l } { p ( \mathbf { y } | \mathbf { x } ) } & { = } & { \displaystyle \int p ( \mathbf { y } , \mathbf { z } | \mathbf { x } ) d \mathbf { z } } \\ { \displaystyle } & { = } & { \displaystyle \int p ( \mathbf { z } | \mathbf { x } ) p ( \mathbf { y } | \mathbf { z } , \mathbf { x } ) d \mathbf { z } } \end{array}
+$$
+
+$$
+{ \begin{array} { r c l } { \log p ( \mathbf { y } | \mathbf { x } ) } & { = } & { \log \int q ( \mathbf { z } | \mathbf { x } , \mathbf { y } , \pi ) { \frac { p ( \mathbf { z } | \mathbf { x } ) p ( \mathbf { y } | \mathbf { z } , \mathbf { x } ) } { q ( \mathbf { z } | \mathbf { x } , \mathbf { y } , \pi ) } } d \mathbf { z } } \\ & { \geq } & { \displaystyle \int q ( \mathbf { z } | \mathbf { x } , \mathbf { y } , \pi ) \log { \frac { p ( \mathbf { z } | \mathbf { x } ) p ( \mathbf { y } | \mathbf { z } , \mathbf { x } ) } { q ( \mathbf { z } | \mathbf { x } , \mathbf { y } , \pi ) } } d \mathbf { z } } \\ & { = } & { \displaystyle \int q ( \mathbf { z } | \mathbf { x } , \mathbf { y } , \pi ) \left( \log { \frac { p ( \mathbf { z } | \mathbf { x } ) } { q ( \mathbf { z } | \mathbf { x } , \mathbf { y } ) } } + \log p ( \mathbf { y } | \mathbf { z } , \mathbf { x } ) \right) d \mathbf { z } } \\ & { = } & { \displaystyle - \mathrm { D } _ { \mathrm { K L } } \left[ q ( \mathbf { z } | \mathbf { x } , \mathbf { y } , \pi ) | | p ( \mathbf { z } | \mathbf { x } ) \right] + \mathbb { E } _ { q ( \mathbf { z } | \mathbf { x } , \mathbf { y } , \pi ) } \left[ \log p ( \mathbf { y } | \mathbf { z } , \mathbf { x } ) \right] } \\ & { = } & { \displaystyle { \mathcal { L } } } \end{array} }
+$$
+
+# B CONDITIONAL GRU
+
+Conditional GRU is implemented in dl4mt. Caglayan et al. (2016) extends Conditional GRU to make it capable of receiving image information as input. The first GRU computes intermediate representation $s _ { j } ^ { \prime }$ as
+
+$$
+\begin{array} { r } { \mathbf { s } _ { j } ^ { \prime } = ( 1 - \mathbf { o } _ { j } ^ { \prime } ) \odot \underline { { \mathbf { s } } } _ { j } ^ { \prime } + \mathbf { o } _ { j } ^ { \prime } \odot \mathbf { s } _ { j - 1 } } \\ { \mathbf { s } _ { j } ^ { \prime } = \operatorname { t a n h } ( W ^ { \prime } E \left[ \mathbf { y } _ { j - 1 } \right] + \mathbf { r } _ { j } ^ { \prime } \odot ( U ^ { \prime } \mathbf { s } _ { j - 1 } ) ) } \\ { \mathbf { r } _ { j } ^ { \prime } = \sigma ( W _ { r } ^ { \prime } E \left[ \mathbf { y } _ { j - 1 } \right] + U _ { r } ^ { \prime } \mathbf { s } _ { j - 1 } ) } \\ { \mathbf { o } _ { j } ^ { \prime } = \sigma ( W _ { o } ^ { \prime } E \left[ \mathbf { y } _ { j - 1 } \right] + U _ { o } ^ { \prime } \mathbf { s } _ { j - 1 } ) } \end{array}
+$$
+
+where $E \in \mathbb { R } ^ { d _ { e m b } \times d _ { t } }$ signifies the target word embedding, $\underline { { \mathbf { s } } } _ { j } ^ { \prime } \in \mathbb { R } ^ { d _ { h } }$ denotes the hidden state, $\mathbf { r } _ { j } ^ { \prime } \in \mathbb { R } ^ { d _ { h } }$ and ${ \bf o } _ { j } ^ { \prime } \in \mathbb { R } ^ { d _ { h } }$ respectively represent the reset and update gate activations. $d _ { t }$ stands for the dimension of target; the unique number of target words. $[ W ^ { \prime } , W _ { r } ^ { \prime } , W _ { o } ^ { \prime } ] \in \mathbb { R } ^ { d _ { h } \times d _ { e m b } } , [ U ^ { \prime } , U _ { r } ^ { \prime } , U _ { o } ^ { \prime } ] \in$ $\mathbb { R } ^ { d _ { h } \times d _ { h } }$ are the parameters to be learned.
+
+Context vector $\mathbf { c } _ { j }$ is obtained as
+
+$$
+\begin{array} { r } { \mathbf { c } _ { j } = \operatorname { t a n h } \left( \displaystyle \sum _ { i = 1 } ^ { T _ { f } } \alpha _ { i j } \mathbf { h } _ { i } \right) } \\ { \displaystyle \alpha _ { i j } = \frac { \exp \left( \mathbf { e } _ { i j } \right) } { \sum _ { k = 1 } ^ { T _ { f } } \exp \left( e _ { k j } \right) } } \\ { \mathbf { e } _ { i j } = U _ { a t t } \mathrm { t a n h } \big ( W _ { c a t t } \mathbf { h } _ { i } + W _ { a t t } \mathbf { s } _ { j } ^ { \prime } \big ) } \end{array}
+$$
+
+where $[ { U _ { a t t } } , { W _ { c a t t } } , { W _ { a t t } } ] \in \mathbb { R } ^ { d _ { h } \times d _ { h } }$ are the parameters to be learned.
+
+The second GRU computes ${ \bf s } _ { j }$ from $\mathbf { s } _ { j } ^ { \prime } , \mathbf { c } _ { j }$ and ${ \bf h } _ { e } ^ { \prime }$ as
+
+$$
+\begin{array} { r } { \mathbf s _ { j } = ( 1 - \mathbf o _ { j } ^ { \prime } ) \odot \underline { { \mathbf s } } _ { j } + \mathbf o _ { j } \odot \mathbf s _ { j } ^ { \prime } } \\ { \underline { { \mathbf s } } _ { j } = \operatorname { t a n h } ( W \mathbf c _ { j } + \mathbf r _ { j } \odot ( U \mathbf s _ { j } ^ { \prime } ) + V \mathbf h _ { e } ^ { \prime } ) } \\ { \mathbf r _ { j } = \sigma ( W _ { r } \mathbf c _ { j } + U _ { r } \mathbf s _ { j } ^ { \prime } + V _ { r } \mathbf h _ { e } ^ { \prime } ) } \\ { \mathbf o _ { j } = \sigma ( W _ { o } \mathbf c _ { j } + U _ { o } \mathbf s _ { j } ^ { \prime } + V _ { o } \mathbf h _ { e } ^ { \prime } ) } \end{array}
+$$
+
+where $\underline { { \mathbf { s } } } _ { j } \in \mathbb { R } ^ { d _ { h } }$ stands for the hidden state, $\mathbf { r } _ { j } \in \mathbb { R } ^ { d _ { h } }$ and $\mathbf { o } _ { j } ~ \in ~ \mathbb { R } ^ { d _ { h } }$ are the reset and update gate activations. $[ W , W _ { r } , W _ { o } ] \ \in \ \mathbb { R } ^ { d _ { h } \times d _ { h } } , [ U , U _ { r } , U _ { o } ] \ \in \ \mathbb { R } ^ { d _ { h } \times d _ { h } } , [ V , V _ { r } , V _ { o } ] \ \in \ \mathbb { R } ^ { d _ { h } \times d _ { z } }$ are the
+
+parameters to be learned. We introduce ${ \bf h } _ { e } ^ { \prime }$ obtained from a latent variable here so that a latent variable can affect the representation ${ \bf s } _ { j }$ through GRU units.
+
+Finally, the probability of $y$ is computed as
+
+$$
+\begin{array} { r } { \mathbf { u } _ { j } = L _ { u } \mathrm { t a n h } ( E \left[ \mathbf { y } _ { j - 1 } \right] + L _ { s } \mathbf { s } _ { j } + L _ { x } \mathbf { c } _ { j } ) } \\ { P ( \mathbf { y } _ { j } | \mathbf { y } _ { j - 1 } , \mathbf { s } _ { j } , \mathbf { c } _ { j } ) = \mathrm { S o f t m a x } ( \mathbf { u } _ { j } ) } \end{array}
+$$
+
+where $L _ { u } \in \mathbb { R } ^ { d _ { t } \times d _ { e m b } }$ , $L _ { s } \in \mathbb { R } ^ { d _ { e m b } \times d _ { h } }$ and $L _ { c } \in \mathbb { R } ^ { d _ { e m b } \times d _ { h } }$ are the parameters to be learned.
+
+# C TRAINING DETAIL
+
+# C.1 HYPERPARAMETERS
+
+Table 2 presents parameters that we use in the experiments.
+
+Table 2: Hyperparameters. The name is the variable name of dl4mt except for dimv and dim pic, which are the dimension of the latent variables and image embeddings. We set dim (number of LSTM unit size) and dim word (dimensions of word embeddings) 256, batchsize 32, maxlen (max output length) 50 and $l r$ (learning rate) 1.0 for all models. decay- $c$ is weights on L2 regularization.   
+
+<table><tr><td colspan="2"></td><td>dimv</td><td>dim_pic</td><td>decay-c</td></tr><tr><td rowspan="3">Our Model</td><td>NMT</td><td>1</td><td>256</td><td>0.001</td></tr><tr><td>VNMT</td><td>256</td><td>256</td><td>0.0005</td></tr><tr><td>G G+O-AVG</td><td>256 256</td><td>512 256</td><td>0.001 0.0005</td></tr></table>
+
+We found that Multi30k dataset is easy to overfit. Figure 8 and Figure 9 present training cost and validation METEOR score graph of the two experimental settings of the NMT model. Table 3 presents the hyperparameters which were used in the experiments. Large decay- $c$ ans small batchsize give the better METEOR scores in the end. Training is stopped if there is no validation cost improvements over the last 10 validations.
+
+![](images/c7bae09f36a43d6018ae579ac15c03de257556b8181a0a9f38fd44944c05724c.jpg)  
+Figure 8: NMT Training Cost
+
+![](images/4cf686d842327ec69a90e4b59544c93c4bbf7f5db98b7ef11c7a1a405e320bf0.jpg)  
+Figure 9: NMT Validation METEOR score
+
+Table 3: Hyperparameters using the experiments in the Figure 8 and 9   
+
+<table><tr><td></td><td>dim</td><td>dim_word</td><td>lr</td><td>decay-c</td><td>maxlen</td><td>batchsie</td></tr><tr><td>1</td><td>256</td><td>256</td><td>1.0</td><td>0.0005</td><td>30</td><td>128</td></tr><tr><td>2</td><td>256</td><td>256</td><td>1.0</td><td>0.001</td><td>50</td><td>32</td></tr></table>
+
+Figure 10 presents the English word length histogram of the Multi30k test dataset. Most sentences in the Multi30k are less than 20 words. We assume that this is one of the reasons why Multi30k is easy to overfit.
+
+![](images/2c9cbbbc325b95ee17810529bec3d8c10b1b4be16b57ee667ba3a6348e29d4a5.jpg)  
+Figure 10: Word Length Histogram of the Multi30k Test Dataset
+
+# C.2 COST GRAPH
+
+Figure 11 and 12 present the training cost and validation cost graph of each models. Please note that VNMT fine-tuned NMT, and other models fine-tuned VNMT.
+
+![](images/06cdb8130b72418e484bd88c7a72c3295a6dd43723f58361d1b6fc7254026797.jpg)  
+Figure 11: Training cost
+
+# C.3 TRANSLATION EXAMPLES
+
+We present some selected translations from VNMT and our proposed model (G). As of translation 3 to 5 our model give the better METEOR scores than VNMT and as of translation 6 to 8 VNMT give the better METEOR scores than our models.
+
+![](images/14471daa059b8d95974e504c430617cd19cc8a3ebbfa34c05662cdee40253162.jpg)  
+Figure 12: Validation cost
+
+![](images/acc29606458a5807494c450d7d98cfbf2019552dbf1817b3f5117cb49d155fc3.jpg)  
+Figure 13: Translation 3
+
+<table><tr><td rowspan=1 colspan=1>Source</td><td rowspan=1 colspan=1> two boys inside a fence jump in the air while holding a basketball.</td></tr><tr><td rowspan=1 colspan=1>Truth</td><td rowspan=1 colspan=1> zwei jungen innerhalb eines zaunes springen in die luft und halten dabei einen basketball.</td></tr><tr><td rowspan=1 colspan=1>VNMT</td><td rowspan=1 colspan=1> zwei jungen in einem zaun springen in die luft, wahrend sie einen basketball hält.</td></tr><tr><td rowspan=1 colspan=1>Our Model (G)</td><td rowspan=1 colspan=1> zwei jungen in einem zaun springen in die luft und halten dabei einen basketball.</td></tr></table>
+
+![](images/23012d4624eca34e1c303667d6e14ec10c97268f0b4680d616f88c774e11979f.jpg)
+
+![](images/40438e3127b0e3dfabe5ef181edd81e6a9767fc1c201406ec2d489eec5be4b9a.jpg)  
+Figure 14: Translation 4
+
+![](images/3899a0a8465e2ce98deaee871de5b2b920dce614f48ba85d244452b665f39c4a.jpg)
+
+![](images/e7151f581c4957dd2df8001ca4e255d512e80383a168a778786ef6cf7af980b9.jpg)  
+Figure 15: Translation 5
+
+![](images/d411a02e14a3e6d08312a40b1f51766c1fe322869b0edcd0e47bc3d2e6bd81c1.jpg)
+
+![](images/bb605f8c5f246dc01410e5a4789cf874f02fe60269a8ccfae2a0e74f7144f6b4.jpg)  
+Figure 16: Translation 6
+
+![](images/401402a8fe1a4881873fd8a84766e65eef1b866c373de7db920db7592bf11743.jpg)
+
+![](images/8be7ff761f48d12a81eaaa70bf4c62d437638b12f62d9d8cd9b8e52448d94dc3.jpg)  
+Figure 17: Translation 7
+
+![](images/f4a6e36a04bba32d9bb47b3aaf084fd5b564ef6b93f245a779d068b254459b67.jpg)
+
+![](images/a9260f0f6290f1c96ecbfc79ab0478644bff0af1a4a394761f746d36cd74f6ab.jpg)  
+Figure 18: Translation 8

parse/train/B1G9tvcgx/B1G9tvcgx_content_list.json

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+    {
+        "type": "text",
+        "text": "NEURAL MACHINE TRANSLATION WITH LATENT SEMANTIC OF IMAGE AND TEXT ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            98,
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+        "page_idx": 0
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+    {
+        "type": "text",
+        "text": "Joji Toyama∗, Masanori Misono∗†, Masahiro Suzuki, Kotaro Nakayama & Yutaka Matsuo   \nGraduate School of Engineering, †Graduate School of Information Science and Technology   \nThe University of Tokyo   \nHongo, Tokyo, Japan   \n{toyama,misono,masa,k-nakayama,matsuo}@weblab.t.u-tokyo.ac.jp ",
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+    },
+    {
+        "type": "text",
+        "text": "ABSTRACT ",
+        "text_level": 1,
+        "bbox": [
+            454,
+            277,
+            544,
+            292
+        ],
+        "page_idx": 0
+    },
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+        "text": "Although attention-based Neural Machine Translation have achieved great success, attention-mechanism cannot capture the entire meaning of the source sentence because the attention mechanism generates a target word depending heavily on the relevant parts of the source sentence. The report of earlier studies has introduced a latent variable to capture the entire meaning of sentence and achieved improvement on attention-based Neural Machine Translation. We follow this approach and we believe that the capturing meaning of sentence benefits from image information because human beings understand the meaning of language not only from textual information but also from perceptual information such as that gained from vision. As described herein, we propose a neural machine translation model that introduces a continuous latent variable containing an underlying semantic extracted from texts and images. Our model, which can be trained endto-end, requires image information only when training. Experiments conducted with an English–German translation task show that our model outperforms over the baseline. ",
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+        "type": "text",
+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
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+            336,
+            564
+        ],
+        "page_idx": 0
+    },
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+        "text": "Neural machine translation (NMT) has achieved great success in recent years (Sutskever et al., 2014; Bahdanau et al., 2015). In contrast to statistical machine translation, which requires huge phrase and rule tables, NMT requires much less memory. However, the most standard model, NMT with attention (Bahdanau et al., 2015) entails the shortcoming that the attention mechanism cannot capture the entire meaning of a sentence because it generates a target word while depending heavily on the relevant parts of the source sentence (Tu et al., 2016). To overcome this problem, Variational Neural Machine Translation (VNMT), which outperforms NMT with attention introduces a latent variable to capture the underlying semantic from source and target (Zhang et al., 2016). We follow the motivation of VNMT, which is to capture underlying semantic of a source. ",
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+        "text": "Image information is related to language. For example, we human beings understand the meaning of language by linking perceptual information given by the surrounding environment and language (Barsalou, 1999). Although it is natural and easy for humans, it is difficult for computers to understand different domain’s information integrally. Solving this difficult task might, however, bring great improvements in natural language processing. Several researchers have attempted to link language and images such as image captioning by Xu et al. (2015) or image generation from sentences by Reed et al. (2016). They described the possibility of integral understanding of images and text. In machine translation, we can expect an improvement using not only text information but also image information because image information can bridge two languages. ",
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+    {
+        "type": "text",
+        "text": "As described herein, we propose the neural machine translation model which introduces a latent variable containing an underlying semantic extracted from texts and images. Our model includes an explicit latent variable z, which has underlying semantics extracted from text and images by introducing a Variational Autoencoder (VAE) (Kingma et al., 2014; Rezende et al., 2014). Our model, which can be trained end-to-end, requires image information only when training. As described herein, we tackle the task with which one uses a parallel corpus and images in training, while using a source corpus in translating. It is important to define the task in this manner because we rarely have a corresponding image when we want to translate a sentence. During translation, our model generates a semantic variable z from a source, integrates variable z into a decoder of neural machine translation system, and then finally generates the translation. The difference between our model and VNMT is that we use image information in addition to text information. ",
+        "bbox": [
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+        "page_idx": 0
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+    {
+        "type": "image",
+        "img_path": "images/7d59f4e9d8e0d16dcda6d9fe5f00e4043acaa4825994a380abfab9cb596829ee.jpg",
+        "image_caption": [
+            "Figure 1: Architecture of Proposed Model. Green dotted lines denote that $\\pi$ and encoded y are used only when training. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "For experiments, we used Multi30k (Elliott et al., 2016), which includes images and the corresponding parallel corpora of English and German. Our model outperforms the baseline with two evaluation metrics: METEOR (Denkowski & Lavie, 2014) and BLEU (Papineni et al., 2002). Moreover, we obtain some knowledge related to our model and Multi30k. Finally, we present some examples in which our model either improved, or worsened, the result. ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Our paper contributes to the neural machine translation research community in three ways. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "• We present the first neural machine translation model to introduce a latent variable inferred from image and text information. We also present the first translation task with which one uses a parallel corpus and images in training, while using a source corpus in translating.   \n• Our translation model can generate more accurate translation by training with images, especially for short sentences.   \n• We present how the translation of source is changed by adding image information compared to VNMT which does not use image information. ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2 BACKGROUND ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Our model is the extension of Variational Neural Machine Translation (VNMT) (Zhang et al., 2016). Our model is also viewed as one of the multimodal translation models. In our model, VAE is used to introduce a latent variable. We describe the background of our model in this section. ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2.1 VARIATIONAL NEURAL MACHINE TRANSLATION ",
+        "text_level": 1,
+        "bbox": [
+            173,
+            840,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "The VNMT translation model introduces a latent variable. This model’s architecture shown in Figure 1 excludes the arrow from $\\pi$ . This model involves three parts: encoder, inferrer, and decoder. In the encoder, both the source and target are encoded by bidirectional-Recurrent Neural Networks (bidirectional-RNN) and a semantic representation is generated. In the inferrer, a latent variable $\\mathbf { z }$ is modeled from a semantic representation by introducing VAE. In the decoder, a latent variable $\\mathbf { z }$ is integrated in the Gated Recurrent Unit (GRU) decoder; also, a translation is generated. ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Our model is followed by architecture, except that the image is also encoded to obtain a latent variable z. ",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2.2 MULTIMODAL TRANSLATION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            185,
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+            199
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Multimodal Translation is the task with which one might one can use a parallel corpus and images. The first papers to study multimodal translation are Elliott et al. (2015) and Hitschler & Riezler (2016). It was selected as a shared task in Workshop of Machine Translation 2016 (WMT161). Although several studies have been conducted (Caglayan et al., 2016; Huang et al., 2016; Calixto et al., 2016; Libovicky et al. ´ , 2016; Rodr´ıguez Guasch & Costa-jussa\\`, 2016; Shah et al., 2016), they do not show great improvement, especially in neural machine translation (Specia et al., 2016). Here, we introduce end-to-end neural network translation models like our model. ",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Caglayan et al. (2016) integrate an image into an NMT decoder. They simply put source context vectors and image feature vectors extracted from ResNet-50’s ‘res4f relu’ layer (He et al., 2016) into the decoder called multimodal conditional GRU. They demonstrate that their method does not surpass the text-only baseline: NMT with attention. ",
+        "bbox": [
+            174,
+            315,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Huang et al. (2016) integrate an image into a head of source words sequence. They extract prominent objects from the image by Region-based Convolutional Neural Networks (R-CNN) (Girshick, 2015). Objects are then converted to feature vectors by VGG-19 (Simonyan & Zisserman, 2014) and are put into a head of source words sequence. They demonstrate that object extraction by R-CNN contributes greatly to the improvement. This model achieved the highest METEOR score in NMTbased models in WMT16, which we compare to our model in the experiment. We designate this model as CMU. ",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Caglayan et al. (2016) argue that their proposed model did not achieve improvement because they failed to benefit from both text and images. We assume that they failed to integrate text and images because they simply put images and text into neural machine translation despite huge gap exists between image information and text information. Our model, however, presents the possibility of benefitting from images and text because text and images are projected to their common semantic space so that the gap of images and text would be filled. ",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2.3 VARIATIONAL AUTO ENCODER ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            584,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "VAE was proposed in an earlier report of the literature Kingma et al. (2014); Rezende et al. (2014). Given an observed variable $\\mathbf { x }$ , VAE introduces a continuous latent variable $\\mathbf { z }$ , with the assumption that $\\mathbf { x }$ is generated from $\\mathbf { z }$ . VAE incorporates $p _ { \\boldsymbol { \\theta } } ( \\mathbf { x } | \\mathbf { z } )$ and $q _ { \\phi } ( { \\bf z } | { \\bf x } )$ into an end-to-end neural network. The lower bound is shown below. ",
+        "bbox": [
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+            611,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/e7e1cffb66ec64837e0cac453d10edb9da5dedffdae576f87147bad40a0f7acb.jpg",
+        "text": "$$\n\\mathcal { L } _ { \\mathrm { V A E } } = - \\mathrm { D } _ { \\mathrm { K L } } \\left[ q _ { \\phi } ( \\mathbf { z } | \\mathbf { x } ) | | p _ { \\theta } ( \\mathbf { z } ) \\right] + \\mathbb { E } _ { q _ { \\phi } ( \\mathbf { z } | \\mathbf { x } ) } \\left[ \\log p _ { \\theta } ( \\mathbf { x } | \\mathbf { z } ) \\right] \\leq \\log p _ { \\theta } ( \\mathbf { x } )\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3 NEURAL MACHINE TRANSLATION WITH LATENT SEMANTIC OF IMAGE AND TEXT ",
+        "text_level": 1,
+        "bbox": [
+            176,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "We propose a neural machine translation model which explicitly has a latent variable containing an underlying semantic extracted from both text and image. This model can be seen as an extension of VNMT by adding image information. ",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Our model can be drawn as a graphical model in Figure 3. Its lower bound is ",
+        "bbox": [
+            174,
+            810,
+            679,
+            827
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/a56e14ddb8c057b7c0069709365a555c8048694ea5de00bf35520da2e5743370.jpg",
+        "text": "$$\n\\mathcal { L } = - \\mathrm { D } _ { \\mathrm { K L } } \\left[ q _ { \\phi } ( \\mathbf { z } | \\mathbf { x } , \\mathbf { y } , \\pi ) | | p _ { \\theta } ( \\mathbf { z } | \\mathbf { x } ) \\right] + \\mathbb { E } _ { q _ { \\phi } ( \\mathbf { z } | \\mathbf { x } , \\mathbf { y } , \\pi ) } \\left[ \\log p _ { \\theta } ( \\mathbf { y } | \\mathbf { z } , \\mathbf { x } ) \\right] ,\n$$",
+        "text_format": "latex",
+        "bbox": [
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+            833,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where ${ \\mathbf { x } } , { \\mathbf { y } } , \\pi , { \\mathbf { z } }$ respectively denote the source, target, image and latent variable, and $p _ { \\theta }$ and $q _ { \\phi }$ respectively denote the prior distribution and the approximate posterior distribution. It is noteworthy in Eq. (2) that we want to model $p ( \\mathbf { z } | \\mathbf { x } , \\mathbf { y } , \\pi )$ , which is intractable. Therefore we model $q _ { \\phi } ( \\mathbf { z } | \\mathbf { x } , \\mathbf { y } , \\pmb { \\pi } )$ ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/be44e2eca20e772743f6f2e21e2702d4272dad150589e6eca8ea1113b2c8c7d9.jpg",
+        "image_caption": [
+            "Figure 2: VNMT "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/c7a23d3386179254d992cf59a6bfb4684fdde8b205007edc2ffd3f3352dbb994.jpg",
+        "image_caption": [
+            "Figure 3: Our model "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "instead, and also model prior $p _ { \\theta } ( \\mathbf { z } | \\mathbf { x } )$ so that we can generate a translation from the source in testing.   \nDerivation of the formula is presented in the appendix. ",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We model all distributions in Eq. (2) by neural networks. Our model architecture is divisible into three parts: 1) encoder, 2) inferrer, and 3) decoder. ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.1 ENCODER ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In the encoder, the semantic representation $\\mathbf { h _ { e } }$ is obtained from the image, source, and target. We propose several methods to encode an image. We show how these methods affect the translation result in the Experiment section. This representation is used in the inferrer. This section links to the green part of Figure 1. ",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.1.1 TEXT ENCODING ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The source and target are encoded in the same way as Bahdanau et al. (2015). The source is converted to a sequence of 1-of- $\\mathbf { \\nabla } _ { k }$ vector and is embedded to $d _ { e m b }$ dimensions. We designate it as the source sequence. Then, a source sequence is put into bidirectional RNN. Representation $\\mathbf { h } _ { i }$ is obtained by concatenating $\\vec { \\mathbf { h } } _ { i }$ and $\\bar { \\mathbf { h } } _ { i } : \\bar { \\vec { \\mathbf { h } } } _ { i } = \\mathrm { R N N } ( \\vec { \\mathbf { h } } _ { i - 1 } , E _ { w _ { i } } ) , \\bar { \\mathbf { h } } _ { i } = \\mathrm { R N N } ( \\bar { \\mathbf { h } } _ { i + 1 } , E _ { w _ { i } } ) , \\mathbf { h } _ { i } = [ \\vec { \\mathbf { h } } _ { i } ; \\bar { \\mathbf { h } } _ { i } ]$ , where $E _ { w _ { i } }$ is the embedded word in a source sentence, $\\mathbf { h } _ { i } \\in \\mathbb { R } ^ { d _ { h } }$ , and $\\vec { \\bf h } _ { i } , \\bar { \\bf h } _ { i } \\in \\mathbb { R } ^ { \\frac { d _ { h } } { 2 } }$ . It is conducted through $i = 0$ to $i = T _ { f }$ , where $T _ { f }$ is the sequence length. GRU is implemented in bidirectional RNN so that it can attain long-term dependence. Finally, we conduct mean-pooling to $\\mathbf { h } _ { i }$ and obtain the source representation vector as $\\begin{array} { r } { \\mathbf { h } _ { f } = \\frac { 1 } { T _ { f } } \\sum _ { i } ^ { T _ { f } } \\mathbf { h } _ { i } } \\end{array}$ . The exact same process is applied to target to obtain target representation $\\mathbf { h } _ { g }$ . ",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.1.2 IMAGE ENCODING AND SEMANTIC REPRESENTATION ",
+        "text_level": 1,
+        "bbox": [
+            174,
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We use Convolutional Neural Networks (CNN) to extract feature vectors from images. We propose several ways of extracting image features. ",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Global (G) The image feature vector is extracted from the image using a CNN. With this method, we use a feature vector in the certain layer as $\\pi$ . Then $\\pi$ is encoded to the image representation vector $\\mathbf { h } _ { \\pi }$ simply by affine transformation as ",
+        "bbox": [
+            173,
+            738,
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/81ce8181818576a9c1ef7b4436af568b765c92f924c961157b1a440ee3e66220.jpg",
+        "text": "$$\n\\mathbf { h } _ { \\pi } = W _ { \\pi } \\pi + b _ { \\pi } \\quad \\mathrm { w h e r e } ~ W _ { \\pi } \\in \\mathbb { R } ^ { d _ { \\pi } \\times d _ { f c 7 } } , b _ { \\pi } \\in \\mathbb { R } ^ { d _ { \\pi } } .\n$$",
+        "text_format": "latex",
+        "bbox": [
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+            787,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Global and Objects $\\mathbf { ( G { + } 0 ) }$ First we extract some prominent objects from images in some way. Then, we obtain fc7 image feature vectors $\\pi$ from the original image and extracted objects using a CNN. Therefore $\\pi$ takes a variable length. We handle $\\pi$ in two ways: average and RNN encoder. ",
+        "bbox": [
+            176,
+            815,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In average $\\mathbf { G { + } O { - } A V G }$ , we first obtain intermediate image representation vector ${ \\bf h } _ { \\pi } ^ { \\prime }$ by affine transformation in Eq. (3). Then, the average of ${ \\bf h } _ { \\pi } ^ { \\prime }$ becomes the image representation vector: $\\begin{array} { r } { \\mathbf { h } _ { \\pi } = \\frac { \\sum _ { i } ^ { l } \\mathbf { h } _ { \\pi _ { i } } ^ { \\prime } } { l } } \\end{array}$ , where $l$ is the length of ${ \\bf h } _ { \\pi } ^ { \\prime }$ . ",
+        "bbox": [
+            232,
+            875,
+            823,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In RNN encoder $\\mathbf { G } { + } \\mathbf { O } { \\mathbf { - } } \\mathbf { R } \\mathbf { N } \\mathbf { N }$ ), we first obtain ${ \\bf h } _ { \\pi } ^ { \\prime }$ by affine transformation in Eq. (3). Then, we encode ${ \\bf h } _ { \\pi } ^ { \\prime }$ in the same way as we encode text in Section 3.1.1 to obtain $\\mathbf { h } _ { \\pi }$ . ",
+        "bbox": [
+            225,
+            103,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Global and Objects into source and target $\\mathbf { \\left( G { + } O { - } T X T \\right) }$ ) Thereby, we first obtain ${ \\bf h } _ { \\pi } ^ { \\prime }$ by affine transformation in Eq. (3). Then, we put sequential vector ${ \\bf h } _ { \\pi } ^ { \\prime }$ into the head of the source sequence and target sequence. In this case, we set $d _ { \\pi }$ to be the same dimension as $d _ { e m b }$ . In fact, the source sequence including ${ \\bf h } _ { \\pi } ^ { \\prime }$ is only used to model $q _ { \\phi } ( \\mathbf { z } | \\mathbf { x } , \\mathbf { y } , \\pmb { \\pi } )$ . Context vector c (Eq. (15)) and $p _ { \\theta } ( \\mathbf { z } | \\mathbf { x } )$ are computed by a source sequence that does not include ${ \\bf h } _ { \\pi } ^ { \\prime }$ . We encode the source sequence including ${ \\bf h } _ { \\pi } ^ { \\prime }$ as Section 3.1.1 to obtain $\\mathbf { h } _ { f }$ and $\\mathbf { h } _ { g }$ . In this case, $\\mathbf { h } _ { \\pi }$ is not obtained. Image information is contained in $\\mathbf { h } _ { f }$ and $\\mathbf { h } _ { g }$ . ",
+        "bbox": [
+            174,
+            138,
+            825,
+            238
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "All representation vectors $\\mathbf { h } _ { f } , \\mathbf { h } _ { g }$ and $\\mathbf { h } _ { \\pi }$ are concatenated to obtain a semantic representation vector as $\\mathbf h _ { e } \\ = \\ [ \\mathbf h _ { f } ; \\mathbf h _ { g } ; \\mathbf h _ { \\pi } ]$ , where $\\bar { \\mathbf { h } } _ { e } \\in \\mathbb { R } ^ { d _ { e } = 2 \\times d _ { h } + d _ { \\pi } }$ (in $\\mathrm { G } { + } \\mathrm { O } \\mathrm { \\mathrm { \\Omega } }$ -TXT: ${ \\bf h } _ { e } ~ = ~ [ { \\bf h } _ { f } ; { \\bf h } _ { g } ]$ , where $\\mathbf { h } _ { e } \\in$ $\\mathbb { R } ^ { d _ { e } = 2 \\times d _ { h } }$ ). It is an input of the multimodal variational neural inferrer. ",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.2 INFERRER ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            318,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We model the posterior $q _ { \\phi } ( \\mathbf { z } | \\mathbf { x } , \\mathbf { y } , \\pmb { \\pi } )$ using a neural network and also the prior $p _ { \\theta } ( \\mathbf { z } | \\mathbf { x } )$ by neural network. This section links to the black and grey part of Figure 1. ",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.2.1 NEURAL POSTERIOR APPROXIMATOR ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            392,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Modeling the true posterior $p _ { \\theta } ( \\mathbf { z } | \\mathbf { x } , \\mathbf { y } , \\pi )$ is usually intractable. Therefore, we consider modeling of an approximate posterior $q _ { \\phi } ( \\mathbf { z } | \\mathbf { x } , \\mathbf { y } , \\pmb { \\pi } )$ by introducing VAE. We assume that the posterior $q _ { \\phi } ( \\mathbf { z } | \\mathbf { x } , \\mathbf { y } , \\boldsymbol { \\pi } )$ has the following form: ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/ccfa72a2ec2ff7edca4f4312964c8243f7c282543990f91671c968c41875b71c.jpg",
+        "text": "$$\n\\begin{array} { r } { q _ { \\phi } ( \\mathbf { z } | \\mathbf { x } , \\mathbf { y } , \\pi ) = \\mathcal { N } ( \\mathbf { z } ; \\mu ( \\mathbf { x } , \\mathbf { y } , \\pi ) , \\pmb { \\sigma } ( \\mathbf { x } , \\mathbf { y } , \\pi ) ^ { 2 } \\mathbf { I } ) . } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The mean $\\pmb { \\mu }$ and standard deviation $\\sigma$ of the approximate posterior are the outputs of neural networks. ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Starting from the variational neural encoder, a semantic representation vector $\\mathbf { h } _ { e }$ is projected to latent semantic space as ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/846bddf000f225251138a3e89465935cc60a3ca957d5dade41a91ee1d2ddf123.jpg",
+        "text": "$$\n{ \\bf h } _ { z } = g ( W _ { z } ^ { ( 1 ) } { \\bf h } _ { e } + { \\bf b } _ { z } ^ { ( 1 ) } ) ,\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where $W _ { z } ^ { ( 1 ) } \\in \\mathbb { R } ^ { d _ { z } \\times ( d _ { e } ) } \\mathbf { b } _ { z } ^ { ( 1 ) } \\in \\mathbb { R } ^ { d _ { z } }$ . $g ( \\cdot )$ is an element-wise activation function, which we set as $\\operatorname { t a n h } ( { \\cdot } )$ . Gaussian parameters of Eq. (4) are obtained through linear regression as ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/70259d0e0a7683914c944fb8a1e952ca9352c46ec72e07fbb0adaf84555a36f1.jpg",
+        "text": "$$\n\\pmb { \\mu } = W _ { \\mu } \\mathbf { h } _ { z } + \\mathbf { b } _ { \\mu } , \\log \\pmb { \\sigma } ^ { 2 } = W _ { \\sigma } \\mathbf { h } _ { z } + \\mathbf { b } _ { \\sigma } ,\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where $\\mu , \\log \\sigma ^ { 2 } \\in \\mathbb { R } ^ { d _ { z } }$ . ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.2.2 NEURAL PRIOR MODEL ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We model the prior distribution $p _ { \\theta } ( \\mathbf { z } | \\mathbf { x } )$ as follows: ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/a983063495e5006dbabbbc66734d275a48316b65a5141943c2d1c94782a309fe.jpg",
+        "text": "$$\n\\begin{array} { r l r } { p _ { \\boldsymbol \\theta } ( \\mathbf { z } | \\mathbf { x } ) } & { = } & { \\mathcal { N } ( \\mathbf { z } ; \\mu ^ { \\prime } ( \\mathbf { x } ) , \\pmb \\sigma ^ { \\prime } ( \\mathbf { x } ) ^ { 2 } \\mathbf { I } ) . } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "$\\mu ^ { \\prime }$ and $\\pmb { \\sigma } ^ { \\prime }$ are generated in the same way as that presented in Section 3.2.1, except for the absence of $\\mathbf { y }$ and $\\pi$ as inputs. Because of the absence of representation vectors, the dimensions of weight in equation (5) for prior model are W ′(1)z $W _ { z } ^ { ' ( 1 ) } \\in \\mathbb { R } ^ { d _ { z } \\times d _ { h } }$ , $\\mathbf { b } _ { z } ^ { ' ( 1 ) } \\in \\mathbb { R } ^ { d _ { z } }$ . We use a reparameterization trick to obtain a representation of latent variable $\\mathbf { z }$ : $\\mathbf h _ { z } ^ { \\prime } = \\pmb { \\mu } + \\pmb { \\sigma } \\pmb { \\epsilon }$ , $\\epsilon \\sim \\mathcal { N } ( 0 , I )$ . During translation, $\\mathbf { h } _ { z } ^ { \\prime }$ is set as the mean of $p _ { \\theta } ( \\mathbf { z } | \\mathbf { x } )$ . Then, $\\mathbf { h } _ { z } ^ { \\prime }$ is projected onto the target space as ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/fcea07378be0eca7db3ccf46a7e91732f1442d9772a1f368e90dce6e0187e23d.jpg",
+        "text": "$$\n\\mathbf { h } _ { e } ^ { \\prime } = g ( W _ { z } ^ { ( 2 ) } \\mathbf { h } _ { z } ^ { \\prime } + \\mathbf { b } _ { z } ^ { ( 2 ) } ) \\quad \\mathrm { w h e r e ~ } \\mathbf { h } _ { e } ^ { \\prime } \\in \\mathbb { R } ^ { d _ { e } } .\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "${ \\bf h } _ { e } ^ { \\prime }$ is then integrated into the neural machine translation’s decoder. ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.3 DECODER ",
+        "text_level": 1,
+        "bbox": [
+            174,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "This section links to the orange part of Figure 1. Given the source sentence $\\mathbf { x }$ and the latent variable $\\mathbf { z }$ , decoder defines the probability over translation $\\mathbf { y }$ as ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "img_path": "images/299dae0bf7b503a86a3de4e96e9f8b69988b20636ff9692e950426a0ab3ffeb3.jpg",
+        "text": "$$\np ( \\mathbf { y } | \\mathbf { z } , \\mathbf { x } ) = \\prod _ { j = 1 } ^ { T } p ( \\mathbf { y } _ { j } | \\mathbf { y } _ { < j } , \\mathbf { z } , \\mathbf { x } ) .\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "How we define the probability over translation $\\mathbf { y }$ is fundamentally the same as VNMT, except for using conditional GRU instead of GRU. Conditional GRU involves two GRUs and an attention mechanism. We integrate a latent variable $\\mathbf { z }$ into the second GRU. We describe it in the appendix. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "3.4 MODEL TRAINING ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Monte Carlo sampling method is used to approximate the expectation over the posterior Eq. (2), $\\begin{array} { r } { \\mathbb { E } _ { q _ { \\phi } ( \\mathbf { z } | \\mathbf { x } , \\mathbf { y } , \\pi ) } \\approx \\frac { 1 } { L } \\sum _ { l = 1 } ^ { L } \\log p _ { \\theta } ( \\mathbf { y } | \\mathbf { x } , \\mathbf { h } _ { z } ^ { ( l ) } ) } \\end{array}$ , where $L$ is the number of samplings. The training objective is defined as ",
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+        "page_idx": 5
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+    {
+        "type": "equation",
+        "img_path": "images/46806f443a5d1b257d6202fc27ff7119c7a1f533c7430b581a327e357fcab959.jpg",
+        "text": "$$\n\\mathcal { L } ( \\boldsymbol { \\theta } , \\boldsymbol { \\phi } ) = - \\mathrm { D } _ { \\mathrm { K L } } \\left[ q _ { \\phi } ( \\mathbf { z } | \\mathbf { x } , \\mathbf { y } , \\boldsymbol { \\pi } ) | | p _ { \\theta } ( \\mathbf { z } | \\mathbf { x } ) \\right] + \\frac { 1 } { L } \\sum _ { l = 1 } ^ { L } \\sum _ { j = 1 } ^ { T } \\log p _ { \\theta } ( \\mathbf { y } _ { j } | \\mathbf { y } _ { < j } , \\mathbf { x } , \\mathbf { h } _ { z } ^ { ( l ) } ) ,\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where $\\mathbf { h } _ { z } = \\pmb { \\mu } + \\pmb { \\sigma } \\cdot \\pmb { \\epsilon } , \\pmb { \\epsilon } \\sim \\mathcal { N } ( 0 , I )$ . The first term, KL divergence, can be computed analytically and is differentiable because both distributions are Gaussian. The second term is also differentiable. We set $L$ as 1. Overall, the objective $\\mathcal { L }$ is differentiable. Therefore, we can optimize the parameter $\\theta$ and variational parameter $\\phi$ using gradient ascent techniques. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4 EXPERIMENTS ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.1 EXPERIMENTAL SETUP ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We used Multi30k (Elliott et al., 2016) as the dataset. Multi30k have an English description and a German description for each corresponding image. We handle 29,000 pairs as training data, 1,014 pairs as validation data, and 1,000 pairs as test data. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Before training, punctuation normalization and lowercase are applied to both English and German sentences by Moses (Koehn et al., 2007) scripts2. Compound-word splitting is conducted only to German sentences using Sennrich et al. $( 2 0 1 \\dot { 6 } ) ^ { 3 }$ . Then we tokenize sentences2 and use them as training data. We produce vocabulary dictionaries from training data. The vocabulary becomes 10,211 words for English and 13,180 words for German after compound-word splitting. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Image features are extracted using VGG-19 CNN (Simonyan & Zisserman, 2014). We use 4096- dimensional fc7 features. To extract the object’s region, we use Fast R-CNN (Girshick, 2015). Fast R-CNN is trained on ImageNet and MSCOCO dataset 4. ",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "All weights are initialized by $\\mathcal { N } ( 0 , 0 . 0 1 \\mathbf { I } )$ . We use the adadelta algorithm as an optimization method. The hyperparameters used in the experiment are presented in the Appendix. All models are trained with early stopping. When training, VNMT is fine-tuned by NMT model and our models are finetuned using VNMT. When translating, we use beam-search. The beam-size is set as 12. Before evaluation, we restore split words to the original state and de-tokenize2 generated sentences. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We implemented proposed models based on $d l 4 m t ^ { 5 }$ . Actually, dl4mt is fundamentally the same model as Bahdanau et al. (2015), except that its decoder employs conditional GRU6. We implemented VNMT also with conditional GRU so small difference exists between our implementation and originally proposed VNMT which employs normal GRU as a decoder. We evaluated results based on METEOR and BLUE using MultEval 7. ",
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+        "page_idx": 5
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+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.2 RESULT ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Table 1 presents experiment results. It shows that our models outperforms the baseline in both METEOR and BLEU. Figure 4 shows the plot of METEOR score of baselines and our models models in validation. Figure 5 shows the plot of METEOR score and the source sentence length. ",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/ba82b395bd30213c57d6b3bf44aafdcbbab8ac2771bc15054d7f9a543da7db27.jpg",
+        "table_caption": [
+            "Table 1: Evaluation Result on Multi30k dataset (English–German). The scores in parentheses are computed with ‘-norm’ parameter. NMT is dl4mt’s NMT (in the session3 directory). The score of the CMU is from (Huang et al., 2016). "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td colspan=\"2\"></td><td colspan=\"2\">METEOR↑</td><td colspan=\"2\">BLEU↑</td></tr><tr><td colspan=\"2\"></td><td>val</td><td>test</td><td>val</td><td>test</td></tr><tr><td rowspan=\"3\"></td><td>NMT</td><td>51.5 (55.8)</td><td>50.5 (54.9)</td><td>35.8</td><td>33.1</td></tr><tr><td>VNMT</td><td>52.2 (56.3)</td><td>51.1 (55.3)</td><td>37.0</td><td>34.9</td></tr><tr><td>CMU</td><td>（）</td><td>1 (54.1)</td><td>1</td><td>1</td></tr><tr><td rowspan=\"4\">Our Model</td><td>G</td><td>50.6 (54.8)</td><td>52.4 (56.0)</td><td>34.5</td><td>36.5</td></tr><tr><td>G+O-AVG</td><td>51.8 (55.8)</td><td>51.8 (55.8)</td><td>35.7</td><td>35.8</td></tr><tr><td>G+O-RNN</td><td>51.8 (56.1)</td><td>51.0 (55.4)</td><td>35.9</td><td>34.9</td></tr><tr><td>G+O-TXT</td><td>52.6 (56.8)</td><td>51.7 (56.0)</td><td>36.6</td><td>35.1</td></tr></table>",
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.3 QUANTITATIVE ANALYSIS ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Table 1 shows that G scores the best in proposed models. In G, we simply put the feature of the original image. Actually, proposed model does not benefit from R-CNN, presumably because we can not handle sequences of image features very well. For example, $\\mathrm { G } { + } \\mathrm { O }$ -AVG uses the average of multiple image features, but it only makes the original image information unnecessarily confusing. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Figure 4 shows that G and $\\mathrm { G } { + } \\mathrm { O } { } \\mathrm { \\cdot }$ -AVG outperforms VNMT almost every time, but all model scores increase suddenly in the 17,000 iteration validation. We have no explanation for this behavior. Figure 4 also shows that G and $\\mathrm { G } { + } \\mathrm { O } { } \\mathrm { \\mathrm { \\Omega } }$ -AVG scores fluctuate more moderately than others. We state that G and $_ \\mathrm { G + O }$ -AVG gain stability by adding image information. When one observes the difference between the test score and the validation score for each model, baseline scores decrease more than proposed model scores. Especially, the G score increases in the test, simply because proposed models produce a better METEOR score on average, as shown in Figure 4. ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Figure 5 shows that G and $\\mathrm { G } { + } \\mathrm { O }$ -AVG make more improvements on baselines in short sentences than in long sentences, presumably because $q _ { \\phi } ( \\mathbf { z } | \\mathbf { x } , \\mathbf { y } , \\boldsymbol { \\pi } )$ can model $\\mathbf { z }$ well when a sentence is short. Image features always have the same dimension, but underlying semantics of the image and text differ. We infer that when the sentence is short, image feature representation can afford to approximate the underlying semantic, but when a sentence is long, image feature representation can not approximate the underlying semantic. ",
+        "bbox": [
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+        "page_idx": 6
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+    {
+        "type": "text",
+        "text": "Multi30k easily becomes overfitted, as shown in Figure 8 and 9 in the appendix. This is presumably because 1) Multi30k is the descriptions of image, making the sentences short and simple, and 2) Multi30k has 29,000 sentences, which could be insufficient. In the appendix, we show how the parameter setting affects the score. One can see that decay-c has a strong effect. Huang et al. (2016) states that their proposed model outperforms the baseline (NMT), but we do not have that observation. It can be assumed that their baseline parameters are not well tuned. ",
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+    },
+    {
+        "type": "text",
+        "text": "4.4 QUALITATIVE ANALYSIS ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We presented the top 30 sentences, which make the largest METEOR score difference between G and VNMT, to native speakers of German and get the overall comments. They were not informed of our model training with image in addition to text. These comments are summarized into two general remarks. One is that G translates the meaning of the source material more accurately than VNMT. The other is that our model has more grammatical errors as prepositions’ mistakes or missing verbs compared to VNMT. We assume these two remarks are reasonable because G is trained with images which mainly have a representation of noun rather than verb, therefore can capture the meaning of materials in sentence. ",
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+    },
+    {
+        "type": "image",
+        "img_path": "images/336f0b01b64b29847f26f5ecff9a7f50cb3d156bfae6b39739bff0d875544a49.jpg",
+        "image_caption": [
+            "Figure 4: METEOR score to the validation data which are calculated for each 1000 iterations. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/5cbe81cb72340f2ba8e4f579766d3dc674988f34d481a805fadc437a74525605.jpg",
+        "image_caption": [
+            "Figure 5: METEOR score on different groups of the source sentence length. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "type": "text",
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+    {
+        "type": "text",
+        "text": "Figure 6 presents the translation results and the corresponding image which G translates more accurately than VNMT in METEOR. Figure 7 presents the translation results and the corresponding image which G translates less accurately than VNMT in METEOR. Again, we note that our model does not use image during translating. In Figure 6, G translates ”a white and black dog” correctly while VNMT translates it incorrectly implying ”a white dog and a black dog”. We assume that G correctly translates the source because G captures the meaning of material in the source. In Figure 7, G incorrectly translates the source. Its translation result is missing the preposition meaning ”at”, which is hardly represented in image.We present more translation examples in appendix. ",
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+    {
+        "type": "image",
+        "img_path": "images/3e6e262a2cb9ed0521cc90b099233c2907e3bb10cdea3ffc73cf509db5803456.jpg",
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+    {
+        "type": "image",
+        "img_path": "images/f5285ea63366850a021ab9f7f8e2cac294f6d2bbde53ffb04b34c0156f44619e.jpg",
+        "image_caption": [
+            "Figure 6: Translation 1 "
+        ],
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+    {
+        "type": "image",
+        "img_path": "images/b0308383548bfd1bdb406863a7474d490fee0deafc740e5feabcee5ef1f7bab4.jpg",
+        "image_caption": [
+            "Figure 7: Translation 2 "
+        ],
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+            375
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "5 CONCLUSION ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            429,
+            320,
+            444
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "As described herein, we proposed the neural machine translation model that explicitly has a latent variable that includes underlying semantics extracted from both text and images. Our model outperforms the baseline in both METEOR and BLEU scores. Experiments and analysis present that our model can generate more accurate translation for short sentences. In qualitative analysis, we present that our model can translate nouns accurately while our model make grammatical errors. ",
+        "bbox": [
+            174,
+            459,
+            825,
+            530
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "REFERENCES ",
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+        "text": "Lucia Specia, Stella Frank, Khalil Sima ’an, and Desmond Elliott. A shared Task on Multimodal Machine Translation and Crosslingual Image Description. In Proceedings of the First Conference on Machine Translation, Berlin, Germany. Association for Computational Linguistics, 2016. ",
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+        "text": "Ilya Sutskever, Oriol Vinyals, and Quoc V Le. Sequence to Sequence Learning with Neural Networks. In NIPS, 2014. ",
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+        "type": "text",
+        "text": "Zhaopeng Tu, Zhengdong Lu, Yang Liu, Xiaohua Liu, and Hang Li. Modeling Coverage for Neural Machine Translation. In ACL, 2016. ",
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+            173,
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "Kelvin Xu, Jimmy Ba, Ryan Kiros, Kyunghyun Cho, Aaron Courville, Ruslan Salakhutdinov, Richard S Zemel, and Yoshua Bengio. Show, Attend and Tell: Neural Image Caption Generation with Visual Attention. In CVPR, 2015. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Biao Zhang, Deyi Xiong, and Jinsong Su. Variational Neural Machine Translation. In EMNLP, 2016. ",
+        "bbox": [
+            176,
+            832,
+            821,
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+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "A DERIVATION OF LOWER BOUNDS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            102,
+            485,
+            118
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "The lower bound of our model can be derived as follows: ",
+        "bbox": [
+            174,
+            132,
+            549,
+            147
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "equation",
+        "img_path": "images/6502f6b973ad8ec97a68b43790daf2182aca15ec76644b4f658449b216fde451.jpg",
+        "text": "$$\n\\begin{array} { l l l } { p ( \\mathbf { y } | \\mathbf { x } ) } & { = } & { \\displaystyle \\int p ( \\mathbf { y } , \\mathbf { z } | \\mathbf { x } ) d \\mathbf { z } } \\\\ { \\displaystyle } & { = } & { \\displaystyle \\int p ( \\mathbf { z } | \\mathbf { x } ) p ( \\mathbf { y } | \\mathbf { z } , \\mathbf { x } ) d \\mathbf { z } } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            380,
+            151,
+            617,
+            217
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "equation",
+        "img_path": "images/f3b82a6e19832c2302eff7d41d12b5e9c5026c1c1b6cbe2164bace73bb36d10d.jpg",
+        "text": "$$\n{ \\begin{array} { r c l } { \\log p ( \\mathbf { y } | \\mathbf { x } ) } & { = } & { \\log \\int q ( \\mathbf { z } | \\mathbf { x } , \\mathbf { y } , \\pi ) { \\frac { p ( \\mathbf { z } | \\mathbf { x } ) p ( \\mathbf { y } | \\mathbf { z } , \\mathbf { x } ) } { q ( \\mathbf { z } | \\mathbf { x } , \\mathbf { y } , \\pi ) } } d \\mathbf { z } } \\\\ & { \\geq } & { \\displaystyle \\int q ( \\mathbf { z } | \\mathbf { x } , \\mathbf { y } , \\pi ) \\log { \\frac { p ( \\mathbf { z } | \\mathbf { x } ) p ( \\mathbf { y } | \\mathbf { z } , \\mathbf { x } ) } { q ( \\mathbf { z } | \\mathbf { x } , \\mathbf { y } , \\pi ) } } d \\mathbf { z } } \\\\ & { = } & { \\displaystyle \\int q ( \\mathbf { z } | \\mathbf { x } , \\mathbf { y } , \\pi ) \\left( \\log { \\frac { p ( \\mathbf { z } | \\mathbf { x } ) } { q ( \\mathbf { z } | \\mathbf { x } , \\mathbf { y } ) } } + \\log p ( \\mathbf { y } | \\mathbf { z } , \\mathbf { x } ) \\right) d \\mathbf { z } } \\\\ & { = } & { \\displaystyle - \\mathrm { D } _ { \\mathrm { K L } } \\left[ q ( \\mathbf { z } | \\mathbf { x } , \\mathbf { y } , \\pi ) | | p ( \\mathbf { z } | \\mathbf { x } ) \\right] + \\mathbb { E } _ { q ( \\mathbf { z } | \\mathbf { x } , \\mathbf { y } , \\pi ) } \\left[ \\log p ( \\mathbf { y } | \\mathbf { z } , \\mathbf { x } ) \\right] } \\\\ & { = } & { \\displaystyle { \\mathcal { L } } } \\end{array} }\n$$",
+        "text_format": "latex",
+        "bbox": [
+            250,
+            236,
+            746,
+            377
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "B CONDITIONAL GRU ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            393,
+            379,
+            411
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Conditional GRU is implemented in dl4mt. Caglayan et al. (2016) extends Conditional GRU to make it capable of receiving image information as input. The first GRU computes intermediate representation $s _ { j } ^ { \\prime }$ as ",
+        "bbox": [
+            173,
+            425,
+            823,
+            469
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "equation",
+        "img_path": "images/82bdaf12150fc3d8e9e717efde53d35c62a587f9dfaba72176b6817c40bdc457.jpg",
+        "text": "$$\n\\begin{array} { r } { \\mathbf { s } _ { j } ^ { \\prime } = ( 1 - \\mathbf { o } _ { j } ^ { \\prime } ) \\odot \\underline { { \\mathbf { s } } } _ { j } ^ { \\prime } + \\mathbf { o } _ { j } ^ { \\prime } \\odot \\mathbf { s } _ { j - 1 } } \\\\ { \\mathbf { s } _ { j } ^ { \\prime } = \\operatorname { t a n h } ( W ^ { \\prime } E \\left[ \\mathbf { y } _ { j - 1 } \\right] + \\mathbf { r } _ { j } ^ { \\prime } \\odot ( U ^ { \\prime } \\mathbf { s } _ { j - 1 } ) ) } \\\\ { \\mathbf { r } _ { j } ^ { \\prime } = \\sigma ( W _ { r } ^ { \\prime } E \\left[ \\mathbf { y } _ { j - 1 } \\right] + U _ { r } ^ { \\prime } \\mathbf { s } _ { j - 1 } ) } \\\\ { \\mathbf { o } _ { j } ^ { \\prime } = \\sigma ( W _ { o } ^ { \\prime } E \\left[ \\mathbf { y } _ { j - 1 } \\right] + U _ { o } ^ { \\prime } \\mathbf { s } _ { j - 1 } ) } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            341,
+            474,
+            622,
+            556
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "where $E \\in \\mathbb { R } ^ { d _ { e m b } \\times d _ { t } }$ signifies the target word embedding, $\\underline { { \\mathbf { s } } } _ { j } ^ { \\prime } \\in \\mathbb { R } ^ { d _ { h } }$ denotes the hidden state, $\\mathbf { r } _ { j } ^ { \\prime } \\in \\mathbb { R } ^ { d _ { h } }$ and ${ \\bf o } _ { j } ^ { \\prime } \\in \\mathbb { R } ^ { d _ { h } }$ respectively represent the reset and update gate activations. $d _ { t }$ stands for the dimension of target; the unique number of target words. $[ W ^ { \\prime } , W _ { r } ^ { \\prime } , W _ { o } ^ { \\prime } ] \\in \\mathbb { R } ^ { d _ { h } \\times d _ { e m b } } , [ U ^ { \\prime } , U _ { r } ^ { \\prime } , U _ { o } ^ { \\prime } ] \\in$ $\\mathbb { R } ^ { d _ { h } \\times d _ { h } }$ are the parameters to be learned. ",
+        "bbox": [
+            173,
+            559,
+            825,
+            623
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Context vector $\\mathbf { c } _ { j }$ is obtained as ",
+        "bbox": [
+            173,
+            630,
+            385,
+            645
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "equation",
+        "img_path": "images/8af5c4d5b27d353d4a326de062e21493febd2eacc9bc99e2fb71b765366ac08a.jpg",
+        "text": "$$\n\\begin{array} { r } { \\mathbf { c } _ { j } = \\operatorname { t a n h } \\left( \\displaystyle \\sum _ { i = 1 } ^ { T _ { f } } \\alpha _ { i j } \\mathbf { h } _ { i } \\right) } \\\\ { \\displaystyle \\alpha _ { i j } = \\frac { \\exp \\left( \\mathbf { e } _ { i j } \\right) } { \\sum _ { k = 1 } ^ { T _ { f } } \\exp \\left( e _ { k j } \\right) } } \\\\ { \\mathbf { e } _ { i j } = U _ { a t t } \\mathrm { t a n h } \\big ( W _ { c a t t } \\mathbf { h } _ { i } + W _ { a t t } \\mathbf { s } _ { j } ^ { \\prime } \\big ) } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            361,
+            650,
+            604,
+            757
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "where $[ { U _ { a t t } } , { W _ { c a t t } } , { W _ { a t t } } ] \\in \\mathbb { R } ^ { d _ { h } \\times d _ { h } }$ are the parameters to be learned. ",
+        "bbox": [
+            173,
+            762,
+            635,
+            780
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "The second GRU computes ${ \\bf s } _ { j }$ from $\\mathbf { s } _ { j } ^ { \\prime } , \\mathbf { c } _ { j }$ and ${ \\bf h } _ { e } ^ { \\prime }$ as ",
+        "bbox": [
+            174,
+            785,
+            519,
+            801
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "equation",
+        "img_path": "images/23f734b0c3a08c3fb01f46f0d47f13e1958a31b641b8ea49c1bb8c45641aeb0b.jpg",
+        "text": "$$\n\\begin{array} { r } { \\mathbf s _ { j } = ( 1 - \\mathbf o _ { j } ^ { \\prime } ) \\odot \\underline { { \\mathbf s } } _ { j } + \\mathbf o _ { j } \\odot \\mathbf s _ { j } ^ { \\prime } } \\\\ { \\underline { { \\mathbf s } } _ { j } = \\operatorname { t a n h } ( W \\mathbf c _ { j } + \\mathbf r _ { j } \\odot ( U \\mathbf s _ { j } ^ { \\prime } ) + V \\mathbf h _ { e } ^ { \\prime } ) } \\\\ { \\mathbf r _ { j } = \\sigma ( W _ { r } \\mathbf c _ { j } + U _ { r } \\mathbf s _ { j } ^ { \\prime } + V _ { r } \\mathbf h _ { e } ^ { \\prime } ) } \\\\ { \\mathbf o _ { j } = \\sigma ( W _ { o } \\mathbf c _ { j } + U _ { o } \\mathbf s _ { j } ^ { \\prime } + V _ { o } \\mathbf h _ { e } ^ { \\prime } ) } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            349,
+            806,
+            614,
+            887
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "where $\\underline { { \\mathbf { s } } } _ { j } \\in \\mathbb { R } ^ { d _ { h } }$ stands for the hidden state, $\\mathbf { r } _ { j } \\in \\mathbb { R } ^ { d _ { h } }$ and $\\mathbf { o } _ { j } ~ \\in ~ \\mathbb { R } ^ { d _ { h } }$ are the reset and update gate activations. $[ W , W _ { r } , W _ { o } ] \\ \\in \\ \\mathbb { R } ^ { d _ { h } \\times d _ { h } } , [ U , U _ { r } , U _ { o } ] \\ \\in \\ \\mathbb { R } ^ { d _ { h } \\times d _ { h } } , [ V , V _ { r } , V _ { o } ] \\ \\in \\ \\mathbb { R } ^ { d _ { h } \\times d _ { z } }$ are the ",
+        "bbox": [
+            174,
+            891,
+            823,
+            926
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "parameters to be learned. We introduce ${ \\bf h } _ { e } ^ { \\prime }$ obtained from a latent variable here so that a latent variable can affect the representation ${ \\bf s } _ { j }$ through GRU units. ",
+        "bbox": [
+            171,
+            103,
+            823,
+            132
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Finally, the probability of $y$ is computed as ",
+        "bbox": [
+            174,
+            138,
+            457,
+            154
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "equation",
+        "img_path": "images/f968de7ed3c90ef7d20c5eef06c2507c4c5715eb815a39c0c100bb701d4b2774.jpg",
+        "text": "$$\n\\begin{array} { r } { \\mathbf { u } _ { j } = L _ { u } \\mathrm { t a n h } ( E \\left[ \\mathbf { y } _ { j - 1 } \\right] + L _ { s } \\mathbf { s } _ { j } + L _ { x } \\mathbf { c } _ { j } ) } \\\\ { P ( \\mathbf { y } _ { j } | \\mathbf { y } _ { j - 1 } , \\mathbf { s } _ { j } , \\mathbf { c } _ { j } ) = \\mathrm { S o f t m a x } ( \\mathbf { u } _ { j } ) } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            346,
+            160,
+            620,
+            198
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "where $L _ { u } \\in \\mathbb { R } ^ { d _ { t } \\times d _ { e m b } }$ , $L _ { s } \\in \\mathbb { R } ^ { d _ { e m b } \\times d _ { h } }$ and $L _ { c } \\in \\mathbb { R } ^ { d _ { e m b } \\times d _ { h } }$ are the parameters to be learned. ",
+        "bbox": [
+            171,
+            203,
+            785,
+            220
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "C TRAINING DETAIL ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            239,
+            362,
+            257
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "C.1 HYPERPARAMETERS ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            272,
+            359,
+            287
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Table 2 presents parameters that we use in the experiments. ",
+        "bbox": [
+            174,
+            299,
+            562,
+            314
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "table",
+        "img_path": "images/883b83a46b4563901602a6c1dc431482e25758f8a151cea196a8465ec6b538d2.jpg",
+        "table_caption": [
+            "Table 2: Hyperparameters. The name is the variable name of dl4mt except for dimv and dim pic, which are the dimension of the latent variables and image embeddings. We set dim (number of LSTM unit size) and dim word (dimensions of word embeddings) 256, batchsize 32, maxlen (max output length) 50 and $l r$ (learning rate) 1.0 for all models. decay- $c$ is weights on L2 regularization. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td colspan=\"2\"></td><td>dimv</td><td>dim_pic</td><td>decay-c</td></tr><tr><td rowspan=\"3\">Our Model</td><td>NMT</td><td>1</td><td>256</td><td>0.001</td></tr><tr><td>VNMT</td><td>256</td><td>256</td><td>0.0005</td></tr><tr><td>G G+O-AVG</td><td>256 256</td><td>512 256</td><td>0.001 0.0005</td></tr></table>",
+        "bbox": [
+            310,
+            401,
+            687,
+            503
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "We found that Multi30k dataset is easy to overfit. Figure 8 and Figure 9 present training cost and validation METEOR score graph of the two experimental settings of the NMT model. Table 3 presents the hyperparameters which were used in the experiments. Large decay- $c$ ans small batchsize give the better METEOR scores in the end. Training is stopped if there is no validation cost improvements over the last 10 validations. ",
+        "bbox": [
+            173,
+            522,
+            826,
+            593
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "image",
+        "img_path": "images/c7bae09f36a43d6018ae579ac15c03de257556b8181a0a9f38fd44944c05724c.jpg",
+        "image_caption": [
+            "Figure 8: NMT Training Cost "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            199,
+            614,
+            475,
+            784
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "image",
+        "img_path": "images/4cf686d842327ec69a90e4b59544c93c4bbf7f5db98b7ef11c7a1a405e320bf0.jpg",
+        "image_caption": [
+            "Figure 9: NMT Validation METEOR score "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            531,
+            614,
+            799,
+            784
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "table",
+        "img_path": "images/c456d60b1958b7c4cc5590dafbc840a9ea90f793a80d17524128d3f410acec0f.jpg",
+        "table_caption": [
+            "Table 3: Hyperparameters using the experiments in the Figure 8 and 9 "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>dim</td><td>dim_word</td><td>lr</td><td>decay-c</td><td>maxlen</td><td>batchsie</td></tr><tr><td>1</td><td>256</td><td>256</td><td>1.0</td><td>0.0005</td><td>30</td><td>128</td></tr><tr><td>2</td><td>256</td><td>256</td><td>1.0</td><td>0.001</td><td>50</td><td>32</td></tr></table>",
+        "bbox": [
+            295,
+            869,
+            700,
+            915
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Figure 10 presents the English word length histogram of the Multi30k test dataset. Most sentences in the Multi30k are less than 20 words. We assume that this is one of the reasons why Multi30k is easy to overfit. ",
+        "bbox": [
+            173,
+            103,
+            825,
+            146
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "image",
+        "img_path": "images/2c9cbbbc325b95ee17810529bec3d8c10b1b4be16b57ee667ba3a6348e29d4a5.jpg",
+        "image_caption": [
+            "Figure 10: Word Length Histogram of the Multi30k Test Dataset "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            346,
+            174,
+            635,
+            348
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "C.2 COST GRAPH ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            411,
+            307,
+            426
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Figure 11 and 12 present the training cost and validation cost graph of each models. Please note that VNMT fine-tuned NMT, and other models fine-tuned VNMT. ",
+        "bbox": [
+            174,
+            438,
+            826,
+            467
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "image",
+        "img_path": "images/06cdb8130b72418e484bd88c7a72c3295a6dd43723f58361d1b6fc7254026797.jpg",
+        "image_caption": [
+            "Figure 11: Training cost "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            194,
+            488,
+            851,
+            763
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "C.3 TRANSLATION EXAMPLES",
+        "text_level": 1,
+        "bbox": [
+            174,
+            824,
+            400,
+            838
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "We present some selected translations from VNMT and our proposed model (G). As of translation 3 to 5 our model give the better METEOR scores than VNMT and as of translation 6 to 8 VNMT give the better METEOR scores than our models. ",
+        "bbox": [
+            174,
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+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "image",
+        "img_path": "images/14471daa059b8d95974e504c430617cd19cc8a3ebbfa34c05662cdee40253162.jpg",
+        "image_caption": [
+            "Figure 12: Validation cost "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            199,
+            132,
+            848,
+            406
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "image",
+        "img_path": "images/acc29606458a5807494c450d7d98cfbf2019552dbf1817b3f5117cb49d155fc3.jpg",
+        "image_caption": [
+            "Figure 13: Translation 3 "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            401,
+            491,
+            676,
+            806
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "table",
+        "img_path": "images/240f2e29898a1b38f193efebd44fb38557f72522869993c09bbcae7d9178a52b.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=1 colspan=1>Source</td><td rowspan=1 colspan=1> two boys inside a fence jump in the air while holding a basketball.</td></tr><tr><td rowspan=1 colspan=1>Truth</td><td rowspan=1 colspan=1> zwei jungen innerhalb eines zaunes springen in die luft und halten dabei einen basketball.</td></tr><tr><td rowspan=1 colspan=1>VNMT</td><td rowspan=1 colspan=1> zwei jungen in einem zaun springen in die luft, wahrend sie einen basketball hält.</td></tr><tr><td rowspan=1 colspan=1>Our Model (G)</td><td rowspan=1 colspan=1> zwei jungen in einem zaun springen in die luft und halten dabei einen basketball.</td></tr></table>",
+        "bbox": [
+            173,
+            810,
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+        ],
+        "page_idx": 13
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+    {
+        "type": "image",
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+        "image_caption": [
+            "Figure 14: Translation 4 "
+        ],
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+        "image_caption": [
+            "Figure 15: Translation 5 "
+        ],
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+            "Figure 16: Translation 6 "
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+            "Figure 17: Translation 7 "
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+            "Figure 18: Translation 8 "
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+]

parse/train/B1uvH_gC-/B1uvH_gC-.md

@@ -0,0 +1,238 @@
+# PARAMETRIC MANIFOLD LEARNING VIA SPARSEMULTIDIMENSIONAL SCALING
+
+Anonymous authors Paper under double-blind review
+
+# ABSTRACT
+
+We propose a metric-learning framework for computing distance-preserving maps that generate low-dimensional embeddings for a certain class of manifolds. We employ Siamese networks to solve the problem of least squares multidimensional scaling for generating mappings that preserve geodesic distances on the manifold. In contrast to previous parametric manifold learning methods we show a substantial reduction in training effort enabled by the computation of geodesic distances in a farthest point sampling strategy. Additionally, the use of a network to model the distance-preserving map reduces the complexity of the multidimensional scaling problem and leads to an improved non-local generalization of the manifold compared to analogous non-parametric counterparts. We demonstrate our claims on point-cloud data and on image manifolds and show a numerical analysis of our technique to facilitate a greater understanding of the representational power of neural networks in modeling manifold data.
+
+# 1 INTRODUCTION
+
+The characterization of distance preserving maps is of fundamental interest to the problem of nonlinear dimensionality reduction and manifold learning. For the purpose of achieving a coherent global representation, it is often desirable to embed the high-dimensional data into a space of low dimensionality while preserving the metric structure of the data manifold. The intrinsic nature of the geodesic distance makes such a representation depend only on the geometry of the manifold and not on how it is embedded in ambient space. In the context of dimensionality reduction this property makes the resultant embedding meaningful.
+
+The success of deep learning has shown that neural networks can be trained as powerful function approximators of complex attributes governing various visual and auditory phenomena. The availability of large amounts of data and computational power, coupled with parallel streaming architectures and improved optimization techniques, have all led to computational frameworks that efficiently exploit their representational power. However, a study of their behavior under geometric constraints is an interesting question which has been relatively unexplored.
+
+In this paper, we use the computational infrastructure of neural networks to model maps that preserve geodesic distances on data manifolds. We revisit the classical geometric framework of multidimensional scaling to find a configuration of points that satisfy pairwise distance constraints. We show that instead of optimizing over the individual coordinates of the points, we can optimize over the function that generates these points by modeling this map as a neural network. This makes the complexity of the problem depend on the number of parameters of the network rather than the number of data points, and thus significantly reduces the memory and computational complexities, a property that comes into practical play when the number of data points is large. Additionally, the choice of modeling the isometric map with a parametric model provides a straightforward out-of-sample extension, which is a simple forward pass of the network.
+
+We exploit efficient sampling techniques that progressively select landmark points on the manifold by maximizing the spread of their pairwise geodesic distances. We demonstrate that a small amount of these landmark points are sufficient to train a network to generate faithful low-dimensional embeddings of manifolds. Figure 1 provides a visualization of the proposed approach. In the interest of gauging their effectiveness in representing manifolds, we perform a numerical analysis to measure the quality of embedding generated by neural networks and associate an order of accuracy to a given architecture. Finally, we demonstrate that parametric models provide better non-local generalization as compared to extrapolation formulas of their non-parametric counter parts.
+
+![](images/70625e1c8d170a331b7b17b153db79441811a3f732f614c93d90325b141700b4.jpg)  
+Figure 1: Learning to unfurl a ribbon: A three dimensional Helical Ribbon and its two dimensional embedding learned using a two-layer MLP. The network was trained using estimated pairwise geodesic distances between only 100 points (marked in black) out of the total 8192 samples.
+
+We advocate strengthening the link between axiomatic computation and parametric learning methodologies. Existing MDS frameworks use a geometrically meaningful objective in a cumbersome non-parametric framework. At the other end, learning based methods such as DrLim Hadsell et al. (2006) use a computationally desirable infrastructure yet a geometrically suboptimal objective requiring too many examples for satisfactory manifold learning. The proposed approach can be interpreted as taking the middle path by using a computationally desirable method of a parametric neural network optimized by the geometrically meaningful cost of multidimensional scaling.
+
+# 2 BACKGROUND AND PRIOR WORK
+
+# 2.1 MANIFOLD LEARNING
+
+The literature on manifold learning is dominated by spectral methods that have a characteristic computational template. The first step involves the computation of the $\mathbf { k }$ -nearest neighbors of all $N$ data points. Then, an $N \times N$ square matrix is populated using some geometric principle which characterizes the nature of the desired low dimensional embedding. The eigenvalue decomposition of this matrix is used to obtain the low-dimensional representation of the manifold. Laplacian Eigenmaps Belkin & Niyogi (2003), LLE Roweis & Saul (2000), HLLE Donoho & Grimes (2003), Diffusion Maps Coifman et al. (2005) etc. are considered to be local methods, since they are designed to minimize some form of local distortion and hence result in embeddings which preserve locality. Methods like Schwartz et al. (1989); Wolfson & Schwartz (1989) and Isomap Tenenbaum et al. (2000) are considered global because they enforce preserving all geodesic distances in the low dimensional embedding. Local methods lead to sparse matrix eigenvalue problems and hence are computationally advantageous. However, global methods are more robust to noise and achieve globally coherent embeddings, in contrast to the local methods which can sometimes lead to excessively clustered results. All spectral techniques are non-parametric in nature and hence do not characterize the map that generates them. Therefore, the computational burden of large spectral decompositions becomes a major drawback when the number of data-points is large. Bengio et al. (2004) and De Silva & Tenenbaum (2004) address this issue by providing formulas for out-of-sample extensions to the spectral algorithms. However, these interpolating formulations are computationally inefficient and exhibit poor non-local generalization of the manifold Bengio et al. (2013).
+
+# 2.2 MULTIDIMENSIONAL SCALING
+
+Multidimensional scaling (henceforth MDS) is a classical problem in geometry processing and data science and a powerful tool for obtaining a global picture of data when only pairwise distances or dissimilarity information is available. The core idea of MDS is to find an embedding $\mathbf { X } = \left[ \mathbf { x _ { 1 } } , \mathbf { x _ { 2 } } , \mathbf { x _ { 3 } } . . . \mathbf { x _ { N } } \right]$ such that the pairwise distances measured in the embedding space are faithful to the desired distances $\bf { D _ { s } } = [ d _ { i j } ^ { 2 } ] _ { i , j = 1 } ^ { i , j = N }$ as much as possible. There are two prominent versions of MDS: Classical Scaling and Least Squares Scaling. Classical Scaling is based on the observation that the double centering of a pairwise squared distance matrix gives an inner-product matrix which can be factored to obtain the desired embedding. Therefore, if $\begin{array} { r } { { \bf H } = { \bf I } - \frac { 1 } { n } { \mathbb { 1 } } { \mathbb { 1 } } ^ { T } } \end{array}$ is the centering matrix, classical scaling minimizes the Strain of the embedding configuration $\mathbf { X }$ given by
+
+$$
+\mathit { S t r a i n } ( \mathbf { X } ) = | | \mathbf { X } \mathbf { X } ^ { T } + \frac { 1 } { 2 } \mathbf { H } \mathbf { D } _ { \mathbf { s } } \mathbf { H } | | _ { F } ^ { 2 } ,
+$$
+
+and is computed conveniently using the eigen-decomposition of the $N \times N$ matrix $- \frac { 1 } { 2 } \mathbf { H D _ { s } H }$ . At the other end, least squares scaling is based on minimizing the misfits between the pairwise distances of $\mathbf { X } = \left[ \mathbf { x _ { 1 } } , \mathbf { x _ { 2 } } , \mathbf { x _ { 3 } } . . . \mathbf { x _ { N } } \right]$ and desired distances $[ \bf d _ { i j } ] _ { i , j = 1 } ^ { i , j = \mathbf { \bar { N } } }$ measured by the Stress function
+
+$$
+\mathit { S t r e s s } ( \mathbf { X } ) = \sum _ { i } \sum _ { j } \ : ( | | \mathbf { x _ { i } } - \mathbf { x _ { j } } | | - \mathbf { d _ { i j } } ) ^ { 2 } .
+$$
+
+In the context of manifold learning and dimensionality reduction, the MDS framework is enabled by estimating all pairwise geodesic distances with a shortest path algorithm like Dijkstra Dijkstra (1959) and using the minimizers of Equations 1 and 2 to generate global embeddings by preserving metric properties of the manifold.
+
+Schwartz et al. (1989); Wolfson & Schwartz (1989) along with Tenenbaum et al. (2000) were the first to suggest populating the inter-geodesic matrix $\mathbf { D _ { s } }$ using Dijkstra’s algorithm for preserving metric properties of manifolds. The SMACOF algorithm of De Leeuw & Mair (2011) and their variants Bronstein et al. (2006) are iterative least squares scaling algorithms for minimizing Stress in Equation (2). The computational bottleneck of dealing with a dense distance matrix requiring all pairwise distances led to faster algorithms like Aflalo $\&$ Kimmel (2013); Shamai et al. (2015) and Boyarski et al. (2017), that used spectral representations of the Laplace-Beltrami Operator of the manifold. Rosman et al. (2010) shows a least squares scaling technique which can overcome holes and non-convex boundaries of the manifold. All these algorithms are non-parametric and few out-of-sample extensions have been suggested De Silva & Tenenbaum (2004) to generalize them to new samples.
+
+# 2.3 NEURAL NETWORKS FOR MANIFOLD LEARNING
+
+Examining the ability of neural networks to represent data manifolds has received considerable interest and has been studied from multiple perspectives. From the viewpoint of unsupervised parametric manifold learning, one notable approach is based on the metric-learning arrangement of the Siamese configuration Hadsell et al. (2006); Bromley et al. (1994); Chopra et al. (2005). Similarly, the parametric version of the Stochastic Neighborhood Embedding van der Maaten (2009) is another example of using a neural network to generate a parametric map that is trained to preserve local structure Maaten & Hinton (2008). However, these techniques demand an extensive training effort requiring large number of training examples in order to generate satisfactory embeddings. Weston et al. (2012) use a parametric network to learn a classifier which enforces a manifold criterion, requiring nearby points to have similar representations. Basri & Jacobs (2017) have argued that neural-networks can efficiently represent manifolds as monotonic chain of linear segments by providing an architectural construction and analysis. However, they do not address the manifold learning problem and their experiments are based on supervised settings where the ground-truth embedding is known a priori. Gong et al. (2006); Mishne et al. (2017); Chui & Mhaskar (2016) use neural networks specifically for solving the out-of-sample extension problem for manifold learning. However, their procedure involves training a network to follow a pre-computed non-parametric embedding rather than adopting an entirely unsupervised approach thereby inheriting some of the deficiencies of the non-parametric methods.
+
+It is advantageous to adopt a parametric approach to non-linear dimensionality reduction and replace the computational block of the matrix construction and eigenvalue decomposition with a straightforward parametric computation. Directly characterizing the non-linear map provides a simple out-ofsample extension which is a plain forward pass of the network. More importantly, it is expected that the reduced and tightly controlled parameters would lead to an improved non-local generalization of the manifold Bengio et al. (2013).
+
+In Hadsell et al. (2006) (henceforth DrLim), it was proposed to use Siamese Networks for manifold learning using the popular hinge-embedding criterion (Equation (3)) as a loss function. A Siamese configuration (Figure 2) comprises of two identical networks that process two separate units of data to achieve output pairs that are compared in a loss function. The contrastive training comprises of constructing pairs $\{ \mathbf { X _ { 1 } ^ { ( k ) } } , \mathbf { X _ { 2 } ^ { ( k ) } } , \lambda ^ { ( k ) } \} _ { k = 1 } ^ { k = N }$ where $\lambda ^ { ( k ) } \in \{ 0 , 1 \}$ is a label for indicating a positive (a neighbor) or negative pair (not a neighbor) by building a nearest neighbor graph from the manifold data.
+
+![](images/2e204ad6304c9ea2bca00a267d9368dd47bc769f7c21d428f3697498d50fe0da.jpg)  
+Figure 2: Siamese Configuration
+
+$$
+\begin{array} { r l } { \displaystyle \mathcal { L } ( \boldsymbol { \Theta } ) = \sum _ { \mathbf { k } } \lambda ^ { ( \mathbf { k } ) } ~ | | \mathcal { F } _ { \boldsymbol { \Theta } } ( \mathbf { X _ { 1 } ^ { ( \mathbf { k } ) } } ) - \mathcal { F } _ { \boldsymbol { \Theta } } ( \mathbf { X _ { 2 } ^ { ( \mathbf { k } ) } } ) | | } & { } \\ { \displaystyle } & { \quad + ( \mathbf { 1 } - \lambda ^ { ( \mathbf { k } ) } ) ~ \operatorname* { m a x } ~ \{ \mathbf { 0 } , ~ \boldsymbol { \mu } - | | \mathcal { F } _ { \boldsymbol { \Theta } } ( \mathbf { X _ { 1 } ^ { ( \mathbf { k } ) } } ) - \mathcal { F } _ { \boldsymbol { \Theta } } ( \mathbf { X _ { 2 } ^ { ( \mathbf { k } ) } } ) | | \} } \end{array}
+$$
+
+Training with the loss in Equation (3) means that at any given update step, a negative pair contributes to the training only when their pairwise distance is less than $\mu$ . This leads to a hard-negative sampling problem where the quality of embedding depends on the selection of negative examples in order to prevent excessive clustering of the neighbors. This typically requires an extensive training effort with a huge amount of training data (30000 positive and approximately 17.9 million negatives for a total of 6000 data samples as reported in Hadsell et al. (2006)).
+
+# 3 A FRAMEWORK FOR PARAMETRIC MULTIDIMENSIONAL SCALING
+
+We propose to incorporate the ideas of Least Squares Scaling into the computational infrastructure of the Siamese configuration as shown in Figure 2. For every $\bar { \mathbf { k } } ^ { t h }$ pair, we estimate the geodesic distance using a shortest path algorithm and train the network to preserve these distances by minimizing the Stress function
+
+$$
+\mathcal { L } ( \boldsymbol { \Theta } ) = \sum _ { \mathbf { k } } \mathrm { ~ ( ~ } | | \mathcal { F } _ { \boldsymbol { \Theta } } ( \mathbf { X } _ { 1 } ^ { ( \mathbf { k } ) } ) - \mathcal { F } _ { \boldsymbol { \Theta } } ( \mathbf { X } _ { 2 } ^ { ( \mathbf { k } ) } ) \mathrm { ~ | | - \mathbf { d } ^ { ( \mathbf { k } ) } ~ ) ^ { 2 } ~ }
+$$
+
+The advantage of adopting the loss in Equation (4) over Equation (3) is that every pair of training data contributes to the learning process thereby eliminating the negative sampling problem. More importantly, it facilitates the use of efficient manifold sampling techniques like the Farthest Point Sampling strategy that make it possible to train with much fewer pairs of examples. The farthest point sampling strategy Bronstein et al. (2008) (also referred to as the MinMax strategy in De Silva & Tenenbaum (2004)) is a method to pick landmarks amongst the points of a discretely sampled manifold such that under certain conditions, these samples uniformly cover the manifold much as possible. Starting from a random selection, the landmarks are chosen one at a time such that, each new selection from the unused samples has the largest geodesic distance to the set of the selected sample points. Figure 3 provides a visualization of this sampling mechanism. We train the network by minimizing the loss in Equation (4) by computing the pairwise geodesic distances of the landmarks. Therefore, the pre-training computational effort is confined to computing the pairwise geodesic distances of only the landmark points. The proposed geometric manifold learning algorithm can be summarized in two steps,
+
+![](images/11c4e9f6c7f703ee00e0f45a02cc7c6d25db28a8f359a7e37e7fccc8199fbfd6.jpg)  
+Figure 3: 2D embeddings of a three dimensional S-Curve Manifold generated by a 2-Layer MLP with 70 hidden nodes, that was trained with varying number of landmark points obtained with the Farthest Point Sampling Algorithm.
+
+Step1: Compute the nearest-neighbor graph from the manifold data and obtain a set of landmarkpoints and their corresponding pairwise graph/geodesic distances using Dijkstra’s algorithm and the Farthest Point Strategy.
+
+Step2: Form a dataset of landmark pairs with corresponding geodesic distances and train network in Siamese configuration using the least-squares M $\{ \mathbf { X _ { 1 } ^ { ( k ) } , X _ { 2 } ^ { ( k ) } , d ^ { ( k ) } } \}$ (4)
+
+# 4 EXPERIMENTS
+
+# 4.1 3D POINT CLOUD DATA
+
+Our first set of experiments are based on point-cloud manifolds, e.g., like the Swiss Roll, S-Curve and the Helical Ribbon. We use a multilayer perceptron (MLP) with the PReLU() as the non-linear activation function, given by
+
+$$
+P R e L U ( x ) = \operatorname* { m a x } ( 0 , x ) + a \ \operatorname* { m i n } ( 0 , x ) ,
+$$
+
+where $a$ is a learnable parameter. The networks are trained using the ADAM optimizer with constants $( \beta _ { 1 } , \beta _ { 2 } ) = ( 0 . 9 5 , 0 . 9 9 )$ and a learning rate of 0.01 for 1000 iterations. We run each optimization 5 times with random initialization to ensure convergence. All experiments are implemented in python using the PyTorch framework Paszke et al. (2017). We used the scikit-learn machine learning library for the nearest-neighbor and scipy-sparse for Dijkstra’s shortest path algorithms.
+
+Figure 1 and 3 show the results of our method on the Helical Ribbon and S-Curve respectively with varying number of training samples (in black) out of a total of 8172 data points. The number of landmarks dictates the approximation quality of the low-dimensional embedding generated by the network. Training with too few samples will result in inadequate generalization which can be inferred from the corrugations of the unfurled results in the first two parts of Figure 3 and increasing the number of landmarks expectedly improves the quality of the embedding. We compute the Stress function (Equation (2)) of the entire point configuration to measure the quality of the MDS fit. Figure 4a shows the decay in the Stress as a function of the number of training points (or Landmarks) of a 2-Layer MLP.
+
+The natural next question to ask is how many landmarks? how many layers? and how many hidden nodes per layer? We observe that these questions relate to an analogous setup in numerical methods for differential equations. For a given numerical technique, the accuracy of the solution depends on the resolution of the spatial grid over which the solution is estimated. Therefore, numerical methods are ranked by an assessment of the order of accuracy their solutions observe. This can be obtained by assuming that the relationship between the approximation error $E$ and the resolution of the grid $h$ is given by
+
+![](images/1192f770f43cf79258d17aecf1b9b90fdc30122acdb142febb67172cda5f83e1.jpg)  
+Figure 4: Exploring the variations in architecture and the number of landmarks: (a) The logarithm of stress of all 8172 points as a function of number of landmarks. (b) Order of accuracy estimates of varying architectures.
+
+$$
+E = C h ^ { P }
+$$
+
+where $P$ is the order of accuracy of the technique and $C$ is some constant. Therefore, $P$ is obtained by computing the slope of the line obtained by charting $\log ( E )$ vs $\log ( h )$ ,
+
+$$
+\log ( E ) = \log ( C ) + P \ \log ( h ) .
+$$
+
+We extend the same principle to evaluate network architectures (in place of numerical algorithms) for estimating the quality of isometric maps. We use the generalized Stress in Equation (2) as the error function for Equation (6). We assume that due to the 2-approximate property of the fartstrategy Hochbaum & Shmoys (1985) the sampling is approximately uniform and hence $h \propto { \frac { 1 } { \sqrt { K } } }$ where $K$ is the number of landmarks. By varying the number of layers and the number of nodes per layer we associate an order of accuracy to each architecture using Equation (7). Figure 4b shows the results of our experiment. It shows that a single layer MLP has the capacity for modeling functions upto the first order of accuracy. Adding an additional layer increases the representational power by moving to a second order result. Adding more layers does not provide any substantive gain arguably due to a larger likelihood of over-fitting as seen in the considerably noisier estimates (in green). Therefore, a two layer MLP with 70 hidden nodes per layer can be construed as a good architecture for approximating the isometric map of the S-Curve of Figure 3 with 200 landmarks.
+
+# 4.2 IMAGE ARTICULATION MANIFOLDS
+
+We extend the parametric MDS framework to image articulation manifolds where each sample point is a binary image governed by the modulation of a few parameters. We specifically deal with image manifolds that are isometric to Euclidean space Donoho & Grimes (2005), that is, the geodesic distance between any two sample points is equal to the euclidean distance between their articulation parameters. In the context of the main discussion of this paper, which is metric preserving properties of manifolds, we find that such datasets provide an appropriate test-bed for evaluating metric preserving algorithms.
+
+We construct a horizon articulation manifold where each image contains two distinct regions separated by a horizon which is modulated by a linear combination of two fixed sinusoidal basis elements. See Figure 5.
+
+$$
+\begin{array} { r c l } { { { \cal I } _ { \alpha _ { 1 } , \alpha _ { 2 } } ( u , v ) } } & { { = } } & { { \mathbb { 1 } _ { \{ v \leq \psi _ { \alpha _ { 1 } , \alpha _ { 2 } } ( u ) \} } } } \\ { { } } & { { } } & { { } } \\ { { \psi _ { \alpha _ { 1 } , \alpha _ { 2 } } ( u ) } } & { { = } } & { { \alpha _ { 1 } \sin ( \omega _ { 1 } u ) + \alpha _ { 2 } \sin ( \omega _ { 2 } u ) } } \end{array}
+$$
+
+Thus, each sample has an intrinsic dimensionality of two - the articulation parameters $\left( \alpha _ { 1 } , \alpha _ { 2 } \right)$ which govern how the sinusoids representing the horizon are mixed. We sample the articulation
+
+![](images/21b58a74e5448145d64324281c028acc2f5278afbafe7ee573e8caef648b3fc3.jpg)  
+Figure 5: Visualizing a horizon articulation manifold: 1000 samples generated as per equations 8 and 9 with $\omega _ { 1 } = 2$ , $\omega _ { 2 } = 7$ . The color is proportional to the magnitude $\sqrt { \alpha _ { 1 } ^ { 2 } + \alpha _ { 2 } ^ { 2 } }$
+
+![](images/3159108861cf69b01d621e79a4006689641c5f95a69042c8651c3b791066bd28.jpg)  
+Figure 6: (a) Comparing metric preserving properties for different manifold learning algorithms on the image articulation manifold dataset. LE: Belkin & Niyogi (2003), DrLim: Hadsell et al. (2006). The proposed method shows maximum fidelity to the ground truth shown in Figure 5 (b) Visualizing the outputs of some filters trained using our method. The $1 ^ { \mathrm { s t } }$ column shows the input images. The filters act to exaggerate $2 ^ { \mathrm { n d } }$ column) and suppress ( $3 ^ { \mathrm { r d } }$ column) a governing frequency in Equation (8).
+
+parameters from a 2D uniform distribution
+
+$$
+( \alpha _ { 1 } , \alpha _ { 2 } ) \sim U ( [ 0 , 1 ] \times [ 0 , 1 ] ) .
+$$
+
+We generate 1000 images of the horizon articulation manifold of size $1 0 0 \times 1 0 0$ . The network architecture comprises of two convolution layers each with kernel sizes 12 and 9, number of kernels 15 and 2 respectively along with a stride of 3 and followed by a fully connected layer mapping the image to a two dimensional entity. We train using the ADAM optimizer Kingma & Ba (2015) with a learning rate of 0.01 and parameters $( \beta _ { 1 } , \beta _ { 2 } ) \stackrel { - } { = } ( 0 . 9 5 , 0 . 9 9 )$ . We train the network using 50 Landmark points.
+
+Figure 6a shows the comparison between our method and other non-parametric counterparts along with the parametric approach of DrLim. Training with the least squares loss of Equation (4) shows high fidelity to the ground truth of Figure 5. Except for Isomap and our proposed method, all other methods show some form of distortion indicating a suboptimal metric preservation property.
+
+Training with the articulation manifold in Figure5 provides an opportunity to get more detail in understanding the parametric action of the neural networks. The $2 ^ { \mathrm { n d } }$ and $3 ^ { \mathrm { { r } \mathrm { { \dot { d } } } } }$ columns in Figure 6b show the outputs of some of the filters in the first layer of the architecture trained on the manifold in Figure 5. The distance preserving loss facilitates the learning of image filters which separate the underlying frequencies governing the non-linear manifold, thereby providing a visual validation of the parametric map.
+
+![](images/df79e49165d87fb4c5d7086dd30330ff97ccaf5409b8afd18d41a28b479623e7.jpg)  
+Figure 7: Comparing with nonparametric out-of-sample extensions: (a) Comparing numerical stress values of embeddings generated for training and test data of our method and the interpolating formulation of Landmark Isomap. (b) Visualizing the non-local generalization properties of our method (top) and Landmark Isomap (bottom). Both algorithms were trained on the same Landmarks (in red) sampled from only a part of the manifold.
+
+# 4.3 COMPARISON WITH LANDMARK ISOMAP
+
+We compare our parametric multi-dimensional scaling approach to its direct non-parametric competitor: Landmark-Isomap De Silva & Tenenbaum (2004). The main idea of Landmark-Isomap is to perform classical scaling on the inter-geodesic distance matrix of only the landmarks and to estimate the embeddings of the remaining points using an interpolating formula (also mentioned in Bengio et al. (2004)). The formula uses the estimated geodesic distance of each new point to the selected Landmarks in order to estimate its low dimensional embedding.
+
+We use the image articulation manifold dataset to provide a quantitative and visual comparison between the two methods. Both the methods are imputed with the same set of landmarks for evaluation. In the first experiment, we generate two independent horizon articulation datasets each containing 1000 samples generated using Equations (8) and (9) for training and testing. We then successively train both algorithms on the training dataset with varying number of Landmark points and then use the examples from the test data-set to evaluate performance. Figure 7 (a) shows that low dimensional embedding of Landmark-Isomap admits smaller stress values (hence better metric preservation) for the training dataset, but behaves poorly on unseen examples. On the other hand, despite larger stress values for training, the network shows better generalizability.
+
+In order to visualize non-local generalization properties, we repeat the previous experiment with a minor modification. We train both algorithms on horizon articulation manifolds with parameters sampled from $( \alpha _ { 1 } , \alpha _ { 2 } ) \sim U ( [ 0 , 0 . 7 5 ] ^ { - } \times [ 0 , 0 . 7 5 ] )$ and visualize the outputs on test datasets with parameters sampled from $( \alpha _ { 1 } , \alpha _ { 2 } ) \sim U ( [ 0 , 1 ] \times [ 0 , 1 ] )$ thereby isolating a part of the manifold during training. As shown in Figure 7b, the output of Landmark-Isomap shows a clustered result due to the lack of non-local data in the geodesic distance calculations for the interpolation. In contrast, the network clearly shows a better generalization property.
+
+# 4.4 CAMERA POSE MANIFOLDS
+
+Finally we test our method on a more realistic dataset where the constraint of being isometric to a low dimensional euclidean space is not necessarily strict. We generate 1369 images obtained by smoothly varying the azimuth and elevation of the camera.
+
+Figure 8 shows the embeddings and associated training times of our method compared to the conceptual (Landmark Isomap) and computational (DrLim Hadsell et al. (2006)) siblings. We see that the fast interpolation scheme of Landmark Isomap demonstrates higher distortion whereas DrLim requires a considerable training effort, requiring all possible $\binom { 1 3 6 9 } { 2 } \stackrel { - } { = } 9 3 6 3 9 6$ pairs. Our integrated approach yields an improved result in a considerably smaller training time (geodesic distances between only $\binom { 6 0 0 } { 2 } = 1 7 9 7 0 0$ pairs). We used the same 600 landmarks from Isomap and the same architecture of DrLim for generating the embedding in Figure 8c.
+
+![](images/73c08738a754ea4c022aeedda0837ef3e7869e334016c3468b84fcf52d1d9483.jpg)  
+(a) Landmark Isomap. Training time $<$ 1s
+
+![](images/fccb551294646faa8bba3229463a00918a7f61158c6c45d1db7f36f7ad8d630b.jpg)  
+(b) DrLim. Training time $\approx 6 6 2 0 \mathrm { s }$
+
+![](images/67613dc0591ad6925f8924d6d58c2963fe047e733c35296d13cd92d3df147dd0.jpg)  
+(c) Our Method. Training time $\approx 8 6 0 \mathrm { s }$   
+Figure 8: Camera Pose Manifold: Embedding results and training times for Landmark-Isomap, DrLim Hadsell et al. (2006) and our approach. Our hybrid parametric approach shows a faithful result for a smaller training time.
+
+# 5 CONCLUSION
+
+In the interest of obtaining a better understanding of neural network behavior, we advocate using learning methodologies for solving geometric problems with data by allowing a limited infusion of axiomatic computation to the learning process. In this paper we demonstrate such a scheme by combining parametric modeling with neural networks and the geometric framework of multidimensional scaling. The result of this union leads to reduction in training effort and improved local and nonlocal generalization abilities. As future work, we intend to further explore methods that leverage learning methodologies for improving the largely axiomatic setups of numerical algorithms.
+
+# REFERENCES
+
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+Alexander M Bronstein, Michael M Bronstein, and Ron Kimmel. Numerical geometry of non-rigid shapes. Springer Science & Business Media, 2008.
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+Adam Paszke, Sam Gross, and Soumith Chintala. Pytorch, 2017.
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parse/train/B1uvH_gC-/B1uvH_gC-_content_list.json

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+    {
+        "type": "text",
+        "text": "PARAMETRIC MANIFOLD LEARNING VIA SPARSEMULTIDIMENSIONAL SCALING",
+        "text_level": 1,
+        "bbox": [
+            202,
+            99,
+            795,
+            146
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Anonymous authors Paper under double-blind review ",
+        "bbox": [
+            183,
+            171,
+            398,
+            198
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "ABSTRACT ",
+        "text_level": 1,
+        "bbox": [
+            454,
+            234,
+            544,
+            251
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "We propose a metric-learning framework for computing distance-preserving maps that generate low-dimensional embeddings for a certain class of manifolds. We employ Siamese networks to solve the problem of least squares multidimensional scaling for generating mappings that preserve geodesic distances on the manifold. In contrast to previous parametric manifold learning methods we show a substantial reduction in training effort enabled by the computation of geodesic distances in a farthest point sampling strategy. Additionally, the use of a network to model the distance-preserving map reduces the complexity of the multidimensional scaling problem and leads to an improved non-local generalization of the manifold compared to analogous non-parametric counterparts. We demonstrate our claims on point-cloud data and on image manifolds and show a numerical analysis of our technique to facilitate a greater understanding of the representational power of neural networks in modeling manifold data. ",
+        "bbox": [
+            233,
+            265,
+            764,
+            444
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            468,
+            336,
+            484
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "The characterization of distance preserving maps is of fundamental interest to the problem of nonlinear dimensionality reduction and manifold learning. For the purpose of achieving a coherent global representation, it is often desirable to embed the high-dimensional data into a space of low dimensionality while preserving the metric structure of the data manifold. The intrinsic nature of the geodesic distance makes such a representation depend only on the geometry of the manifold and not on how it is embedded in ambient space. In the context of dimensionality reduction this property makes the resultant embedding meaningful. ",
+        "bbox": [
+            174,
+            498,
+            825,
+            597
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "The success of deep learning has shown that neural networks can be trained as powerful function approximators of complex attributes governing various visual and auditory phenomena. The availability of large amounts of data and computational power, coupled with parallel streaming architectures and improved optimization techniques, have all led to computational frameworks that efficiently exploit their representational power. However, a study of their behavior under geometric constraints is an interesting question which has been relatively unexplored. ",
+        "bbox": [
+            174,
+            603,
+            823,
+            688
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "In this paper, we use the computational infrastructure of neural networks to model maps that preserve geodesic distances on data manifolds. We revisit the classical geometric framework of multidimensional scaling to find a configuration of points that satisfy pairwise distance constraints. We show that instead of optimizing over the individual coordinates of the points, we can optimize over the function that generates these points by modeling this map as a neural network. This makes the complexity of the problem depend on the number of parameters of the network rather than the number of data points, and thus significantly reduces the memory and computational complexities, a property that comes into practical play when the number of data points is large. Additionally, the choice of modeling the isometric map with a parametric model provides a straightforward out-of-sample extension, which is a simple forward pass of the network. ",
+        "bbox": [
+            173,
+            694,
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+            833
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "We exploit efficient sampling techniques that progressively select landmark points on the manifold by maximizing the spread of their pairwise geodesic distances. We demonstrate that a small amount of these landmark points are sufficient to train a network to generate faithful low-dimensional embeddings of manifolds. Figure 1 provides a visualization of the proposed approach. In the interest of gauging their effectiveness in representing manifolds, we perform a numerical analysis to measure the quality of embedding generated by neural networks and associate an order of accuracy to a given architecture. Finally, we demonstrate that parametric models provide better non-local generalization as compared to extrapolation formulas of their non-parametric counter parts. ",
+        "bbox": [
+            174,
+            840,
+            825,
+            924
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/70625e1c8d170a331b7b17b153db79441811a3f732f614c93d90325b141700b4.jpg",
+        "image_caption": [
+            "Figure 1: Learning to unfurl a ribbon: A three dimensional Helical Ribbon and its two dimensional embedding learned using a two-layer MLP. The network was trained using estimated pairwise geodesic distances between only 100 points (marked in black) out of the total 8192 samples. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            174,
+            63,
+            823,
+            162
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            174,
+            262,
+            821,
+            290
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "We advocate strengthening the link between axiomatic computation and parametric learning methodologies. Existing MDS frameworks use a geometrically meaningful objective in a cumbersome non-parametric framework. At the other end, learning based methods such as DrLim Hadsell et al. (2006) use a computationally desirable infrastructure yet a geometrically suboptimal objective requiring too many examples for satisfactory manifold learning. The proposed approach can be interpreted as taking the middle path by using a computationally desirable method of a parametric neural network optimized by the geometrically meaningful cost of multidimensional scaling. ",
+        "bbox": [
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+            297,
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2 BACKGROUND AND PRIOR WORK ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            422,
+            485,
+            439
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2.1 MANIFOLD LEARNING ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            459,
+            372,
+            473
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "The literature on manifold learning is dominated by spectral methods that have a characteristic computational template. The first step involves the computation of the $\\mathbf { k }$ -nearest neighbors of all $N$ data points. Then, an $N \\times N$ square matrix is populated using some geometric principle which characterizes the nature of the desired low dimensional embedding. The eigenvalue decomposition of this matrix is used to obtain the low-dimensional representation of the manifold. Laplacian Eigenmaps Belkin & Niyogi (2003), LLE Roweis & Saul (2000), HLLE Donoho & Grimes (2003), Diffusion Maps Coifman et al. (2005) etc. are considered to be local methods, since they are designed to minimize some form of local distortion and hence result in embeddings which preserve locality. Methods like Schwartz et al. (1989); Wolfson & Schwartz (1989) and Isomap Tenenbaum et al. (2000) are considered global because they enforce preserving all geodesic distances in the low dimensional embedding. Local methods lead to sparse matrix eigenvalue problems and hence are computationally advantageous. However, global methods are more robust to noise and achieve globally coherent embeddings, in contrast to the local methods which can sometimes lead to excessively clustered results. All spectral techniques are non-parametric in nature and hence do not characterize the map that generates them. Therefore, the computational burden of large spectral decompositions becomes a major drawback when the number of data-points is large. Bengio et al. (2004) and De Silva & Tenenbaum (2004) address this issue by providing formulas for out-of-sample extensions to the spectral algorithms. However, these interpolating formulations are computationally inefficient and exhibit poor non-local generalization of the manifold Bengio et al. (2013). ",
+        "bbox": [
+            173,
+            487,
+            825,
+            752
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2.2 MULTIDIMENSIONAL SCALING",
+        "text_level": 1,
+        "bbox": [
+            176,
+            777,
+            428,
+            791
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Multidimensional scaling (henceforth MDS) is a classical problem in geometry processing and data science and a powerful tool for obtaining a global picture of data when only pairwise distances or dissimilarity information is available. The core idea of MDS is to find an embedding $\\mathbf { X } = \\left[ \\mathbf { x _ { 1 } } , \\mathbf { x _ { 2 } } , \\mathbf { x _ { 3 } } . . . \\mathbf { x _ { N } } \\right]$ such that the pairwise distances measured in the embedding space are faithful to the desired distances $\\bf { D _ { s } } = [ d _ { i j } ^ { 2 } ] _ { i , j = 1 } ^ { i , j = N }$ as much as possible. There are two prominent versions of MDS: Classical Scaling and Least Squares Scaling. Classical Scaling is based on the observation that the double centering of a pairwise squared distance matrix gives an inner-product matrix which can be factored to obtain the desired embedding. Therefore, if $\\begin{array} { r } { { \\bf H } = { \\bf I } - \\frac { 1 } { n } { \\mathbb { 1 } } { \\mathbb { 1 } } ^ { T } } \\end{array}$ is the centering matrix, classical scaling minimizes the Strain of the embedding configuration $\\mathbf { X }$ given by ",
+        "bbox": [
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+        "bbox": [
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+        "type": "equation",
+        "img_path": "images/bf1f3693d156037b9601dfce3c9f001d7aa6afe83ffab9f332154499a012667d.jpg",
+        "text": "$$\n\\mathit { S t r a i n } ( \\mathbf { X } ) = | | \\mathbf { X } \\mathbf { X } ^ { T } + \\frac { 1 } { 2 } \\mathbf { H } \\mathbf { D } _ { \\mathbf { s } } \\mathbf { H } | | _ { F } ^ { 2 } ,\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "and is computed conveniently using the eigen-decomposition of the $N \\times N$ matrix $- \\frac { 1 } { 2 } \\mathbf { H D _ { s } H }$ . At the other end, least squares scaling is based on minimizing the misfits between the pairwise distances of $\\mathbf { X } = \\left[ \\mathbf { x _ { 1 } } , \\mathbf { x _ { 2 } } , \\mathbf { x _ { 3 } } . . . \\mathbf { x _ { N } } \\right]$ and desired distances $[ \\bf d _ { i j } ] _ { i , j = 1 } ^ { i , j = \\mathbf { \\bar { N } } }$ measured by the Stress function ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/a79b8d87b1ff51e41dae1568ed792d8505f689a9468de0f7a6462fd97ee57d77.jpg",
+        "text": "$$\n\\mathit { S t r e s s } ( \\mathbf { X } ) = \\sum _ { i } \\sum _ { j } \\ : ( | | \\mathbf { x _ { i } } - \\mathbf { x _ { j } } | | - \\mathbf { d _ { i j } } ) ^ { 2 } .\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In the context of manifold learning and dimensionality reduction, the MDS framework is enabled by estimating all pairwise geodesic distances with a shortest path algorithm like Dijkstra Dijkstra (1959) and using the minimizers of Equations 1 and 2 to generate global embeddings by preserving metric properties of the manifold. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Schwartz et al. (1989); Wolfson & Schwartz (1989) along with Tenenbaum et al. (2000) were the first to suggest populating the inter-geodesic matrix $\\mathbf { D _ { s } }$ using Dijkstra’s algorithm for preserving metric properties of manifolds. The SMACOF algorithm of De Leeuw & Mair (2011) and their variants Bronstein et al. (2006) are iterative least squares scaling algorithms for minimizing Stress in Equation (2). The computational bottleneck of dealing with a dense distance matrix requiring all pairwise distances led to faster algorithms like Aflalo $\\&$ Kimmel (2013); Shamai et al. (2015) and Boyarski et al. (2017), that used spectral representations of the Laplace-Beltrami Operator of the manifold. Rosman et al. (2010) shows a least squares scaling technique which can overcome holes and non-convex boundaries of the manifold. All these algorithms are non-parametric and few out-of-sample extensions have been suggested De Silva & Tenenbaum (2004) to generalize them to new samples. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2.3 NEURAL NETWORKS FOR MANIFOLD LEARNING ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Examining the ability of neural networks to represent data manifolds has received considerable interest and has been studied from multiple perspectives. From the viewpoint of unsupervised parametric manifold learning, one notable approach is based on the metric-learning arrangement of the Siamese configuration Hadsell et al. (2006); Bromley et al. (1994); Chopra et al. (2005). Similarly, the parametric version of the Stochastic Neighborhood Embedding van der Maaten (2009) is another example of using a neural network to generate a parametric map that is trained to preserve local structure Maaten & Hinton (2008). However, these techniques demand an extensive training effort requiring large number of training examples in order to generate satisfactory embeddings. Weston et al. (2012) use a parametric network to learn a classifier which enforces a manifold criterion, requiring nearby points to have similar representations. Basri & Jacobs (2017) have argued that neural-networks can efficiently represent manifolds as monotonic chain of linear segments by providing an architectural construction and analysis. However, they do not address the manifold learning problem and their experiments are based on supervised settings where the ground-truth embedding is known a priori. Gong et al. (2006); Mishne et al. (2017); Chui & Mhaskar (2016) use neural networks specifically for solving the out-of-sample extension problem for manifold learning. However, their procedure involves training a network to follow a pre-computed non-parametric embedding rather than adopting an entirely unsupervised approach thereby inheriting some of the deficiencies of the non-parametric methods. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "It is advantageous to adopt a parametric approach to non-linear dimensionality reduction and replace the computational block of the matrix construction and eigenvalue decomposition with a straightforward parametric computation. Directly characterizing the non-linear map provides a simple out-ofsample extension which is a plain forward pass of the network. More importantly, it is expected that the reduced and tightly controlled parameters would lead to an improved non-local generalization of the manifold Bengio et al. (2013). ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "In Hadsell et al. (2006) (henceforth DrLim), it was proposed to use Siamese Networks for manifold learning using the popular hinge-embedding criterion (Equation (3)) as a loss function. A Siamese configuration (Figure 2) comprises of two identical networks that process two separate units of data to achieve output pairs that are compared in a loss function. The contrastive training comprises of constructing pairs $\\{ \\mathbf { X _ { 1 } ^ { ( k ) } } , \\mathbf { X _ { 2 } ^ { ( k ) } } , \\lambda ^ { ( k ) } \\} _ { k = 1 } ^ { k = N }$ where $\\lambda ^ { ( k ) } \\in \\{ 0 , 1 \\}$ is a label for indicating a positive (a neighbor) or negative pair (not a neighbor) by building a nearest neighbor graph from the manifold data. ",
+        "bbox": [
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+    },
+    {
+        "type": "image",
+        "img_path": "images/2e204ad6304c9ea2bca00a267d9368dd47bc769f7c21d428f3697498d50fe0da.jpg",
+        "image_caption": [
+            "Figure 2: Siamese Configuration "
+        ],
+        "image_footnote": [],
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+        "type": "text",
+        "text": "",
+        "bbox": [
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+    },
+    {
+        "type": "equation",
+        "img_path": "images/3c392512f0fced5edccdf2537d5e50a4dd7b1aced3b5be269dec808b045b5f82.jpg",
+        "text": "$$\n\\begin{array} { r l } { \\displaystyle \\mathcal { L } ( \\boldsymbol { \\Theta } ) = \\sum _ { \\mathbf { k } } \\lambda ^ { ( \\mathbf { k } ) } ~ | | \\mathcal { F } _ { \\boldsymbol { \\Theta } } ( \\mathbf { X _ { 1 } ^ { ( \\mathbf { k } ) } } ) - \\mathcal { F } _ { \\boldsymbol { \\Theta } } ( \\mathbf { X _ { 2 } ^ { ( \\mathbf { k } ) } } ) | | } & { } \\\\ { \\displaystyle } & { \\quad + ( \\mathbf { 1 } - \\lambda ^ { ( \\mathbf { k } ) } ) ~ \\operatorname* { m a x } ~ \\{ \\mathbf { 0 } , ~ \\boldsymbol { \\mu } - | | \\mathcal { F } _ { \\boldsymbol { \\Theta } } ( \\mathbf { X _ { 1 } ^ { ( \\mathbf { k } ) } } ) - \\mathcal { F } _ { \\boldsymbol { \\Theta } } ( \\mathbf { X _ { 2 } ^ { ( \\mathbf { k } ) } } ) | | \\} } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Training with the loss in Equation (3) means that at any given update step, a negative pair contributes to the training only when their pairwise distance is less than $\\mu$ . This leads to a hard-negative sampling problem where the quality of embedding depends on the selection of negative examples in order to prevent excessive clustering of the neighbors. This typically requires an extensive training effort with a huge amount of training data (30000 positive and approximately 17.9 million negatives for a total of 6000 data samples as reported in Hadsell et al. (2006)). ",
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+    },
+    {
+        "type": "text",
+        "text": "3 A FRAMEWORK FOR PARAMETRIC MULTIDIMENSIONAL SCALING",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We propose to incorporate the ideas of Least Squares Scaling into the computational infrastructure of the Siamese configuration as shown in Figure 2. For every $\\bar { \\mathbf { k } } ^ { t h }$ pair, we estimate the geodesic distance using a shortest path algorithm and train the network to preserve these distances by minimizing the Stress function ",
+        "bbox": [
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+    {
+        "type": "equation",
+        "img_path": "images/1ec51c80d80d9979b708950fb6aa3f8e181c5487ae1cb146326260e4ee359779.jpg",
+        "text": "$$\n\\mathcal { L } ( \\boldsymbol { \\Theta } ) = \\sum _ { \\mathbf { k } } \\mathrm { ~ ( ~ } | | \\mathcal { F } _ { \\boldsymbol { \\Theta } } ( \\mathbf { X } _ { 1 } ^ { ( \\mathbf { k } ) } ) - \\mathcal { F } _ { \\boldsymbol { \\Theta } } ( \\mathbf { X } _ { 2 } ^ { ( \\mathbf { k } ) } ) \\mathrm { ~ | | - \\mathbf { d } ^ { ( \\mathbf { k } ) } ~ ) ^ { 2 } ~ }\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The advantage of adopting the loss in Equation (4) over Equation (3) is that every pair of training data contributes to the learning process thereby eliminating the negative sampling problem. More importantly, it facilitates the use of efficient manifold sampling techniques like the Farthest Point Sampling strategy that make it possible to train with much fewer pairs of examples. The farthest point sampling strategy Bronstein et al. (2008) (also referred to as the MinMax strategy in De Silva & Tenenbaum (2004)) is a method to pick landmarks amongst the points of a discretely sampled manifold such that under certain conditions, these samples uniformly cover the manifold much as possible. Starting from a random selection, the landmarks are chosen one at a time such that, each new selection from the unused samples has the largest geodesic distance to the set of the selected sample points. Figure 3 provides a visualization of this sampling mechanism. We train the network by minimizing the loss in Equation (4) by computing the pairwise geodesic distances of the landmarks. Therefore, the pre-training computational effort is confined to computing the pairwise geodesic distances of only the landmark points. The proposed geometric manifold learning algorithm can be summarized in two steps, ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/11c4e9f6c7f703ee00e0f45a02cc7c6d25db28a8f359a7e37e7fccc8199fbfd6.jpg",
+        "image_caption": [
+            "Figure 3: 2D embeddings of a three dimensional S-Curve Manifold generated by a 2-Layer MLP with 70 hidden nodes, that was trained with varying number of landmark points obtained with the Farthest Point Sampling Algorithm. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Step1: Compute the nearest-neighbor graph from the manifold data and obtain a set of landmarkpoints and their corresponding pairwise graph/geodesic distances using Dijkstra’s algorithm and the Farthest Point Strategy. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Step2: Form a dataset of landmark pairs with corresponding geodesic distances and train network in Siamese configuration using the least-squares M $\\{ \\mathbf { X _ { 1 } ^ { ( k ) } , X _ { 2 } ^ { ( k ) } , d ^ { ( k ) } } \\}$ (4) ",
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+    },
+    {
+        "type": "text",
+        "text": "4 EXPERIMENTS ",
+        "text_level": 1,
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.1 3D POINT CLOUD DATA ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Our first set of experiments are based on point-cloud manifolds, e.g., like the Swiss Roll, S-Curve and the Helical Ribbon. We use a multilayer perceptron (MLP) with the PReLU() as the non-linear activation function, given by ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/056c55e83f05f2f9a5b8d809148ee337b2154b3b58de244e89fd69fb40c3e816.jpg",
+        "text": "$$\nP R e L U ( x ) = \\operatorname* { m a x } ( 0 , x ) + a \\ \\operatorname* { m i n } ( 0 , x ) ,\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "where $a$ is a learnable parameter. The networks are trained using the ADAM optimizer with constants $( \\beta _ { 1 } , \\beta _ { 2 } ) = ( 0 . 9 5 , 0 . 9 9 )$ and a learning rate of 0.01 for 1000 iterations. We run each optimization 5 times with random initialization to ensure convergence. All experiments are implemented in python using the PyTorch framework Paszke et al. (2017). We used the scikit-learn machine learning library for the nearest-neighbor and scipy-sparse for Dijkstra’s shortest path algorithms. ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Figure 1 and 3 show the results of our method on the Helical Ribbon and S-Curve respectively with varying number of training samples (in black) out of a total of 8172 data points. The number of landmarks dictates the approximation quality of the low-dimensional embedding generated by the network. Training with too few samples will result in inadequate generalization which can be inferred from the corrugations of the unfurled results in the first two parts of Figure 3 and increasing the number of landmarks expectedly improves the quality of the embedding. We compute the Stress function (Equation (2)) of the entire point configuration to measure the quality of the MDS fit. Figure 4a shows the decay in the Stress as a function of the number of training points (or Landmarks) of a 2-Layer MLP. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "The natural next question to ask is how many landmarks? how many layers? and how many hidden nodes per layer? We observe that these questions relate to an analogous setup in numerical methods for differential equations. For a given numerical technique, the accuracy of the solution depends on the resolution of the spatial grid over which the solution is estimated. Therefore, numerical methods are ranked by an assessment of the order of accuracy their solutions observe. This can be obtained by assuming that the relationship between the approximation error $E$ and the resolution of the grid $h$ is given by ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/1192f770f43cf79258d17aecf1b9b90fdc30122acdb142febb67172cda5f83e1.jpg",
+        "image_caption": [
+            "Figure 4: Exploring the variations in architecture and the number of landmarks: (a) The logarithm of stress of all 8172 points as a function of number of landmarks. (b) Order of accuracy estimates of varying architectures. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "img_path": "images/067f94adf55c46127a90161eb05f3fb40f35eae1e24282393a2e207e5bf0c625.jpg",
+        "text": "$$\nE = C h ^ { P }\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where $P$ is the order of accuracy of the technique and $C$ is some constant. Therefore, $P$ is obtained by computing the slope of the line obtained by charting $\\log ( E )$ vs $\\log ( h )$ , ",
+        "bbox": [
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+    },
+    {
+        "type": "equation",
+        "img_path": "images/1e0e72e284db26e93a4bb04264800d80160a28d61248115414e2408bf0ab5e79.jpg",
+        "text": "$$\n\\log ( E ) = \\log ( C ) + P \\ \\log ( h ) .\n$$",
+        "text_format": "latex",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We extend the same principle to evaluate network architectures (in place of numerical algorithms) for estimating the quality of isometric maps. We use the generalized Stress in Equation (2) as the error function for Equation (6). We assume that due to the 2-approximate property of the fartstrategy Hochbaum & Shmoys (1985) the sampling is approximately uniform and hence $h \\propto { \\frac { 1 } { \\sqrt { K } } }$ where $K$ is the number of landmarks. By varying the number of layers and the number of nodes per layer we associate an order of accuracy to each architecture using Equation (7). Figure 4b shows the results of our experiment. It shows that a single layer MLP has the capacity for modeling functions upto the first order of accuracy. Adding an additional layer increases the representational power by moving to a second order result. Adding more layers does not provide any substantive gain arguably due to a larger likelihood of over-fitting as seen in the considerably noisier estimates (in green). Therefore, a two layer MLP with 70 hidden nodes per layer can be construed as a good architecture for approximating the isometric map of the S-Curve of Figure 3 with 200 landmarks. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "4.2 IMAGE ARTICULATION MANIFOLDS ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We extend the parametric MDS framework to image articulation manifolds where each sample point is a binary image governed by the modulation of a few parameters. We specifically deal with image manifolds that are isometric to Euclidean space Donoho & Grimes (2005), that is, the geodesic distance between any two sample points is equal to the euclidean distance between their articulation parameters. In the context of the main discussion of this paper, which is metric preserving properties of manifolds, we find that such datasets provide an appropriate test-bed for evaluating metric preserving algorithms. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We construct a horizon articulation manifold where each image contains two distinct regions separated by a horizon which is modulated by a linear combination of two fixed sinusoidal basis elements. See Figure 5. ",
+        "bbox": [
+            176,
+            801,
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+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "img_path": "images/0bdb60483ad25ce126717db85f6420092f580bcf4a3dea150a9b13298f12ef55.jpg",
+        "text": "$$\n\\begin{array} { r c l } { { { \\cal I } _ { \\alpha _ { 1 } , \\alpha _ { 2 } } ( u , v ) } } & { { = } } & { { \\mathbb { 1 } _ { \\{ v \\leq \\psi _ { \\alpha _ { 1 } , \\alpha _ { 2 } } ( u ) \\} } } } \\\\ { { } } & { { } } & { { } } \\\\ { { \\psi _ { \\alpha _ { 1 } , \\alpha _ { 2 } } ( u ) } } & { { = } } & { { \\alpha _ { 1 } \\sin ( \\omega _ { 1 } u ) + \\alpha _ { 2 } \\sin ( \\omega _ { 2 } u ) } } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Thus, each sample has an intrinsic dimensionality of two - the articulation parameters $\\left( \\alpha _ { 1 } , \\alpha _ { 2 } \\right)$ which govern how the sinusoids representing the horizon are mixed. We sample the articulation ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/21b58a74e5448145d64324281c028acc2f5278afbafe7ee573e8caef648b3fc3.jpg",
+        "image_caption": [
+            "Figure 5: Visualizing a horizon articulation manifold: 1000 samples generated as per equations 8 and 9 with $\\omega _ { 1 } = 2$ , $\\omega _ { 2 } = 7$ . The color is proportional to the magnitude $\\sqrt { \\alpha _ { 1 } ^ { 2 } + \\alpha _ { 2 } ^ { 2 } }$ "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/3159108861cf69b01d621e79a4006689641c5f95a69042c8651c3b791066bd28.jpg",
+        "image_caption": [
+            "Figure 6: (a) Comparing metric preserving properties for different manifold learning algorithms on the image articulation manifold dataset. LE: Belkin & Niyogi (2003), DrLim: Hadsell et al. (2006). The proposed method shows maximum fidelity to the ground truth shown in Figure 5 (b) Visualizing the outputs of some filters trained using our method. The $1 ^ { \\mathrm { s t } }$ column shows the input images. The filters act to exaggerate $2 ^ { \\mathrm { n d } }$ column) and suppress ( $3 ^ { \\mathrm { r d } }$ column) a governing frequency in Equation (8). "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            225,
+            338,
+            761,
+            537
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "parameters from a 2D uniform distribution ",
+        "bbox": [
+            174,
+            640,
+            454,
+            654
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "equation",
+        "img_path": "images/b3a79b4142cbc27ded70e8f2769057186f23e49766eedcd8367d541d1ead13a2.jpg",
+        "text": "$$\n( \\alpha _ { 1 } , \\alpha _ { 2 } ) \\sim U ( [ 0 , 1 ] \\times [ 0 , 1 ] ) .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            400,
+            661,
+            598,
+            679
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "We generate 1000 images of the horizon articulation manifold of size $1 0 0 \\times 1 0 0$ . The network architecture comprises of two convolution layers each with kernel sizes 12 and 9, number of kernels 15 and 2 respectively along with a stride of 3 and followed by a fully connected layer mapping the image to a two dimensional entity. We train using the ADAM optimizer Kingma & Ba (2015) with a learning rate of 0.01 and parameters $( \\beta _ { 1 } , \\beta _ { 2 } ) \\stackrel { - } { = } ( 0 . 9 5 , 0 . 9 9 )$ . We train the network using 50 Landmark points. ",
+        "bbox": [
+            173,
+            686,
+            825,
+            770
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Figure 6a shows the comparison between our method and other non-parametric counterparts along with the parametric approach of DrLim. Training with the least squares loss of Equation (4) shows high fidelity to the ground truth of Figure 5. Except for Isomap and our proposed method, all other methods show some form of distortion indicating a suboptimal metric preservation property. ",
+        "bbox": [
+            174,
+            776,
+            823,
+            833
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Training with the articulation manifold in Figure5 provides an opportunity to get more detail in understanding the parametric action of the neural networks. The $2 ^ { \\mathrm { n d } }$ and $3 ^ { \\mathrm { { r } \\mathrm { { \\dot { d } } } } }$ columns in Figure 6b show the outputs of some of the filters in the first layer of the architecture trained on the manifold in Figure 5. The distance preserving loss facilitates the learning of image filters which separate the underlying frequencies governing the non-linear manifold, thereby providing a visual validation of the parametric map. ",
+        "bbox": [
+            173,
+            839,
+            825,
+            924
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/df79e49165d87fb4c5d7086dd30330ff97ccaf5409b8afd18d41a28b479623e7.jpg",
+        "image_caption": [
+            "Figure 7: Comparing with nonparametric out-of-sample extensions: (a) Comparing numerical stress values of embeddings generated for training and test data of our method and the interpolating formulation of Landmark Isomap. (b) Visualizing the non-local generalization properties of our method (top) and Landmark Isomap (bottom). Both algorithms were trained on the same Landmarks (in red) sampled from only a part of the manifold. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            171,
+            99,
+            816,
+            344
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "4.3 COMPARISON WITH LANDMARK ISOMAP ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            454,
+            496,
+            468
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "We compare our parametric multi-dimensional scaling approach to its direct non-parametric competitor: Landmark-Isomap De Silva & Tenenbaum (2004). The main idea of Landmark-Isomap is to perform classical scaling on the inter-geodesic distance matrix of only the landmarks and to estimate the embeddings of the remaining points using an interpolating formula (also mentioned in Bengio et al. (2004)). The formula uses the estimated geodesic distance of each new point to the selected Landmarks in order to estimate its low dimensional embedding. ",
+        "bbox": [
+            174,
+            481,
+            825,
+            564
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "We use the image articulation manifold dataset to provide a quantitative and visual comparison between the two methods. Both the methods are imputed with the same set of landmarks for evaluation. In the first experiment, we generate two independent horizon articulation datasets each containing 1000 samples generated using Equations (8) and (9) for training and testing. We then successively train both algorithms on the training dataset with varying number of Landmark points and then use the examples from the test data-set to evaluate performance. Figure 7 (a) shows that low dimensional embedding of Landmark-Isomap admits smaller stress values (hence better metric preservation) for the training dataset, but behaves poorly on unseen examples. On the other hand, despite larger stress values for training, the network shows better generalizability. ",
+        "bbox": [
+            174,
+            571,
+            825,
+            696
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "In order to visualize non-local generalization properties, we repeat the previous experiment with a minor modification. We train both algorithms on horizon articulation manifolds with parameters sampled from $( \\alpha _ { 1 } , \\alpha _ { 2 } ) \\sim U ( [ 0 , 0 . 7 5 ] ^ { - } \\times [ 0 , 0 . 7 5 ] )$ and visualize the outputs on test datasets with parameters sampled from $( \\alpha _ { 1 } , \\alpha _ { 2 } ) \\sim U ( [ 0 , 1 ] \\times [ 0 , 1 ] )$ thereby isolating a part of the manifold during training. As shown in Figure 7b, the output of Landmark-Isomap shows a clustered result due to the lack of non-local data in the geodesic distance calculations for the interpolation. In contrast, the network clearly shows a better generalization property. ",
+        "bbox": [
+            174,
+            704,
+            825,
+            801
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "4.4 CAMERA POSE MANIFOLDS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            820,
+            408,
+            833
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Finally we test our method on a more realistic dataset where the constraint of being isometric to a low dimensional euclidean space is not necessarily strict. We generate 1369 images obtained by smoothly varying the azimuth and elevation of the camera. ",
+        "bbox": [
+            174,
+            847,
+            823,
+            888
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Figure 8 shows the embeddings and associated training times of our method compared to the conceptual (Landmark Isomap) and computational (DrLim Hadsell et al. (2006)) siblings. We see that the fast interpolation scheme of Landmark Isomap demonstrates higher distortion whereas DrLim requires a considerable training effort, requiring all possible $\\binom { 1 3 6 9 } { 2 } \\stackrel { - } { = } 9 3 6 3 9 6$ pairs. Our integrated approach yields an improved result in a considerably smaller training time (geodesic distances between only $\\binom { 6 0 0 } { 2 } = 1 7 9 7 0 0$ pairs). We used the same 600 landmarks from Isomap and the same architecture of DrLim for generating the embedding in Figure 8c. ",
+        "bbox": [
+            174,
+            895,
+            821,
+            924
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/73c08738a754ea4c022aeedda0837ef3e7869e334016c3468b84fcf52d1d9483.jpg",
+        "image_caption": [
+            "(a) Landmark Isomap. Training time $<$ 1s "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            217,
+            69,
+            467,
+            291
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "image",
+        "img_path": "images/fccb551294646faa8bba3229463a00918a7f61158c6c45d1db7f36f7ad8d630b.jpg",
+        "image_caption": [
+            "(b) DrLim. Training time $\\approx 6 6 2 0 \\mathrm { s }$ "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            544,
+            80,
+            769,
+            276
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "image",
+        "img_path": "images/67613dc0591ad6925f8924d6d58c2963fe047e733c35296d13cd92d3df147dd0.jpg",
+        "image_caption": [
+            "(c) Our Method. Training time $\\approx 8 6 0 \\mathrm { s }$ ",
+            "Figure 8: Camera Pose Manifold: Embedding results and training times for Landmark-Isomap, DrLim Hadsell et al. (2006) and our approach. Our hybrid parametric approach shows a faithful result for a smaller training time. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            357,
+            328,
+            658,
+            560
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            173,
+            672,
+            825,
+            747
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "5 CONCLUSION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            784,
+            318,
+            800
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "In the interest of obtaining a better understanding of neural network behavior, we advocate using learning methodologies for solving geometric problems with data by allowing a limited infusion of axiomatic computation to the learning process. In this paper we demonstrate such a scheme by combining parametric modeling with neural networks and the geometric framework of multidimensional scaling. The result of this union leads to reduction in training effort and improved local and nonlocal generalization abilities. As future work, we intend to further explore methods that leverage learning methodologies for improving the largely axiomatic setups of numerical algorithms. ",
+        "bbox": [
+            173,
+            825,
+            825,
+            924
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "REFERENCES ",
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parse/train/BJe0Gn0cY7/BJe0Gn0cY7.md

@@ -0,0 +1,398 @@
+# PREVENTING POSTERIOR COLLAPSE WITH δ-VAES
+
+Ali Razavi   
+Deepmind   
+alirazavi@google.com
+
+Aaron van den Oord ¨ Deepmind avdnoord@google.com
+
+Ben Poole   
+Google Brain   
+pooleb@google.com   
+Oriol Vinyals   
+Deepmind   
+vinyals@google.com
+
+# ABSTRACT
+
+Due to the phenomenon of “posterior collapse,” current latent variable generative models pose a challenging design choice that either weakens the capacity of the decoder or requires altering the training objective. We develop an alternative that utilizes the most powerful generative models as decoders, optimize the variational lower bound, and ensures that the latent variables preserve and encode useful information. Our proposed $\delta$ -VAEs achieve this by constraining the variational family for the posterior to have a minimum distance to the prior. For sequential latent variable models, our approach resembles the classic representation learning approach of slow feature analysis. We demonstrate our method’s efficacy at modeling text on LM1B and modeling images: learning representations, improving sample quality, and achieving state of the art log-likelihood on CIFAR-10 and ImageNet $3 2 \times 3 2$ .
+
+# 1 INTRODUCTION
+
+Deep latent variable models trained with amortized variational inference have led to advances in representation learning on high-dimensional datasets (Kingma & Welling, 2013; Rezende et al., 2014). These latent variable models typically have simple decoders, where the mapping from the latent variable to the input space is unimodal, for example using a conditional Gaussian decoder. This typically results in representations that are good at capturing the global structure in the input, but fail at capturing more complex local structure (e.g. texture (Larsen et al., 2016)). In parallel, advances in autoregressive models have led to drastic improvements in density modeling and sample quality without explicit latent variables (van den Oord et al., 2016b). While these models are good at capturing local statistics, they often fail to produce globally coherent structures (Ostrovski et al., 2018).
+
+Combining the power of tractable densities from autoregressive models with the representation learning capabilities of latent variable models could result in higher-quality generative models with useful latent representations. While much prior work has attempted to join these two models, a common problem remains. If the autoregressive decoder is expressive enough to model the data density, then the model can learn to ignore the latent variables, resulting in a trivial posterior that collapses to the prior. This phenomenon has been frequently observed in prior work and has been referred to as optimization challenges of VAEs by Bowman et al. (2015), the information preference property by Chen et al. (2016), and the posterior collapse problems by several others (e.g. van den Oord et al., 2017; Kim et al., 2018; Dieng et al., 2018). Ideally, an approach that mitigates posterior collapse would not alter the evidence lower bound (ELBO) training objective, and would allow the practitioner to leverage the most recent advances in powerful autoregressive decoders to improve performance. To the best of our knowledge, no prior work has succeeded at this goal. Most common approaches either change the objective (Higgins et al., 2017; Alemi et al., 2017; Zhao et al., 2017; Chen et al., 2016; Lucas & Verbeek, 2017; Goyal et al., 2017), or weaken the decoder (Bowman et al., 2015; Gulrajani et al., 2016). Additionally, these approaches are often challenging to tune and highly sensitive to hyperparameters (Alemi et al., 2017; Chen et al., 2016).
+
+In this paper, we propose $\delta$ -VAEs, a simple framework for selecting variational families that prevent posterior collapse without altering the ELBO training objective or weakening the decoder. By restricting the parameters or family of the posterior, we ensure that there is a minimum KL divergence, $\delta$ , between the posterior and the prior.
+
+We demonstrate the effectiveness of this approach at learning latent-variable models with powerful decoders on images (CIFAR-10, and ImageNet $3 2 \times 3 2$ ), and text (LM1B). We achieve state of the art log-likelihood results with image models by additionally introducing a sequential latent-variable model with an anti-causal encoder structure. Our experiments demonstrate the utility of $\delta$ -VAEs at learning useful representations for downstream tasks without sacrificing performance on density modeling.
+
+# 2 MITIGATING POSTERIOR COLLAPSE WITH $\delta$ -VAES
+
+Our proposed $\delta$ -VAE builds upon the framework of variational autoencoders (VAEs) (Kingma & Welling, 2013; Rezende et al., 2014) for training latent-variable models with amortized variational inference. Our goal is to train a generative model $p ( x , z )$ to maximize the marginal likelihood $\log p ( x )$ on a dataset. As the marginal likelihood requires computing an intractable integral over the unobserved latent variable $z$ , VAEs introduce an encoder network $q ( z | x )$ and optimize a tractable lower bound (the ELBO): $\begin{array} { r } { \log p ( x ) \ge \mathbb { E } _ { z \sim q ( z \vert x ) } \left[ \log p ( x \vert z ) \right] - D _ { \mathrm { K L } } ( q ( z \vert x ) \| p ( z ) ) } \end{array}$ . The first term is typically referred to as the reconstruction term, and the second term (KL) the rate term, as it measures how many nats on average are required to send the latent variables from the encoder $( q ( \boldsymbol { z } | \boldsymbol { x } ) )$ to the decoder $( p ( z | x ) )$ using a code designed for the prior $( p ( z ) )$ (Hoffman et al., 2016; Alemi et al., 2017).
+
+The problem of posterior collapse is that the rate term, $D _ { \mathrm { K L } } ( q ( z | x ) | | p ( z ) )$ reduces to 0. In this case, the approximate posterior $q ( \tilde { \boldsymbol { z } | } \boldsymbol { x } )$ equals the prior $p ( z )$ , thus the latent variables do not carry any information about the input $x$ . A necessary condition if we want representations to be meaningful is to have the rate term be positive.
+
+In this paper we address the posterior collapse problem with structural constraints so that the KL divergence between the posterior and prior is lower bounded by design. This can be achieved by choosing families of distributions for the prior and approximate posterior, $p _ { \boldsymbol { \theta } } ( \mathbf { z } )$ and $q _ { \phi } ( { \bf z } | { \bf x } )$ such that $\begin{array} { r } { \operatorname* { m i n } _ { \theta , \phi } D _ { \mathrm { K L } } ( q _ { \phi } ( \mathbf { z } | \mathbf { x } ) \| p _ { \theta } ( \mathbf { z } ) ) \geq \delta } \end{array}$ . We refer to $\delta$ as the committed rate of the model.
+
+Note that a trivial choice for $p$ and $q$ to have a non-zero committed rate is to set them to Gaussian distributions with fixed (but different) variance term. We study a variant of this case in the experiments, and provide more details of this setup in Appendix D. In the following section we describe our choices for $p _ { \theta }$ and $q _ { \phi }$ , but others should also be explored in future work.
+
+# 2.1 $\delta$ -VAE WITH SEQUENTIAL LATENT VARIABLES
+
+Data such as speech, natural images and text exhibit strong spatio-temporal continuity. Our aim is to model variations in such data through latent variables, so that we have control over not just the global characteristics of the generated samples (e.g., existence of an object), but also can influence their finer, often shifting attributes such as texture and pose in the case of natural images, tone, volume and accent in the case of speech, or style and sentiment in the case of natural language. Sequences of latent variables can be an effective modeling tool for expressing the occurrence and evolution of such features throughout the sequence.
+
+To construct a $\delta$ -VAE in the sequential setting, we combine a mean field posterior with a correlated prior in time. We model the posterior distribution of each timestep as $\begin{array} { r l } { q ( \mathbf { z } _ { t } | \mathbf { x } ) } & { { } = } \end{array}$ $\mathcal { N } ( \mathbf { z } _ { t } ; \bar { \mu _ { t } } ( \mathbf { x } ) , \sigma _ { t } ( \mathbf { x } ) )$ . For the prior, we use a first-order linear autoregressive process (AR(1)), where $\mathbf { z } _ { t } = \alpha \mathbf { z } _ { t - 1 } + \epsilon _ { t }$ with $\epsilon _ { t }$ zero mean Gaussian noise with constant variance $\sigma _ { \epsilon } ^ { 2 }$ . The conditional probability for the latent variable can be expressed as $p ( \mathbf { z } _ { t } | \mathbf { z } _ { < t } ) = \mathcal { N } ( \mathbf { z } _ { t } ; \alpha \mathbf { z } _ { t - 1 } , \sigma _ { \epsilon } )$ . This process is wide-sense stationary (that is, having constant sufficient statistics through its time evolution) if $| \alpha | < 1$ . If so, then $\mathbf { z } _ { t }$ has zero mean and variance of $\frac { \sigma _ { \epsilon } ^ { 2 } } { 1 - \alpha ^ { 2 } }$ . It is thus convenient to choose $\sigma _ { \epsilon } = \sqrt { 1 - \alpha ^ { 2 } }$ so that the variance is constant over time. The mismatch in the correlation structure of the prior and the posterior results in the following positive lower bound on the KL-divergence between the two distributions (see Appendix $\textrm { C }$ for derivation):
+
+$$
+D _ { \mathrm { K L } } ( q ( \mathbf { z } | \mathbf { x } ) \| p ( \mathbf { z } ) ) \geq \frac { 1 } { 2 } \sum _ { k = 1 } ^ { d } ( n - 2 ) \ln ( 1 + \alpha _ { k } ^ { 2 } ) - \ln ( 1 - \alpha _ { k } ^ { 2 } )
+$$
+
+where $n$ is the length of the sequence and $d$ is the dimension of the latent variable at each timestep. The committed rate between the prior and the posterior is easily controlled by equating the right hand side of the inequality in equation 1 to a given rate $\delta$ and solving for $\alpha$ . In Fig. 1, we show the scaling of the minimum rate as a function of $\alpha$ and the behavior of $\delta$ -VAE in 2d.
+
+![](images/e5f600e3710989565574d1d29fed7d3994bf9a4e038d6de369a7826c88d58a9c.jpg)  
+Figure 1: Effect of $\delta$ in a toy model. Fitting an uncorrelated Gaussian for the posterior, $q _ { \phi } ( z )$ , to a correlated Gaussian prior, $p _ { \alpha } ( z )$ , by minimizing $D _ { \mathrm { K L } } ( q _ { \phi } ( z ) \| p _ { \alpha } ( z ) )$ over $\phi$ . Left: committed rate $( \delta )$ as a function of the prior squared correlation $\alpha$ and the dimensionality $n$ . Right: contours of the optimal posterior and prior in 2d. As the correlation increases, the minimum rate grows.
+
+# 2.1.1 RELATION TO PROBABILISTIC SLOWNESS PRIOR
+
+The AR(1) prior over the latent variables specifies the degree of temporal correlation in the latent space. As the correlation $\alpha$ approaches one, the prior trajectories get smoother . On the other hand in the limit of $\alpha$ approaching 0, the prior becomes the same as the independent standard Gaussian prior where there are no correlations between timesteps. This pairing of independent posterior with a correlated prior is related to the probabilistic counterpart to Slow Feature Analysis (Wiskott & Sejnowski, 2002) in Turner & Sahani (2007). SFA has been shown to be an effective method for learning invariant spatio-temporal features (Wiskott & Sejnowski, 2002). In our models, we infer latent variables with multiple dimensions per timestep, each with a different slowness filter imposed by a different value of $\alpha$ , corresponding to features with different speed of variation.
+
+# 2.2 ANTI-CAUSAL ENCODER NETWORK
+
+Having a high capacity autoregressive network as the decoder implies that it can accurately estimate $p ( \mathbf { x } _ { t } | \mathbf { x } _ { < t } )$ . Given this premise, what kind of complementary information can latent variables provide? Encoding information about the past seems wasteful as the autoregressive decoder has full access to past observations already. On the other hand, if we impose conditional independence between observations and latent variables at other timesteps given the current one (i.e., $p ( \bar { \mathbf { x } } _ { t } | \mathbf { z } ) = p ( \mathbf { x } _ { t } | \mathbf { z } _ { t } ) )$ , there will then be at best (by the data processing inequality (Cover $\&$ Thomas, 2006)) a break-even situation between the KL cost of encoding information in $\mathbf { z } _ { t }$ and the resulting improvement in the reconstruction loss. There is therefore no advantage for the model to utilize the latent variable even if it would transmit to the decoder the unobserved $\mathbf { x } _ { t }$ . The situation is different when $\mathbf { z } _ { t }$ can inform the decoder at multiple timesteps, encoding information about $\mathbf { x } _ { t }$ and $\mathbf { x } _ { > t }$ . In this setting, the decoder pays the KL cost for the mutual information once, but is able to leverage the transmitted information multiple times to reduce its entropy about future predictions.
+
+To encourage the generative model to leverage the latents for future timesteps, we introduce an anti-causal structure for the encoder where the parameters of the variational posterior for a timestep cannot depend on past observations (Fig. 2). Alternatively, one can consider a non-causal structure that allows latents be inferred from all observations. In this non-causal setup there is no temporal order in either the encoder or the decoder, thus the model resembles a standard non-temporal latentvariable model. While the anti-causal structure is a subgraph of the non-causal structure, we find that the anti-causal structure often performs better, and we compare both approaches in different settings in Appendix F.1.
+
+![](images/b72e61eeb4c483028eab5b9b3fdca1eaf0f245c20c9835c46ff228876a8ef17f.jpg)  
+Figure 2: Generative structures for the inference of sequential latent variables. The anti-causal structure introduces an inductive bias to encode in each latent variable information about the future
+
+# 3 RELATED WORK
+
+The main focus of our work is on representation learning and density modeling in latent variable models with powerful decoders. Earlier work has focused on this kind of architecture, but has addressed the problem of posterior collapse in different ways.
+
+In terms of our architecture, the decoders for our image models build on advances in autoregressive modeling from van den Oord et al. (2016b); Salimans et al. (2017); Chen et al. (2017); Parmar et al. (2018). Unlike prior models, we use sequential latent variables to generate the image row by row. This differs from Gregor et al. (2016), where the latent variables are sequential but the entire image is generated at each timestep. Our sequential image generation model resembles latent variable models used for timeseries (Chung et al., 2015; Babaeizadeh et al., 2017; Denton & Fergus, 2018) but does not rely on KL annealing, and has an additional autoregressive dependence of the outputs over time (rows of the image). Another difference between our work and previous sequential latent variable models is our proposed anti-causal structure for the inference network (see Sect. 2.2). We motivate this structure from a coding efficiency and representation learning standpoint and demonstrate its effectiveness empirically in Sect. 4. For textual data, we use the Transformer architecture from Vaswani et al. (2017) as our main blueprint for the decoder. As shown in Sect. 4, our method is able to learn informative latent variables while preserving the performance of these models in terms of likelihoods.
+
+To prevent posterior collapse, most prior work has focused on modifying the training objective. Bowman et al. (2015); Yang et al. (2017); Kim et al. (2018) and Gulrajani et al. (2016) use an annealing strategy, where they anneal the weight on the rate from 0 to 1 over the course of training. This approach does not directly optimize a lower bound on likelihood for most of training, and tuning the annealing schedule to prevent collapse can be challenging (see Sect. 4). Similarly, Higgins et al. (2017) proposes using a fixed coefficient $> 1$ on the rate term to learn disentangled representations. Zhao et al. (2017) adds a term to the objective to pick the model with maximal rate. Other works use auxiliary tasks such as secondary low-resolution reconstructions with non-autoregressive decoders (Lucas & Verbeek, 2017) or predicting the state of the backward LSTM in the encoder (Goyal et al., 2017) to encourage the utilization of latent variables. Chen et al. (2016); Kingma et al. (2016) use free-bits to allow the model to hit a target minimum rate, but the objective is non-smooth which leads to optimization difficulties in our hands, and deviations from a lower bound on likelihood when the soft version is used with a coefficient less than 1. Alemi et al. (2017) argue that the ELBO is a defective objective function for representation learning as it does not distinguish between models with different rates, and advocate for model selection based on downstream tasks. Their method for sweeping models was to use $\beta$ -VAE with different coefficients, which can be challenging as the mapping from $\beta$ to rate is highly nonlinear, and model- and data-dependent. While we adopt the same rate-distortion perspective as Alemi et al. (2017), we present a new way of achieving a target rate while optimizing the vanilla ELBO objective.
+
+Most similar to our approach is work on constraining the variational family to regularize the model. VQ-VAE (van den Oord et al., 2017) uses discrete latent variables obtained by vector quantization of the latent space that, given a uniform prior over the outcome, yields a fixed KL divergence equal to $\log K$ , where $K$ is the size of the codebook. A number of recent papers have also used the von Mises-Fisher (vMF) distribution to obtain a fixed KL divergence and mitigate the posterior collapse problem. In particular, Guu et al. (2017); Xu & Durrett (2018); Davidson et al. (2018) use $\mathbf { v M F } ( { \boldsymbol { \mu } } , { \boldsymbol { \kappa } } )$ with a fixed $\kappa$ as their posterior, and the uniform distribution (i.e. $\mathbf { v M F } ( \cdot , 0 ) )$ ) as the prior. The mismatching prior-posterior thus give a constant KL divergence. As such, this approach can be considered as the continuous analogue of VQ-VAE. Unlike the VQ-VAE and vMF approaches which have a constant KL divergence for every data point, $\delta$ -VAE can allow higher KL for different data points. This allows the model to allocate more bits for more complicated inputs, which has been shown to be useful for detecting outliers in datasets (Alemi et al., 2018). As such, $\delta$ -VAE may be considered a generalisation of these fixed-KL approaches.
+
+The Associative Compression Networks (ACN) (Graves & Menick, 2014) is a new method for learning latent variables with powerful decoders that exploits the associations between training examples in the dataset by amortizing the description length of the code among many similar training examples. ACN deviates from the i.i.d training regime of the classical methods in statistics and machine learning, and is considered a procedure for compressing whole datasets rather than individual training examples. GECO (Jimenez Rezende & Viola, 2018) is a recently proposed method to stabilize the training of $\beta$ -VAEs by finding an automatic annealing schedule for the KL that satisfies a tolerance constraint for maximum allowed distortion, and solving the resulting Lagrange multiplier for the KL penalty. The value of $\beta$ , however, does not necessarily approach one, which means that the optimized objective may not be a lower bound for the marginal likelihood.
+
+# 4 EXPERIMENTS
+
+# 4.1 NATURAL IMAGES
+
+We applied our method to generative modeling of images on the CIFAR-10 (Krizhevsky et al.) and downsampled ImageNet (Deng et al., 2009) $3 2 \times 3 2$ as prepared in van den Oord et al. (2016a)) datasets. We describe the main components in the following. The details of our hyperparameters can be found in Appendix E.
+
+Decoder: Our decoder network is closest to PixelSNAIL (Chen et al., 2017) but also incorporates elements from the original GatedPixelCNN (van den Oord et al., 2016b). In particular, as introduced by Salimans et al. (2017) and used in Chen et al. (2017), we use a single channel network to output the components of discretised mixture of logistics distributions for each channel, and linear dependencies between the RGB colour channels. As in PixelSNAIL, we use attention layers interleaved with masked gated convolution layers. We use the same architecture of gated convolution introduced in van den Oord et al. (2016b). We also use the multi-head attention module of Vaswani et al. (2017). To condition the decoder, similar to Transformer and unlike PixelCNN variants that use 1x1 convolution, we use attention over the output of the encoder. The decoder-encoder attention is causally masked to realize the anti-causal inference structure, and is unmasked for the non-causal structure.
+
+Encoder. Our encoder also uses the same blueprint as the decoder. To introduce the anti-causal structure the input is reversed, shifted and cropped by one in order to obtain the desired future context. Using one latent variable for each pixel is too inefficient in terms of computation so we encode each row of the image with a multidimensional latent variable.
+
+Auxiliary Prior. Tomczak & Welling (2017); Hoffman et al. (2016); Jimenez Rezende & Viola (2018) show that VAE performance can suffer when there is a significant mismatch between the prior and the aggregate posterior, $q ( \boldsymbol { z } ) = \mathbb { E } _ { \boldsymbol { x } \sim \mathcal { D } } \left[ q ( \boldsymbol { z } | \boldsymbol { x } ) \right]$ . When such a gap exists, the decoder is likely to have never seen samples from regions of the prior distribution where the aggregate posterior assigns small probability density. This phenomenon, also known as the “posterior holes” problem (Jimenez Rezende & Viola, 2018), can be exacerbated in $\delta$ -VAEs, where the systematic mismatch between the prior and the posterior might induce a large gap between the prior and aggregate posterior. Increasing the complexity of the variational family can reduce this gap (Rezende & Mohamed, 2015), but require changes in the objective to control the rate and prevent posterior collapse (Kingma et al., 2016). To address this limitation, we adopt the approaches of van den Oord et al. (2017); Roy et al. (2018) and train an auxiliary prior over the course of learning to match the aggregate posterior, but that does not influence the training of the encoder or decoder. We used a simple autoregressive model for the auxiliary prior $p ^ { a u x }$ : a single-layer LSTM network with conditional-Gaussian outputs.
+
+# 4.1.1 DENSITY ESTIMATION RESULTS
+
+We begin by comparing our approach to prior work on CIFAR-10 and downsampled ImageNet $3 2 \mathrm { x } 3 2 $ in Table 1. As expected, we found that the capacity of the employed autoregressive decoder had a large impact on the overall performance. Nevertheless, our models with latent variables have a negligible gap compared to their powerful autoregressive latent-free counterparts, while also learning informative latent variables. In comparison, (Chen et al., 2016) had a 0.03 bits per dimension gap between their latent variable model and $\mathrm { P i x e l C N N + + }$ architecture1. On ImageNet $3 2 \mathrm { x } 3 2 $ , our latent variable model achieves on par performance with purely autoregressive Image Transformer (Parmar et al., 2018). On CIFAR-10 we achieve a new state of the art of 2.83 bits per dimension, again matching the performance of our autoregressive baseline. Note that the values for KL appear quite small as they are reported in bits per dimension (e.g. 0.02 bits/dim translates to 61 bits/image encoded in the latents). The results on CIFAR-10 also demonstrate the effect of the auxiliary prior on improving the efficiency of the latent code; it leads to more than $5 0 \%$ (on average 30 bits per image) reduction in the rate of the model to achieve the same performance.
+
+Table 1: Estimated upper bound on negative log-likelihood along with KL-divergence (in parenthesis) in bits per dimension for CIFAR-10 and downsampled ImageNet.   
+
+<table><tr><td></td><td>CIFAR-10 Test</td><td>ImageNet 32 × 32 Valid</td></tr><tr><td>Latent VariableModels ConvDraw (Gregor et al. (2016))</td><td>≤3.85</td><td></td></tr><tr><td>DenseNet VLAE (Chen et al. (2016)) δ-VAE +PixelSNAIL + AR(1) Prior</td><td>≈ 2.95 ≤ 2.85 (0.02)</td><td></td></tr><tr><td>δ-VAE+PixelSNAIL +Auxiliary Prior</td><td> 2.83 (0.01)</td><td>≤ 3.78 (0.08) 3.77 (0.07)</td></tr><tr><td>Autoregressive Models</td><td></td><td></td></tr><tr><td>Gated PixelCNN(van den Oord et al. (2016b))</td><td>3.03</td><td>3.83</td></tr><tr><td>PixelCNN++ (Salimans et al. (2017))</td><td>2.92</td><td>1</td></tr><tr><td>PixelRNN (van den Oord et al. (2016a))</td><td>3.00</td><td>1</td></tr><tr><td>ImageTransformer (Parmar et al. (2018))</td><td>2.90</td><td>3.77</td></tr><tr><td>PixelSNAIL (Chen et al. (2017))</td><td>2.85</td><td>3.80</td></tr><tr><td></td><td></td><td></td></tr><tr><td>Our Decoder baseline</td><td>2.83</td><td>3.77</td></tr></table>
+
+# 4.2 UTILIZATION OF LATENT VARIABLES
+
+In this section, we aim to demonstrate that our models learn meaningful representations of the data in the latent variables. We first investigate the effect of z on the generated samples from the model. Fig. 3 depicts samples from an ImageNet model (see Appendix for CIFAR-10), where we sample from the decoder network multiple times conditioned on a fixed sample from the auxiliary prior. We see similar global structure (e.g. same color background, scale and structure of objects) but very different details. This indicates that the model is using the latent variable to capture global structure, while the autoregressive decoder is filling in local statistics and patterns.
+
+For a more quantitative assessment of how useful the learned representations are for downstream tasks, we performed linear classification from the representation to the class labels on CIFAR-10. We also study the effect of the chosen rate of the model on classification accuracy as illustrated in Fig. 4b, along with the performance of other methods. We find that generally a model with higher rate gives better classification accuracy, with our highest rate model, encoding 92 bits per image, giving the best accuracy of $6 8 \%$ . However, we find that improved log-likelihood does not necessarily lead to better linear classification results. We caution that an important requirement for this task is the linear separability of the learned feature space, which may not align with the desire to learn highly compressed representations.
+
+# 4.3 ABLATION STUDIES
+
+We performed more extensive comparisons of $\delta$ -VAE with other approaches to prevent posterior collapse on the CIFAR-10 dataset. We employ the same medium sized encoder and decoder for evaluating all methods as detailed in Appendix E. Fig. 4a reports the rate-distortion results of our experiments for the CIFAR-10 test set. To better highlight the difference between models and to put into perspective the amount of information that latent variables capture about images, the rate and distortion results in Fig. 4a are reported in bits per images. We only report results for models that encode a non-negligible amount information in latent variables. Unlike the committed information rate approach of $\delta$ -VAE, most alternative solutions required considerable amount of effort to get the training converge or prevent the KL from collapsing altogether. For example, with linear annealing of KL (Bowman et al., 2015), despite trying a wide range of values for the end step of the annealing schedule, we were not able to train a model with a significant usage of latent variables; the KL collapsed as soon as $\beta$ approached one. A practical advantage of our approach is its simple formula to choose the target minimum rate of the model. Targeting a desired rate in $\beta$ -VAE, on the other hand, proved to be difficult, as many of our attempts resulted in either collapsed KL, or very large KL values that led to inefficient inference. As reported in Chen et al. (2016), we also observed that optimising models with the free-bits loss was challenging and sensitive to hyperparameter values.
+
+![](images/ea4c6f6e7f7c7594da3267dc9d65daa9b0e1e437c3b0b9046985c9964175169f.jpg)  
+Figure 3: Random samples from our ImageNet $3 2 \times 3 2$ model. Each column in Fig. 3a shows multiple samples from $p ( \mathbf { x } | \mathbf { z } )$ for a fixed $\mathbf { z } \sim p _ { a u x } ( \mathbf { z } )$ . Each image in Fig. 3b is decoded using a different sample from $p _ { a u x } ( \mathbf { z } )$ .
+
+To assess each methods tendency to overfit across the range of rates, we also report the rate-distortion results for CIFAR-10 training sets in Appendix F. While $\beta$ -VAEs do find points along the ratedistortion optimal frontier on the training set, we found that they overfit more than $\delta$ -VAEs, with $\delta$ -VAEs dominating the rate-distortion frontier on heldout data.
+
+Next, we compare the performance of the anti-causal encoder structure with the non-causal structure on the CIFAR-10 dataset discussed in Sect. 2.2. The results for several configurations of our model are reported in the Appendix Table 6. In models where the decoder is not powerful enough (such as our 6-layer PixelCNN that has no attention and consequently a receptive field smaller than the causal context for most pixels), the anti-causal structure does not perform as well as the noncausal structure. The performance gap is however closed as the decoder becomes more powerful and its receptive field grows by adding self-attention and more layers. We observed that the anticausal structure outperforms the non-causal encoder for very high capacity decoders, as well as for medium size models with a high rate. We also repeated these experiments with both anti-causal and non-causal structures but without imposing a committed information rate or using other mitigation strategies, and found that neither structure by itself is able to mitigate the posterior collapse issue; in both cases the KL divergence drops to negligible values $\leq 1 0 ^ { - 8 }$ bits per dimension) only after a few thousand training steps, and never recovers.
+
+![](images/5b8fcdfd3cb5559beea74f50cbd4bb81c6517a11fc99cb616f189bde25dc07ba.jpg)  
+Figure 4: Comparison of CIFAR-10 test performance of $\delta$ -VAEs vs. models trained with free-bits and $\beta$ -VAE across many rates. $\delta$ -VAE is significantly more stable, achieves competitive density estimation results across different rates, and its learned representations perform better in the downstream linear classification task.
+
+# 4.4 TEXT
+
+For our experiments on natural language, we used the 1 Billion Words or LM1B (Chelba et al., 2013) dataset in its processed form in the Tensor2Tensor (Vaswani et al., 2018) codebase 2. Our employed architecture for text closely follows the Transformer network of Vaswani et al. (2017). Our sequence of latent variables has the same number of elements as in the number of tokens in the input, each having two dimensions with $\alpha = 0 . 2$ and 0.4. Our decoder uses causal self-attention as in Vaswani et al. (2017). For the anti-causal structure in the encoder, we use the inverted causality masks as in the decoder to only allow looking at the current timestep and the future.
+
+Quantitatively, our model achieves slightly worse log-likelihood compared to its autoregressive counterpart (Table 2), but makes considerable use of latent variables, as demonstrated by the samples and interpolations in Appendix H.
+
+Table 2: The result of our text experiments on LM1B in nats / token.   
+
+<table><tr><td></td><td>AR(1) ELBO (KL)</td><td>AuX prior ELBO (KL)</td><td>AR baseline NLL</td></tr><tr><td>δ-VAE</td><td>3.61(0.2)</td><td>≤ 3.58(0.17)</td><td>3.55</td></tr></table>
+
+# 5 DISCUSSION
+
+In this work, we have demonstrated that $\delta$ -VAEs provide a simple, intuitive, and effective solution to posterior collapse in latent variable models, enabling them to be paired with powerful decoders. Unlike prior work, we do not require changes to the objective or weakening of the decoder, and we can learn useful representations as well as achieving state-of-the-art likelihoods. While our work presents two simple posterior-prior pairs, there are a number of other possibilities that could be explored in future work. Our work also points to at least two interesting challenges for latentvariable models: (1) can they exceed the performance of a strong autoregressive baseline, and (2) can they learn representations that improve downstream applications such as classification?
+
+# ACKNOWLEDGMENTS
+
+We would like to thank Danilo J. Rezende, Sander Dieleman, Jeffrey De Fauw, Jacob Menick, Nal Kalchberner, Andy Brock, Karen Simonyan and Jeff Donahue for their help, insightful discussions and valuable feedback.
+
+# REFERENCES
+
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+
+A DERIVATION OF THE KL DIVERGENCE FOR SEQUENTIAL LATENT VARIABLES
+
+$$
+\begin{array} { r l } { \epsilon _ { 1 } = \int _ { - \infty } ^ { \infty } d u \exp \left( \frac { \epsilon _ { 1 } } { \omega } \right) \sin \omega } & { = } \\ & { - \displaystyle \frac { \hat { \gamma } } { \omega } \displaystyle \frac { \hat { \gamma } } { \omega } \frac { \hat { \gamma } } { \omega } \sin \omega \sum _ { i = 1 } ^ { \infty } \omega \sum _ { j = 1 } ^ { N } \omega \log \omega _ { i } \ln \omega } \\ & { - \displaystyle \frac { \hat { \gamma } } { \omega } \displaystyle \frac { \hat { \gamma } } { \omega } \frac { \hat { \gamma } } { \omega } \sin \omega \sum _ { i = 1 } ^ { N } \omega \exp \left( - \frac { \omega ^ { 2 } \omega ^ { 2 } } { \omega ^ { 2 } } \right) - \sum _ { j = 1 } ^ { N } \exp \left( \frac { \omega ^ { 2 } \omega ^ { 2 } } { \omega ^ { 2 } } \right) \sin \omega } \\ & { - \displaystyle \frac { \hat { \gamma } } { \omega } \displaystyle \frac { \hat { \gamma } } { \omega } \frac { \hat { \gamma } } { \omega } \sin \omega \sum _ { i = 1 } ^ { N } \omega \exp \left( - \frac { \omega ^ { 2 } \omega ^ { 2 } } { \omega ^ { 2 } } \right) \sin \omega \Big [ \omega \sin \omega \omega \Big ] } \\ & { - \displaystyle \frac { \hat { \gamma } } { \omega } \displaystyle \frac { \hat { \gamma } } { \omega } \frac { \hat { \gamma } } { \omega } \frac { \hat { \gamma } } { \omega } \sin \omega \sum _ { j = 1 } ^ { N } \omega \omega \sum _ { i = 1 } ^ { N } \omega \frac { \hat { \gamma } } { \omega ^ { 2 } } \int _ { - \infty } ^ { \infty } d u \sin \omega \exp \left( - \frac { \omega ^ { 2 } \omega ^ { 2 } } { \omega ^ { 2 } } \right) \sin \omega } \\ & { - \displaystyle \sum _ { j = 1 } ^ { N } \int _ { - \infty } ^ { \infty } \int _ { - \infty } ^ { \infty } \int _ { 0 } ^ { \infty } u \exp \left( - \frac { \omega ^ { 2 } \omega ^ { 2 } } { \omega ^ { 2 } } \right) \exp \left( - \frac { \omega ^ { 2 } } { \omega ^ { 2 } } \right) \sin \omega } \\ & { - \displaystyle \frac { \hat { \gamma } } { \omega } \displaystyle \frac { \hat { \gamma } } { \omega } \frac { \hat { \gamma } } { \omega } \left( u \omega \times u \right) \sin \omega } \end{array}
+$$
+
+# B DERIVATION OF THE KL-DIVERGENCE BETWEEN AR(1) AND DIAGONAL GAUSSIAN, AND ITS LOWER-BOUND
+
+$$
+\begin{array} { r } { \mathbf { z } _ { i } \in \mathbb { R } ^ { d } , \mathbf { z } _ { 0 } \in \{ 0 \} ^ { d } \quad } \\ { p ( \mathbf { z } _ { 1 } ) = \mathcal { N } ( 0 , 1 ) \qquad } \\ { p ( \mathbf { z } _ { i } | \mathbf { z } _ { i - 1 } ) = \mathcal { N } ( \alpha \mathbf { z } _ { i - 1 } , \sqrt { 1 - \alpha ^ { 2 } } ) \quad i > 1 } \\ { q ( \mathbf { z } _ { i } | \mathbf { x } ) = \mathcal { N } ( \mu _ { i } ^ { \theta } ( \mathbf { x } ) , \sigma _ { i } ^ { \theta } ( \mathbf { x } ) ) \qquad } \end{array}
+$$
+
+Noting the analytic form for the KL-divergence for two uni-variate Gaussian distributions:
+
+$$
+D _ { \mathrm { K L } } ( \mathcal { N } ( \mu _ { q } , \sigma _ { q } ) \| \mathcal { N } ( \mu _ { p } , \sigma _ { p } ) ) = \frac { 1 } { 2 } [ \mathrm { l n } ( ( \frac { \sigma _ { p } } { \sigma _ { q } } ) ^ { 2 } ) + \frac { \sigma _ { q } ^ { 2 } + ( \mu _ { p } - \mu _ { q } ) ^ { 2 } } { \sigma _ { p } ^ { 2 } } - 1 ]
+$$
+
+we now derive the lower-bound for KL-divergence. To avoid clutter we assume a single dimension per timestep but extend the results to the general multivariate case at the end of this section.
+
+$$
+\begin{array} { l } { \displaystyle \mathcal { D } _ { \mathrm { K L } } \big ( q ( \mathbf { z } | \mathbf { x } ) \| p ( \mathbf { z } ) \big ) = \mathbb { E } _ { z _ { i - 1 } \sim q ( z _ { i - 1 } | \mathbf { x } ) } \big [ \displaystyle \sum _ { i = 1 } ^ { n } D _ { \mathrm { K L } } \big ( \mathcal { N } ( \mu _ { q _ { i } } , \sigma _ { q _ { i } } ) \| \mathcal { N } ( \mu _ { p _ { i } } , \sigma _ { p _ { i } } ) \big ) \big ] } \\ { \displaystyle \qquad = \frac { 1 } { 2 } \mathbb { E } _ { z _ { i - 1 } } \big [ - \ln ( \sigma _ { 1 } ^ { 2 } ) + \sigma _ { 1 } ^ { 2 } - 1 + \mu _ { 1 } ^ { 2 } + \displaystyle \sum _ { i = 2 } ^ { n } \ln ( \frac { 1 - \alpha ^ { 2 } } { \sigma _ { i } ^ { 2 } } ) + \frac { \sigma _ { i } ^ { 2 } } { 1 - \alpha ^ { 2 } } - 1 + \frac { \big ( \mu _ { i } - \alpha z _ { 1 } \big ) } { 1 - \alpha } } \\ { \displaystyle \qquad = \frac { 1 } { 2 } \big ( f _ { 1 } ( \sigma _ { 1 } ^ { 2 } ) + \mu _ { 1 } ^ { 2 } + \displaystyle \sum _ { i = 2 } ^ { n } f _ { 1 } ( \frac { \sigma _ { i } ^ { 2 } } { 1 - \alpha ^ { 2 } } ) + \frac { 1 } { 1 - \alpha ^ { 2 } } \mathbb { E } _ { z _ { i - 1 } } \big [ \big ( \mu _ { i } - \alpha z _ { i - 1 } \big ) ^ { 2 } \big ] \big ) } \end{array}
+$$
+
+Where $f _ { a } ( x ) = a x - l n ( x ) - 1$ . Using the fact that $\sigma _ { i } ^ { 2 } = \mathbb { E } [ ( \mathsf { z } _ { i } - \mu _ { i } ) ^ { 2 } ] = \mathbb { E } ( \mathsf { z } _ { i } ^ { 2 } ) - \mu _ { i } ^ { 2 }$ , the expectation inside the summation can be simplified as follows.
+
+$$
+\begin{array} { r l } { \mathbb { E } _ { \mathbf { z } _ { i - 1 } } [ ( \mu _ { i } - \alpha \mathbf { z } _ { i - 1 } ) ^ { 2 } ) ] ) = } & { } \\ & { = \mathbb { E } _ { \mathbf { z } _ { i - 1 } } [ \mu _ { i } ^ { 2 } - 2 \mu _ { i } \alpha \mathbf { z } _ { i - 1 } + \alpha ^ { 2 } \mathbf { z } _ { i - 1 } ^ { 2 } ] } \\ & { = \mu _ { i } ^ { 2 } - 2 \alpha \mu _ { i } \mathbb { E } _ { \mathbf { z } _ { i - 1 } } [ \mathbf { z } _ { i - 1 } ] + \alpha ^ { 2 } \mathbb { E } _ { \mathbf { z } _ { i - 1 } } [ \mathbf { z } _ { i - 1 } ^ { 2 } ] } \\ & { = \mu _ { i } ^ { 2 } - 2 \alpha \mu _ { i } \mu _ { i - 1 } + \alpha ^ { 2 } \sigma _ { i - 1 } ^ { 2 } + \alpha ^ { 2 } \mu _ { i - 1 } ^ { 2 } } \\ & { = ( \mu _ { i } - \alpha \mu _ { i - 1 } ) ^ { 2 } + \alpha ^ { 2 } \sigma _ { i - 1 } ^ { 2 } } \end{array}
+$$
+
+Plugging this back gives us the following analytic form for the KL-divergence for the sequential latent variable $\mathbf { z }$ .
+
+$$
+D _ { \mathrm { K L } } ( q ( \mathbf { z } | \mathbf { x } ) | | p ( \mathbf { z } ) ) = \frac { 1 } { 2 } ( f _ { 1 } ( \sigma _ { 1 } ^ { 2 } ) + \mu _ { 1 } ^ { 2 } + \sum _ { i = 2 } ^ { n } [ f _ { 1 } ( \frac { \sigma _ { i } ^ { 2 } } { 1 - \alpha ^ { 2 } } ) + \frac { ( \mu _ { i } - \alpha \mu _ { i - 1 } ) ^ { 2 } + \alpha ^ { 2 } \sigma _ { i - 1 } ^ { 2 } } { 1 - \alpha ^ { 2 } } ] )
+$$
+
+# C DERIVATION OF THE LOWER-BOUND
+
+Removing non-negative quadratic terms involving $\mu _ { i }$ in equation 3 and expanding back $f$ inside the summation yields
+
+$$
+\begin{array} { l } { { \displaystyle { \cal D } _ { \mathrm { K L } } \big ( q ( { \bf z } | { \bf x } ) \| p ( { \bf z } ) \big ) \geq \frac { 1 } { 2 } \big ( f _ { 1 } ( \sigma _ { 1 } ^ { 2 } ) + \frac { \alpha ^ { 2 } \sigma _ { 1 } ^ { 2 } } { 1 - \alpha ^ { 2 } } + \sum _ { i = 2 } ^ { n - 1 } [ \frac { \sigma _ { i } ^ { 2 } ( 1 + \alpha ^ { 2 } ) } { 1 - \alpha ^ { 2 } } - \ln ( \frac { \sigma _ { i } ^ { 2 } } { 1 - \alpha ^ { 2 } } ) - 1 ] + f _ { 1 } ( \frac { \sigma _ { n } ^ { 2 } } { 1 - \alpha ^ { 2 } } ) \big ) } } \\ { { \displaystyle \qquad = \frac { 1 } { 2 } ( f _ { \frac { 1 } { 1 - \alpha ^ { 2 } } } ( \sigma _ { 1 } ^ { 2 } ) + \sum _ { i = 2 } ^ { n - 1 } f _ { 1 + \alpha ^ { 2 } } ( \frac { \sigma _ { i } ^ { 2 } } { 1 - \alpha ^ { 2 } } ) + f _ { 1 } ( \frac { \sigma _ { n } ^ { 2 } } { 1 - \alpha ^ { 2 } } ) ) } } \end{array}
+$$
+
+$f _ { a } ( x ) = a x - \ln ( x ) - 1$ and its first and second order d obtains its minimum value of tivat $\begin{array} { r } { f _ { a } ^ { \prime } ( x ) = a - \frac { 1 } { x } } \end{array}$ andting $f _ { a } ^ { \prime \prime } ( x ) \geq 0$ $f _ { a }$ $\ln ( a )$ $x = a ^ { - 1 }$ $\sigma _ { 1 } ^ { 2 } = 1 - \alpha ^ { 2 }$ , $\sigma _ { n } ^ { 2 } = 1 - \alpha ^ { 2 }$ and $\textstyle \sigma _ { i } ^ { 2 } = { \frac { 1 - \alpha ^ { 2 } } { 1 + \alpha ^ { 2 } } }$ yields the following lower-bound for the KL:
+
+$$
+D _ { \mathrm { K L } } ( q ( \mathbf { z } | \mathbf { x } ) \| p ( \mathbf { z } ) ) \geq { \frac { 1 } { 2 } } [ ( n - 2 ) \ln ( 1 + \alpha ^ { 2 } ) - \ln ( 1 - \alpha ^ { 2 } ) ]
+$$
+
+When using multi-dimensional $\mathbf { z } _ { i }$ at each timestep, the committed rate is the sum of the $\mathrm { K L }$ for each individual dimension:
+
+$$
+D _ { \mathrm { K L } } ( q ( \mathbf { z } | \mathbf { x } ) | | p ( \mathbf { z } ) ) \geq \frac { 1 } { 2 } [ \sum _ { k = 1 } ^ { D } ( n - 2 ) \ln ( 1 + \alpha _ { k } ^ { 2 } ) - \ln ( 1 - \alpha _ { k } ^ { 2 } ) ]
+$$
+
+# D INDEPENDENT $\delta$ -VAES
+
+The most common choice for variational families is to assume that the components of the posterior are independent, for example using a multivariate Gaussian with a diagonal covariance: $q _ { \phi } ( \mathbf { z } | \mathbf { x } ) = \mathcal { N } ( \mathbf { z } ; \mu _ { q } ( \mathbf { x } ) , \sigma _ { q } ( \mathbf { x } ) )$ . When paired with a standard Gaussian prior, $p \bar { ( \mathbf { z } ) } = \mathcal { N } ( \mathbf { z } ; 0 , 1 )$ , we can guarantee a committed information rate $\delta$ by constraining the mean and variance of the variational family (see Appendix C)
+
+$$
+\mu _ { q } ^ { 2 } \ge 2 \delta + 1 + \ln ( \sigma _ { q } ^ { 2 } ) - \sigma _ { q } ^ { 2 }
+$$
+
+We can, thus, numerically solve
+
+$$
+\ln ( \sigma _ { q } ^ { 2 } ) - \sigma _ { q } ^ { 2 } + 2 r + 1 \ge 0
+$$
+
+to obtain the feasible interval $[ \sigma _ { q } ^ { l } , \sigma _ { q } ^ { u } ]$ where the above equation has a solution for $\mu _ { q }$ , and the committed rate $\delta$ . Posterior parameters can thus be parameterised as:
+
+$$
+\begin{array} { l } { { \displaystyle { \sigma _ { q } = \sigma _ { q } ^ { l } + ( \sigma _ { q } ^ { u } - \sigma _ { q } ^ { l } ) \frac { 1 } { 1 + e ^ { - \sigma _ { \phi } ( x ) } } } } } \\ { { \displaystyle { \mu _ { q } = 2 \delta + 1 + \ln ( \sigma _ { q } ^ { 2 } ) - \sigma _ { q } ^ { 2 } + \operatorname* { m a x } ( 0 , \mu _ { \phi } ( { \bf x } ) ) } } } \end{array}
+$$
+
+Where $\phi$ parameterises the data-dependent part of $\mu _ { q }$ ad $\sigma _ { q }$ , which allow the rate to go above the designated lower-bound $\delta$ .
+
+We compare this model with the temporal version of $\delta$ -VAE discussed in the paper and report the results in Table 3. While independent $\delta$ -VAE also prevents the posterior from collapsing to prior, its performance in density modeling lags behind temporal $\delta$ -VAE.
+
+<table><tr><td>Method</td><td>Test ELBO (KL)</td><td>Accuracy</td></tr><tr><td>Independent δ-VAE (δ = 0.08)</td><td>3.08 (0.08)</td><td>66%</td></tr><tr><td>Temporal δ-VAE (δ = 0.08)</td><td>3.02 (0.09)</td><td>65%</td></tr></table>
+
+Table 3: Comparison of independent Gaussian delta-VAE and temporal delta-VAE with AR(1) prior on CIFAR-10 both targeting the same rate. While both models achieve a KL around the target rate and perform similarly in the downstream linear classification task, the temporal model with AR(1) prior achieves significantly better marginal likelihood.
+
+# E ARCHITECTURE DETAILS
+
+# E.1 IMAGE MODELS
+
+In this section we provide the details of our architecture used in our experiments. The overall architecture diagram is depicted in Fig. 5. To establish the anti-causal context for the inference network we first reverse the input image and pad each spatial dimension by one before feeding it to the encoder. The output of the encoder is cropped and reversed again. As show in Fig. 5, this gives each pixel the anti-causal context (i.e., pooling information from its own value and future values). We then apply average pooling to this representation to give us row-wise latent variables, on which the decoder network is conditioned.
+
+![](images/d9ac3eb72cff0ab1952145c446d9c81ab402f04283b477e56ee5561a2cd312f5.jpg)  
+Figure 5: Architecture for images
+
+The exact hyper-parameters of our network is detailed in Table 4. We used dropout only in our decoder and applied it the activations of the hidden units as well as the attention matrix. As in (Vaswani et al., 2017), we used rectified linear units and layer normalization (Ba et al., 2016) after the multi-head attention layers. We found layer normalization to be essential for stabilizing training. We trained with the Adam optimizer (Kingma & Ba, 2014) and used the learning rate schedule proposed in (Vaswani et al., 2017) with a few tweaks as in the following formulae:
+
+$$
+\begin{array} { r l r } { L R _ { i m a g e N e t } } & { = 0 . 1 8 \times h _ { d } ^ { - 0 . 5 } \operatorname* { m i n } ( s t e p . n u m ^ { 0 . 3 5 } , s t e p . n u m \times 4 0 0 ^ { 0 . 5 } ) } & \\ { L R _ { c i f a r 1 0 } } & { = 0 . 3 6 \times h _ { d } ^ { - 0 . 5 } \operatorname* { m i n } ( s t e p . n u m ^ { 0 . 3 5 } , s t e p . n u m \times 8 0 0 0 ^ { 1 . 5 } ) } & \\ { L R _ { a b l a t i o n } } & { = 0 . 0 0 0 1 } & \end{array}
+$$
+
+We use multi-dimensional latent variables per each timestep, with different slowness factors linearly spaced between a chosen interval. For our ablation studies, we chose corresponding hyperparameters of each method we compare against to target rates between 25-100 bits per image.
+
+<table><tr><td></td><td>le/ld</td><td>he/hd/haux</td><td>re/rd</td><td>ae/ad</td><td>ah</td><td>ndmol</td><td>dod</td><td>2</td><td>a</td></tr><tr><td>Best Imagenet</td><td>6/20</td><td>128/512/1024</td><td>1024/2048</td><td>2/5</td><td>8</td><td>32</td><td>0.3</td><td>16</td><td>[0.5, 0.95]</td></tr><tr><td>CIFAR-10</td><td>20/30</td><td>128/256/1024</td><td>1024/1024</td><td>11/16</td><td>8</td><td>32</td><td>0.5</td><td>8</td><td>[0.3,0.99]</td></tr><tr><td>Ablations</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>[0.5,</td></tr><tr><td>CIFAR-10</td><td>8/8</td><td>128/128/1024</td><td>1024/1024</td><td>2/2</td><td>2</td><td>32</td><td>0.2</td><td>32</td><td>0.68-0.99]</td></tr></table>
+
+Table 4: Hyperparameter values for the models used for experiments. The subscripts $e$ , $d .$ , aux respectively denote the encoder, the decoder, and the LSTM auxiliary prior. $l$ is the number of layers, $h$ is the hidden size of each layer, $r$ is the size of the residual filter, $a$ is the number of attention layers interspersed with gated convolution layers of PixelCNN, $n _ { d m o l }$ is the number of components in the discrete mixture of logistics distribution, $d o _ { d }$ is the probability of dropout applied to the decoder, $z$ is the dimensionality of the latent variable used for each row, and the alpha column gives the range of the AR(1) prior hyper-parameter for each latent.
+
+We developed our code using Tensorflow (Abadi et al., 2016). Our experiments on natural images were conducted on Google Cloud TPU accelerators. For ImageNet, we used 128 TPU cores with batch size of 1024. We used 8 TPU cores for CIFAR-10 with batch size of 64.
+
+# E.2 TEXT MODELS
+
+The architecture of our model for text experiment is closely based on the Transformer network of Vaswani et al. (2017). We realize the encoder anti-causal structure by inverting the causal attention masks to upper triangular bias matrices. The exact hyper-parameters are summarized in Table 5.
+
+$$
+\frac { | \mathit { l } \mathit { \Delta } | } { \mathrm { L M l B } \ | \ 4 \quad 5 1 2 \quad 2 0 4 8 \quad 8 \quad 0 . 1 \quad 2 \quad [ 0 . 2 , 0 . 4 ] }
+$$
+
+Table 5: Hyperparameter values for our LM1B experiments. $l$ is the number of layers, $h$ is the hidden size of each layer, $r$ is the size of the residual filters, do is the probability of dropout, $z$ is the dimensionality of the latent variable, and the alpha column gives the range of the AR(1) prior hyper-parameter for each latent dimension.
+
+# F ABLATION STUDIES
+
+For our ablation studies on CIFAR-10, we trained our model with the configuration listed in Table 4. After training the model, we inferred the mean of the posterior distribution corresponding to each training example in the CIFAR-10 test set, and subsequently trained a multi-class logistic regression classifier on top of it. For each model, the linear classifier was optimized for 100 epochs using the Adam optimizer with the starting learning rate of 0.003. The learning rate was decayed by a factor of 0.3 every 30 epochs.
+
+We also report the rate-distortion curves for the CIFAR-10 training set in Fig. 6. In contrast to the graph of Fig. 4a for the test set, $\delta$ -VAE achieves relatively higher negative log-likelihood on the training set compared to other methods, especially for larger rates. This suggests that $\delta$ -VAE is less prone to overfitting compared to $\beta$ -VAE and free-bits.
+
+![](images/71e38d7855d8c1501cf4144a5362be1e10438aff96ece5ada6013e45b01cbc66.jpg)  
+Figure 6: Rate-Distortion for CIFAR-10 training set.
+
+# F.1 ENCODER ABLATION
+
+In table Table 6, we report the details of evaluating our proposed anti-causal encoder architecture (discussed in Sect. 2.2) against the non-causal architecture in which there is no restriction on the connectivity of the encoder network. The reported experiments are conducted on the CIFAR-10 dataset. We trained 4 different configurations of our model to provide comparison in different capacity and information rate regimes, using the temporal $\delta$ -VAE approach to prevent posterior collapse. We found that the anti-causal structure is beneficial when the decoder has sufficiently large receptive field, and also when encoding relatively high amount of information in latent variables.
+
+Table 6: Ablation of anti-causal vs. non-causal structure. $l$ : number of layers, $h$ : hidden size, $a$ : number of attention layers. Subscripts $e$ and $d$ respectively denote encoder and decoder sizes when they were different. The low-rate (high-rate) models had latent dimension of 8 (64) with alpha linearly placed in [0.5, 0.95] ([0.5, 0.99]) which gives the total rate of 79.44 (666.6) bits per image.   
+
+<table><tr><td rowspan=2 colspan=1></td><td rowspan=1 colspan=1>1=6h=128</td><td rowspan=1 colspan=1>1=8h=128</td><td rowspan=1 colspan=1>1=8h=128</td><td rowspan=2 colspan=1>le = 20,he =128ld = 30,hd = 256a=6low-rate</td></tr><tr><td rowspan=1 colspan=1>a=0low-rate</td><td rowspan=1 colspan=1>a=2low-rate</td><td rowspan=1 colspan=1>a=2high-rate</td></tr><tr><td rowspan=1 colspan=1>Non-Causal AR(1)Non-Causal Aux</td><td rowspan=1 colspan=1>3.04 (0.02)3.03 (0.01)</td><td rowspan=1 colspan=1>3.01 (0.03)2.98 (0.004)</td><td rowspan=1 colspan=1>3.32 (0.22)3.11 (0.02)</td><td rowspan=1 colspan=1>2.88 (0.05)2.85 (0.01)</td></tr><tr><td rowspan=1 colspan=1>Anti-Causal AR(1)Anti-Causal Aux</td><td rowspan=1 colspan=1>3.07 (0.02)3.06 (0.01)</td><td rowspan=1 colspan=1>3.01 (0.03)2.98 (0.006)</td><td rowspan=1 colspan=1>3.22 (0.22)3.03 (0.03)</td><td rowspan=1 colspan=1>2.87 (0.05)2.84 (0.02)</td></tr></table>
+
+# G VISUALIZATION OF THE LATENT SPACE
+
+It is generally expected that images from the same class are mapped to the same region of the latent space. Fig. 7 illustrates the t-SNE (van der Maaten & Hinton, 2008) plot of latent variables inferred from 3000 examples from the test set of CIFAR-10 colour coded based on class labels. As can also be seen on the right hand plot, classes that are closest are also mostly the one that have close semantic and often visual relationships (e.g., cat and dog, or deer and horse).
+
+H ADDITIONAL SAMPLES
+
+![](images/fe417643a99a0ceda3e0b4be6a03a883620491ab77a54003ab692a9eb399ee73.jpg)  
+Figure 7: t-SNE plot of the posterior mean for 3000 CIFAR-10 images. Note the adjacent groups and mixed regions of the plot: cats and dogs images are mostly interspersed as are automobiles and trucks.The highest concentration of horses are on top of the region right above where deer examples are.
+
+![](images/5348af1b07de5fc5b3a7891e6ad85c035a314d13a82705329e080025fec46b58.jpg)  
+Figure 8: Additional ImageNet samples. Top left: Each column is interpolation in the latent space. Top right: ”Day dream” samples where we alternate between sampling $\bar { \mathbf { x } } \sim p ( \mathbf { x } | \mathbf { z } )$ and $\mathbf { z } \sim q ( \mathbf { z } | \mathbf { x } )$ . Bottom left: Each half-column contains in order an original image from the validation set, occlusion of that image, and two reconstructions from different posterior samples. Bottom right: Each halfcolumn contains in order an original image from the validation set, followed by 3 reconstructions from different posterior samples.
+
+![](images/94d032f1c3325469b78beccc19909bac153bf0ccb50777b626fcea67e63afe26.jpg)  
+Figure 9: Additional CIFAR-10 samples. Top left: Each column is interpolation in the latent space. Top right: ”Day dream” samples where we alternate between sampling $\bar { \mathbf { x } } \sim p ( \mathbf { x } | \mathbf { z } )$ and $\mathbf { z } \sim q ( \mathbf { z } | \mathbf { x } )$ . Bottom left: Each half-column contains in order an original image from the test set, occlusion of that image, and two reconstructions from different posterior samples. Bottom right: Each half-column contains in order an original image from the test set, followed by 3 reconstructions from different posterior samples.
+
+![](images/5ecd201862786c6ad281b48bb97cdce0067c60d5498fe11249b820472fae4d40.jpg)  
+Figure 10: Random samples from the auxiliary (left) and AR(1) (right) priors of our high-rate (top) and low-rate(bottom) CIFAR-10 models. The high-rate (low-rate) model has -ELBO of 2.90 (2.83) and KL of 0.10 (0.01) bits/dim. Notice that in the high rate model that has a larger value of $\alpha$ , samples from the AR(1) prior can turn out too smooth compared to natural images. This is because of the gap between the prior and the marginal posterior, which is closed by the auxiliary prior.
+
+![](images/d90b7a61554fabf3756a2bec321b3c2fe76175f5e55b88f9e4c4a34dcb64b3f6.jpg)  
+Figure 11: Additional unconditional random samples from Imagenet $3 2 \mathbf { x } 3 2$ . Each half-column in each block contains 4 decodings of the same sample $\mathbf { z } \sim p _ { a u x } ( \mathbf { z } )$
+
+![](images/dbb386a2b44f233f01291f7e774e9642b0cef23096f96e8aa5fc53bec1fe62c8.jpg)  
+Figure 12: One at a time interpolation of latent dimensions of a sample from the AR(1) prior. The sentences of each segment are generated by sampling a 32 element sequence of 2D random vectors from the autoregressive prior, fixing one dimension interpolating the other dimension linearly between $\mu \pm 3 \sigma$ .
+
+![](images/96d9addc22e60e168ff5d1e7958bdff93343f2a45d2e61040a28536d05f6e151.jpg)  
+Figure 13: One at a time interpolation of latent dimensions of a sample from the auxiliary prior. The generation procedure is identical to Fig. 12 with the exception that the initial vector is sampled from the auxiliary prior.
+
+![](images/e5338177f56634b35fb001fd21122b31e3d521eb39f8ac0e56250f18ec418ac2.jpg)  
+Figure 14: Text completion samples. For each sentence we prime the decoder with a fragment of a random sample from the validation set (shown in bold), and condition the decoder on interpolations between two samples from the latent space.

parse/train/BJgza6VtPB/BJgza6VtPB.md

@@ -0,0 +1,276 @@
+# LANGUAGE GANS FALLING SHORT
+
+Massimo Caccia∗ Mila, Universite de Montr´ eal´ massimo.p.caccia@gmail.com
+
+Lucas Caccia∗   
+Mila, McGill University   
+lucas.page-caccia@mail.mcgill.ca
+
+William Fedus Mila, Universite de Montr ´ eal ´ Google Brain, Montreal ´
+
+Hugo Larochelle Google Brain, Montreal´ Mila, Universite de Montr ´ eal ´ Canada CIFAR AI Chair
+
+Joelle Pineau ¨ Mila, McGill University Facebook AI Research, Montreal´ Canada CIFAR AI Chair
+
+Laurent Charlin Mila, HEC Montreal´ Canada CIFAR AI Chair
+
+# ABSTRACT
+
+Traditional natural language generation (NLG) models are trained using maximum likelihood estimation (MLE) which differs from the sample generation inference procedure. During training the ground truth tokens are passed to the model, however, during inference, the model instead reads its previously generated samples - a phenomenon coined exposure bias. Exposure bias was hypothesized to be a root cause of poor sample quality and thus many generative adversarial networks (GANs) were proposed as a remedy since they have identical training and inference. However, many of the ensuing GAN variants validated sample quality improvements but ignored loss of sample diversity. This work reiterates the fallacy of quality-only metrics and clearly demonstrate that the well-established technique of reducing softmax temperature can outperform GANs on a quality-only metric. Further, we establish a definitive quality-diversity evaluation procedure using temperature tuning over local and global sample metrics. Under this, we find that MLE models consistently outperform the proposed GAN variants over the whole quality-diversity space. Specifically, we find that 1) exposure bias appears to be less of an issue than the complications arising from non-differentiable, sequential GAN training; 2) MLE trained models provide a better quality/diversity tradeoff compared to their GAN counterparts, all while being easier to train, easier to cross-validate, and less computationally expensive.1
+
+# 1 INTRODUCTION
+
+Generating fluent natural language is a central aim in Natural Language Processing (NLP). Transformer architectures (Vaswani et al., 2017) with hundreds of millions or billions of parameters regularly reestablish state-of-the-art on held-out validation perplexities, however, the generated samples can still often lack coherence. It was hypothesized that exposure bias, differences in the training and inference procedures, is the root cause for poor sample quality. Therefore, numerous GANs (Goodfellow et al., 2014) for text generation were proposed since they do not suffer from exposure bias due a training objective that directly seeks to improve sample quality (to a learned critic).
+
+While many of the early GAN variants demonstrated improvements in sample quality (Yu et al., 2017; Guo et al., 2017), they often ignored loss of sample diversity. This is not only a theoretical concern because it is well-documented that GANs exhibit mode collapse (Che et al., 2016; Salimans et al., 2016) where the generator produces a subset of the ”modes” in the training data, reducing diversity. Evaluating generated samples remains challenging (Liu et al., 2016; Zhao et al., 2017), but C´ıfka et al. (2018) recommends assessing generated samples along two dimensions: 1) the quality of each sentence; 2) the diversity across sentences. However, this too is problematic because now the assessment relies on two measures which can make it difficult to compare models. Without further information about the relative trade-off between the two dimensions it is impossible to claim which is superior (Figure 1, left subplot).
+
+![](images/1f29a04568f394bf533ee075c77fc1d4392323e684e74043cba15e4eda162d36.jpg)  
+Figure 1: The importance of temperature for evaluating NLG models on quality and diversity. Each sub-figure plots inverse quality against inverse diversity (lower is better for both metrics). Left: current way of comparing NLG models. In this case, it is impossible to come to any meaningful conclusions about which model (red or blue) dominates the other. Middle: With our proposed NLG evaluation framework, the temperature sweep shines a light on the relative performance of the models: the red model should be used for high-diversity samples and the blue model for high-quality samples. Right: A second simulated scenario (consistent with the left Figure) where the temperature sweep reveals that the blue model dominates the red. That is, for any desired diversity-level, there is a temperature for which the blue model outperforms the red in terms of quality (and vice versa).
+
+In this work, we build on the natural relationship between a model’s softmax temperature and the resultant quality-diversity trade-off: lower temperatures generate less diverse, higher-quality samples; higher temperatures increase the entropy of the distribution and produce more diverse, lower-quality samples. We propose a temperature sweep as a computationally efficient method to characterize the quality-diversity trade-off of different models. By explicitly controlling the temperature we remove a potential source of bias (models may have different ”implicit” temperatures) and obtain a more complete understanding of each model’s behavior (Figure 1 middle and right).
+
+Additionally, we address that temperature modulation changes the entropy of the conditional distributions, as opposed to changing the entropy of the joint distribution. We explore other ways to navigate the quality-diversity space with less bias, including stochastic beam search and generator rejection. Although these methods provide small gains in the quality-diversity trade-off they have other computational limitations.
+
+Despite the dizzying array of text-GAN variants and algorithms (Yu et al., 2017; Che et al., 2017; Lin et al., 2017; Zhang et al., 2017; Guo et al., 2017; Fedus et al., 2018; Lu et al., 2018a; Shi et al., 2018; Xu et al., 2018; Chen et al., 2018; Nie et al., 2019; d’Autume et al., 2019) our conclusions using temperature sweeps are clear: MLE models still dominate GANs. According to all metrics we studied, changing the temperature of MLE models at generation time leads to a better qualitydiversity trade-off compared to GANs. This evaluation technique provides a definitive boundary for future GAN research and our hope is that it will help the NLP community accurately assess natural-language generation progress.
+
+# 2 ADVERSARIAL TEXT GENERATION
+
+GANs are implicit generative models learned via a competition between a generator network $G _ { \theta }$ and a discriminator network $D _ { \phi }$ . The generator network $G _ { \theta }$ produces samples from a probability distribution $p _ { m o d e l } ( x )$ . The discriminator $D _ { \phi } ( x )$ attempts to distinguish whether an input value $x$ is real (training data) or generated. Mathematically, the GAN objective can be formulated as a minimax game
+
+$$
+\mathcal { L } = \underset { \theta } { m i n } \ : m a x \ : \mathbb { E } _ { { x } \sim { p _ { d a t a } } } [ \log D _ { \phi } ( x ) ] + \mathbb { E } _ { { x } \sim { G _ { \theta } } } [ 1 - \log D _ { \phi } ( x ) ]
+$$
+
+GANs were first proposed for continuous domains since their training procedure differentiates through the discriminator into the generator. However, modeling text, which is both discrete and typically modeled sequentially requires a challenging adaptation for GANs which, in their original formulation, were built upon “one-shot” continuous data. Discrete (sequential) data require an alternative approach. Yu et al. (2017) estimate the gradient to the generator via REINFORCE policy gradients (Williams, 1992). In their formulation, the discriminator evaluates full sequences. Therefore, to provide error attribution earlier for incomplete sequences and to reduce the variance of gradients, they perform $k$ Monte-Carlo rollouts until the sentence is completed.
+
+Yu et al. (2017) advertise their model using two tasks which we argue (with hindsight) are flawed. First, they introduce a synthetic evaluation procedure where the underlying data distribution $P$ is known and can be queried. By representing $P$ with an LSTM (referred to as an oracle in the literature), they directly compute the likelihood of samples drawn from a generative model $G _ { \theta }$ . The issue is that they benchmark models against each other on this likelihood alone, i.e., the diagnostic is entirely blind to diversity. For example, a model that always outputs the same highly likely sequence would easily outperform other potentially superior models. For real data, there was no agreed-upon metric to evaluate the quality of unconditional NLG at the time. This led the authors to propose a new metric, Corpus-level BLEU, which computes the fraction of n-grams in a sample that appears in a reference corpus. Again, this metric is agnostic to diversity. Generating a single good sentence over and over will give a perfect BLEU score.
+
+This paper sparked a stream of works that adopt their evaluation framework. Notably, RankGAN (Lin et al., 2017), MaliGAN (Che et al., 2017), TextGAN (Zhang et al., 2017), LeakGAN (Guo et al., 2017) and IRL-GAN (Shi et al., 2018) were proposed soon after.
+
+All but one of the aforementioned papers evaluate sample quality alone. As a remedy, Zhu et al. (2018) propose a metric that compares a generated sentence with a corpus of generated sentences, called Self-BLEU. They, along with Lu et al. (2018b), provide an extensive comparison of GANs using quality (negative BLEU) and diversity (Self-Bleu). However, it is not clear which algorithm is superior, as evidenced by Figure 2, because no model simultaneously outperforms the other on both metrics. It is now standard for language GANs to evaluate simultaneously quality and diversity.
+
+GANs Trained without RL Reinforcement Learning (RL) is often difficult to optimize, unstable, and sensitive to hyperparameters. Because of this, GAN-variants have recently been
+
+![](images/1266ec0367a09686c0920c0bbaec46286e697474e8954caf2cf263765da54f5c.jpg)  
+Figure 2: Negative BLEU-5 versus SBLEU5 (lower is better for both metrics) on the EMNLP2017 News dataset taken from (Lu et al., 2018b) and this work (train data and FM-GAN). These scatter plots do not clearly show which algorithm is preferred since none strictly dominates on both metrics simultaneously.
+
+proposed that eschew RL-techniques in favor of fully-differentiable objectives. Cooperative training (CoT) (Lu et al., 2018a) and feature mover GAN (FM-GAN) Chen et al. (2018) are notable approaches.
+
+Research in both RL and non-RL GANs is still very active (e.g., Xu et al. (2018); Nie et al. (2019); d’Autume et al. (2019); Li et al. (2019); Gagnon-Marchand et al. (2019)) and so our review is not exhaustive.
+
+# 3 TEMPERATURE SWEEP: TOWARDS ROBUST NLG EVALUATION
+
+During natural language generation, a single spurious sampled token can lead to an overall lowquality and incoherent sequence. In other words, a high-entropy conditional distribution may result in poor sample quality at inference. To address this problem, one can modulate the entropy of $G _ { \theta } \mathbf { \bar { ( } } x _ { t } \mid x _ { 1 : t - 1 } \mathbf { \bar { ) } }$ with a Boltzmann temperature parameter $\alpha$ (Ackley et al., 1988). If $o _ { t }$ is the generator’s pre-logit activation and $W$ is the word embedding matrix, then the conditional distribution of the generator is given by $G _ { \theta } ( x _ { t } \mid x _ { 1 : t - 1 } ) = \operatorname { s o f t m a x } ( o _ { t } \cdot W / \alpha )$ . Decreasing $\alpha$ below 1.0 will increase $o _ { t }$ and thus decrease the entropy of $G$ ’s conditional probability. Temperature tuning naturally moves the model in quality/diversity space. We demonstrate this in Table 1.
+
+# α Samples
+
+<table><tr><td colspan="2">2.0 (1) If you go at watch crucial characters putting awareness in Washington ,forget there are now unique developments organized personally then why charge .</td></tr><tr><td></td><td>(2)Front wants zero house blood number places than above spin 5 provide school projects which youth particularly teenager temporary dollars plenty of investors enjoy headed Japan about if federal assets own,at 41 .</td></tr><tr><td>1.0 this point .</td><td>(1) Researchers are expected to comment on where a scheme is sold , but it is no longer this big name at (2) We know you ’re going to build the kind of home you ’re going to be expecting it can give us a better understanding of what ground test we’re on this year ,he explained .</td></tr><tr><td>0.7</td><td>(1) The other witnesses are believed to have been injured ,the police said in a statement ,adding that there was no immediate threat to any other witnesses . (2) The company ’ s net income fell to 5 .29 billion ,or 2 cents per share ,on the same period last year .</td></tr><tr><td>0.0</td><td>(1) The company’s shares rose 1.5 percent to 1.81 percent,the highest since the end of the year. (2) The company ’s shares rose 1 . 5 percent to 1 .81 percent,the highest since the end of the year .</td></tr></table>
+
+Table 1: The effect of temperature on samples from an language model trained via MLE on the EMNLP17 News dataset. At a temperature of $\alpha = 1 . 0$ the samples are syntactically correct but often lack in global coherence. The sample quality varies predictably with temperature. At $\alpha > 1 . 0$ , the syntax breaks down and at $\alpha = 0 . 0$ the model always outputs the same sequence. At $\alpha = 0 . 7$ the samples are both of high quality and of sufficient diversity.
+
+The evaluation protocol for NLG explained in Section 2 is to compare models with respect to both quality and diversity metrics. Often this results in a situation where it is impossible to tell which model is superior, as shown in Figure 2 and further exemplified in Figure 1 (Left). One can then control the quality-diversity trade-off of autoregressive text generators using temperature. We can leverage this tool to design a new evaluation framework that shines a light on the real performance of each model. More precisely, we propose to generate samples at s temperatures for each model in order to compute temperature curves in quality-diversity space. This is exemplified in Figure 1. We refer to this procedure as temperature sweep. This new way of evaluating NLG models allows practitioners to answer questions such as: which model to use if interested in high quality (or diversity) samples? Does a new model improve upon others in the quality/diversity space or is it just reducing the entropy of the distribution? It could also be leveraged as a cross-validation tool e.g., early-stop once the best temperature curve is achieved according to a heuristic.
+
+In the next section we show, using temperature sweep, that MLE models consistently outperform the new proposed GAN variants everywhere in the quality-diversity space. MLE performs equally on synthetic data to CoT and outperforms it on real data, whilst being computationally and algorithmically less complicated. Our results are further validated in independent follow-up works (d’Autume et al., 2019; Alihosseini et al., 2019)where temperature sweeps show MLE outperforming GANs.
+
+To implement temperature sweep we have taken advantage of the fact that our model factorizes the joint distribution over an observation as a product of conditional distributions over single tokens given all previous tokens (this is a property of most autoregressive neural networks). We change the temperature of these conditionals, which is straightforward to implement. However, this is different from changing the temperature of the joint probability distribution. The samples generated in this way are biased towards having lower entropy at the beginning of sentences compared to samples obtained by changing the entropy of the joint distribution. Changing the entropy of the joint distribution quickly becomes intractable with respect to vocabulary size and/or the total number of timesteps. We show below some entropy reducing techniques are less biased than changing the temperature of the conditionals and might achieve a better quality-diversity trade-off. However, we argue that theses methods aren’t suitable for our evaluation protocol due to computational inefficiency (see Section 5.4).
+
+Stochastic Beam Search is a popular approximate decoding technique. It is computationally expensive but leads to higher-likelihood samples than greedy decoding. Here, we focus on its stochastic version (not to be confused with the locally optimal one local beam search). In Stochastic beam search with beam size $k$ , the $k$ most likely hypotheses (sampled so far) are kept at every decoding steps. In Appendix A, we detail this technique and explain how it is less biased than temperature tuning regarding the reduction of the joint distribution’s entropy. Finally, the more traditional local (deterministic) beam search removes all sample diversity and is not useful in our setting.
+
+Generator Rejection Sampling works as follow: generate some sentences; compute their likelihood under the generator’s own distribution; accept/reject the sample given a threshold. The threshold enables the practitioner to modulate the quality-diversity trade-off. In Appendix B, we explain how it is less biased than temperature tuning, why it is computationally expensive, and how the discriminator can be used in rejection sampling.
+
+# 4 RELATED WORK
+
+Concurrent with our work, Semeniuta et al. (2018) demonstrated the issues of local n-gram metrics. Their extensive empirical evaluation of GAN models and language models (LM) did not result in evidence of GAN-trained models outperforming on the new and improved global metrics from C´ıfka et al. (2018). Our analysis further explores this path by examining the performance of these models under a sweep of temperatures. We believe this difference to be of utmost importance, as it is the necessary ingredient towards definitively showing MLE models outperform current GAN variants on quality-diversity global metrics. Work from Ott et al. (2018) thoroughly examines the local beam search strategy for neural machine translation. In their analysis, the authors compare local beam search and generator rejection sampling and find the beam search is quite effective at finding highlikelihood regions. However, their work focuses on conditional text generation, where quality-only metrics measures performance.
+
+Guo et al. (2017) suggest that increasing the temperature at training time leads to more diverse samples. However, we argue that this procedure leads to the opposite outcome as a model can adapt to the temperature change. This would have the net result of lowering the entropy at test time. We discuss this issue and propose a study in Appendix F.
+
+# 5 EMPIRICAL RESULTS
+
+Using our evaluation approach (Section 3), we examine several recent GAN text generation models and compare against an MLE baseline. The experiments consist of two parts: synthetic data generation and long-text generation. We provide strong empirical evidence for both types of data that MLE trained models reliably outperform textual GANs in the quality-diversity space. For these experiments, we only use temperature tuning, as it is the only technique that gives a smooth control over said trade-off whilst being computationally efficient (see Section 5.4).
+
+# 5.1 EXPERIMENTAL DETAILS
+
+The ever-growing body of RL trained language GANs makes writing, running hyperparameter searches and cross-validations on all the variants prohibitively expensive.2 We implemented our own language GAN, including improvements/functionalities proposed in several text GAN papers. We ensure that each functionality can be toggled during training. Then for each dataset, we ran a hyperparameter search of 300 trials encompassing all possible combinations of said functionalities. We refer to this model as RL-GAN. It is based on SeqGAN (Yu et al., 2017) with additional improvements shown to be useful including: MLE pretraining (Yu et al., 2017), leaky discriminator (Guo et al., 2017), step-level loss instead of sequence level (Fedus et al., 2018), learned baseline to reduce variance (Fedus et al., 2018), regularizing REINFORCE with a maximum-entropy loss (Williams & Peng, 1991) and alternating adversarial loss with MLE loss (Guo et al., 2017).
+
+Through comparisons with previously reported results and results obtained via running the official repositories, we show that RL-GAN is the state-of-the-art RL trained GAN. Our MLE model is trained with the same codebase (adversarial training turned off) and only one-sixth of the trials. Moreover, we report SeqGAN and LeakGAN results in the synthetic data experiment. These were obtained with the official repositories that we modified in order to obtain samples at different temperatures. Finally, the SeqGAN, LeakGAN, RankGAN, and MaliGAN results in Figure 4a are taken from (Lu et al., 2018b), which was written by the authors of SeqGAN and LeakGAN.
+
+Finally, we conducted experiments differently for non-RL GANs. The CoT (Lu et al., 2018a) results are obtained with the official repository via a careful hyperparameter search guided by a discussion with the authors. The FM-GAN (Chen et al., 2018) results were obtained with the best performing model that was provided by the authors.
+
+Selecting temperature sweep range. We describe how we selected the range of temperatures in the temperate sweeps. We found that in practice, both the quality and the diversity axes induce bounds beyond which results are non-informative. On the diversity dimension, we found no value in increasing the entropy of the MLE model because minimizing the forward KL does not lead to an underestimation of the real data entropy. Hence, we decreased the temperatures of the other models until a similar diversity to the MLE model was reached. On the quality dimension, we decreased the temperatures to $\alpha = 0$ but did not report the complete curves for the following reasons. First, with synthetic data (Figure 3) the $N L L _ { t e s t }$ explodes when diversity is decreased too much, so we reduce the temperature of the MLE model until the difference in performance compared to the GAN results was evident. Second, in the real data in Figure $^ { 4 \mathrm { b } }$ , we stopped decreasing the temperature when the models achieved a Reverse LM score equal to the perplexity achieved by a 1-gram (unigram) model. This means that the generated dataset is almost non-informative for the (Reverse) language model to learn on i.e., it is as informative as counting tokens. This also coincides with severe mode collapse and a temperature of $< 0 . 5$ for the MLE model. In Figure 4a, we once more decreased the temperature until the difference in performance of MLE with respect to the other models is unambiguous.
+
+Table 2: NLLoracle measured on the synthetic task (lower is better). All results are taken from their respective papers. An MLE-trained model with reduced temperature easily improves upon these GAN variants, producing the highest quality sample.   
+
+<table><tr><td>Model</td><td>NLLoracle</td></tr><tr><td>SeqGAN(Yu et al., 2017) RankGAN (Lin et al., 2017) LeakGAN (Guo et al., 2017)</td><td>8.74 8.25 7.04</td></tr><tr><td>IRL (Shi et al., 2018)</td><td>6.91</td></tr><tr><td>MLE(α = 1.0) MLE (α = 0.4)</td><td>9.40</td></tr><tr><td>MLE (α = 0.001)</td><td>5.50 4.58</td></tr></table>
+
+![](images/89a710e6ced3625a11e248fec87dfeea71ca3e21b27c78876d09e52ce012345c.jpg)  
+Figure 3: Effect of temperature tuning on the global metrics (lower is better for both metrics) for the synthetic task.
+
+# 5.2 SYNTHETIC DATA EXPERIMENT
+
+In the synthetic experiment, we learn a generative model of data produced from a fixed LSTM oracle Yu et al. (2017) with a hidden dimension of 32 with parameters drawn from a standard normal distribution. This allows us to compute a perfect quality metric, the likelihood under the Oracle $\mathrm { N L L } _ { o r a c l e }$ . In Table 2, we see that artificially reducing the temperature at inference achieves stateof-the-art as evaluated by the ${ \mathrm { N L L } } _ { o r a c l e }$ . As we and others have argued, evaluating quality alone is misleading. The MLE-trained model with extremely low temperature will repeatedly output only a single sequence. It is therefore essential to evaluate the resulting sample diversity which we evaluate using the log-likelihood that a generator assigns to held-out data $( N L L _ { t e s t } )$ ). We report the result of a temperature sweep in Figure 3.
+
+![](images/f993cd4f5146404c29140048f94bea8ae21c0b90b29d10bb16d319d9b644b653.jpg)  
+Figure 4: Results on the EMNLP 2017 News dataset. (lower is better for all metrics). MLE under a temperature sweep achieves better quality-diversity trade-off compared to the GAN approaches.
+
+Our RL-GAN benchmark is superior to the official SeqGAN and LeakGAN implementations. Nonetheless, MLE outperforms GANs everywhere in the quality-diversity space. Semeniuta et al. (2018) suggest that the best-performing GANs tend to stay close to the solution given by maximumlikelihood training. We find support for this conclusion, as the best performing RL-GAN models have the smallest learning rate and a considerable amount of pretraining. CoT achieves similar performance to MLE, but with dramatically increased algorithmic complexity. This is unsurprising as their objectives are somewhat similar (see Section 4). Alihosseini et al. (2019) replicated this experiment on synthetic data and arrived at the same conclusions.
+
+# 5.3 LONG-TEXT GENERATION
+
+Next, we study long-text generation using EMNLP News 2017. We first compare an MLE model to the reported GAN results on the local metrics Negative BLEU and Self-BLEU. Negative BLEU5 and SBLEU-5 are used for Figure 4a and results for (Self-)BLEU-2 to (Self-)BLEU-4 are reported in Appendix D. Again, the conclusions are the same: MLE outperforms all RL GANs considered in the quality-diversity trade-off. Moreover, MLE outperforms FM-GAN, the state-of-the-art non-RL Language GAN. Note that the FM-GAN results were obtained with a combination of temperature tuning and noise reduction in order to achieve the best possible results. We provide additional details in Appendix H. We compare MLE to GANs using recently proposed global metrics, the Language Model score (quality) and Reverse Language Model score (diversity+quality) (C´ıfka et al., 2018; Semeniuta et al., 2018). See Figure 4b for a comparison of the training scheme in quality-diversity space. The conclusion is the same as with BLEU and Self-BLEU: MLE outperforms all GANs everywhere in the quality-diversity space. Further results on this dataset as well as on the IMDB movie reviews (Maas et al., 2011) and WikiText-103 (Merity et al., 2016) datasets are presented in independent follow-up works (d’Autume et al., 2019; Alihosseini et al., 2019) where MLE is also shown to outperform GANs using temperature sweeps.
+
+# 5.4 EMPIRICAL REMARKS
+
+These findings are illustrative: a body of research is predicated on exposure bias as the culprit for poor sample quality. Therefore, under this hypothesis, MLE should be at its weakest on long-text generation tasks. However, our results are evidence that exposure bias is less of an issue than optimization problems arising from GAN training combined with the non-differentiability of the original objective function. There is also another way to interpret these results. It seems that MLE (pre)training leaves the generator with a better policy according to quality-diversity. However, because GAN training removes entropy from the learned distribution (see Fig. 5 in Appendix ??), which results in high-quality samples, it can lead one to believe that GAN trained models are superior.
+
+![](images/03979eb1832a55dff2d4982a15dfaed1b86a25a7cf279b10f11963b5118f22fa.jpg)  
+Figure 6: Analysis of decoding methods. (lower is better for all metrics). Left: Less biased methods provided a better quality/diversity trade-off. Right: However, they are computationally much more expensive.
+
+Methods to approximately reduce the entropy of the joint distribution We analyze the different decoding mechanisms as tools to move in the quality-diversity space and as an alternative to temperature sweep. We evaluate these tools by decoding from the best performing MLE model on the EMNLP2017 News dataset. We also consider the different properties of these tools, including their ability to provide smooth control over the quality-diversity trade-off and their computational efficiency. The purpose of this experiment is thus not to find the best performing strategy i.e., a model combined with a decoding method but rather to compare decoding methods. Further, a comparison between MLE and RL-GAN using these approaches is in Appendix I and it supports our prior results.
+
+Figure 6a compares three methods for navigating the quality (Language Model, LM) diversity (Reverse LM) space: temperature sweep, generator rejection,3 and beam search. We first note that temperature tuning and generator rejection sampling yield a similar trade-off in the high-diversity regime. However, as the bias incurred by temperature tuning grows, so does the gap between both methods. An important finding is that generation rejection sampling gets exponentially slower as the threshold increases (see Figure 6b). It is for this reason that the generator rejection sampling curve doesn’t span further in the high-quality part of the space.
+
+Beam search, a less biased method, also seems to offer a better trade-off compared to temperature sweep. However, beam search has a major drawback: unitary increases in beam size leads to drastic leaps in qualitydiversity space. In Figure 6a we report beam sizes of 1 (right dot), 2 (middle dot), and 3 (left dot). This study shows that although the less biased methods seem to offer at least small gains in the quality-diversity space, temperature tuning still has important advantages to assess a model’s quality-diversity trade-off efficiently. The discreteness of beam search and the computational inefficacy of generator rejection sampling are important drawbacks. However, if one’s goal is to obtain the best samples possible, we advocate for their use.
+
+GAN Training Reduces Entropy Figure 5 shows the evolution of a generator’s entropy with respect to epochs. We observe that as soon as adversarial training starts, a drastic entropy reduction occurs. Future work investigates if GAN training changes the learned distribution or simply reduces the entropy in an ineffective way with respect to the quality-diversity trade-off.
+
+![](images/5f48d48a79b42b8cd8328a508fb1fd72a229c158d24512ded9834936e2917fa1.jpg)  
+Figure 5: Dotted line indicates the start of GAN training. We notice a clear drop in entropy (spike in $\mathrm { N L L } _ { t e s t . }$ ) when moving from maximum-likelihood to adversarial updates.
+
+# 6 DISCUSSION
+
+We demonstrate that well-adjusted language models are a strong baseline and that temperature sweeping can provide an unambiguous characterization of model performance in terms of quality and diversity. A well-adjusted language model outperforms the considered GAN variants as evaluated on both local, and more surprisingly, global metrics of quality and diversity. Our temperature sweeping framework shares characteristics with a Receiver Operating Curve. Analogously, if one needed a single scalar to compare NLG models, one could compute the area under the curve and seek the model with the smallest value (lower is better for our considered metrics).
+
+GAN-based generative models have been proven effective on real-valued data. However, there exist many difficult pernicious issues involved in moving to discrete data. These issues must be overcome before they will improve over the strong MLE baselines for unconditional language generation. On the datasets and tasks considered, potential issues caused by exposure bias were less severe than the ones arising from adversarial training combined with learning the non-differentiability of the original objective function. GAN training may prove fruitful eventually, but this research lays forth clear boundaries that it must first surpass.
+
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+
+# A STOCHASTIC BEAM SEARCH.
+
+Beam search is a popular approximate decoding technique. It is computationally expensive but usually leads to higher-likelihood samples than greedy decoding. Here, we focus on its stochastic version, not to be confused with the locally optimal one, Local Beam Search. In Stochastic Beam Search with beam size $k$ , words are sampled sequentially starting from the first one. At the first timestep $k$ words are sampled, each represents a hypothesis. At subsequent timesteps, $k$ next words are sampled conditioned on each of the $k$ current hypotheses, resulting in $k ^ { 2 }$ hypotheses. The $k$ most likely are kept and so on. Because an increase in beam size results in higher-likelihood samples, beam size can be leveraged to modulate the quality-diversity trade-off. Moreover, an infinite beam size would result in sampling the most likely sentences under the generator’s distribution. This is not what we can expect from setting the temperature to 0, which is equivalent to greedy decoding. For this reason, we can hypothesize that Stochastic Beam Search is less biased regarding the reduction of the joint distribution’s entropy. However, unlike temperature tuning, one cannot smoothly trade quality for diversity, as the beam size is a discrete parameter. The more traditional local (deterministic) beam search removes all sample diversity. Thus, it is not useful in our setting.
+
+# B GENERATOR REJECTION SAMPLING.
+
+Generator Rejection Sampling works as follow: generate some sentences; compute their likelihood under the Generator’s own distribution; accept/reject the sample given a threshold. The threshold enables the practitioner to modulate the quality-diversity trade-off. Similar to Stochastic Beam Search, increasing the threshold to a maximum level would result in always sampling the most likely sentence. We can again hypothesize that this method achieves a better quality-diversity trade-off compared to temperature tuning, since it is not biased towards having sentences with a lower entropy prefix. However, the running time of this procedure increases significantly as the acceptance threshold lowers, as discussed in Section 5.4. We also experimented with a rejection sampling scheme where the score is determined by a discriminator but it did not provide any additional insights.
+
+# C QUALITATIVE ANALYSIS OF THE SAMPLES
+
+For completeness, we show samples of SeqGAN, LeakGAN, and MLE from both datasets in Table 3. In this experiment, we used the Image COCO dataset (Lin et al., 2014) in order to generate shorter sentences as well. In this case, the samples of all models appear similar. This is because generating captions is a relatively easier task. For the EMNLP2017 News dataset, we would like to point out interesting facts from our samples. In our first sample (1), the model generates the sequence “post Brexit strategy”. This is n-gram is not present in the training set. In our second sample (2), the token “leak” and the n-gram “Freedom of Information request” never appear together in the training dataset. The extrapolations show that the model learns a certain level of generalization beyond the training set. Additional samples are presented further in Appendix J.
+
+# D FULL BLEU AND SELF-BLEU RESULTS
+
+Full BLEU and Self-BLEU results are shown in Table 4.
+
+# E THE LIMITATIONS OF BLEU
+
+In this section, we want to highlight an important flaw in using BLEU as a proxy for quality. We tuned the temperature in order to find a MLE model with BLEU score equal to the training data’s. We show three randomly sampled sentences from the model in Table 6. Although sometimes grammatically correct, the samples lack in semantic and/or global coherence. It seems the generated text has poor information content. Surprisingly, in order to get great samples on a consistent basis, the temperature needs to be reduced to a level where BLEU-5 is twice as large as the training data’s. Thus, it seems like BLEU is not always a good proxy of sample quality. Again, we think it is of utmost importance to develop better metrics and modernize NLG’s canonical evaluation framework.
+
+<table><tr><td>Datasets</td><td>imageCOCO</td><td>EMNLP2017NeWs</td></tr><tr><td rowspan="2">SeqGAN</td><td>(1)A woman is riding a bike on the street next to a bus.</td><td>(1) You only certainly might not rush it down for those circumstances where we are when they were the heads, and when she&#x27;s name.</td></tr><tr><td>(2)A silver stove,the refrigera- tor, sitting in a kitchen.</td><td>(2) I think you should really really leave for because we hadn&#x27;t been busy, where it goes to one,&quot;he wrote.</td></tr><tr><td rowspan="2">LeakGAN</td><td>(1）A woman holding an um- brella while standing against the sidewalk.</td><td>(1)A man has been arrested at age 28,a resident in Seattle,which was widely reported in 2007.</td></tr><tr><td>(2) A bathroom with a toilet and sink and mirror (1）A narrow kitchenwith</td><td>(2) I also think that&#x27;s a good place for us,I&#x27;m sure that this would be a good opportunity for me to get in touch.</td></tr><tr><td rowspan="2">MLE</td><td>woodencabinetsandwhite appliances .</td><td>(1） The company will be able to provide a post Brexit strategy,which will be published in the coming weeks</td></tr><tr><td>(2） There are several bikes parked in front of a tall building with four cars .</td><td>(2) The leak was obtained by a Freedom of Informa- tion request，which is based on the number of people claiming to be a victim of fraud .</td></tr></table>
+
+Table 3: Samples from the different models on Image COCO and EMNLP2017 WMT News. For SeqGAN and LeakGAN, samples were taken from (Guo et al., 2017). It’s the first two samples found in their appendix. For our samples, we reduced the temperature of the model till we achieved similar BLEU scores to the ones reported in (Guo et al., 2017) in order to keep comparison fair.   
+Table 4: BLEU (left) and Self-BLEU (right) on test data of EMNLPNEWS 2017. (Higher BLEU and lower Self-BLEU is better).   
+
+<table><tr><td></td><td colspan="4">BLEU</td><td colspan="4">Self-BLEU</td></tr><tr><td></td><td>2</td><td>3</td><td>4</td><td>5</td><td>2</td><td>3</td><td>4</td><td>5</td></tr><tr><td>Training Data</td><td>0.86</td><td>0.61</td><td>0.38</td><td>0.23</td><td>0.86</td><td>0.62</td><td>0.38</td><td>0.24</td></tr><tr><td>SeqGAN Yu et al. (2017)</td><td>0.72</td><td>0.42</td><td>0.18</td><td>0.09</td><td>0.91</td><td>0.70</td><td>0.46</td><td>0.27</td></tr><tr><td>MaliGAN Che et al. (2017)</td><td>0.76</td><td>0.44</td><td>0.17</td><td>0.08</td><td>0.91</td><td>0.72</td><td>0.47</td><td>0.25</td></tr><tr><td>RankGAN Lin et al. (2017)</td><td>0.69</td><td>0.39</td><td>0.18</td><td>0.09</td><td>0.90</td><td>0.68</td><td>0.45</td><td>0.30</td></tr><tr><td>TextGAN Zhang et al. (2017)</td><td>0.21</td><td>0.17</td><td>0.15</td><td>0.13</td><td>1.00</td><td>0.98</td><td>0.97</td><td>0.96</td></tr><tr><td>LeakGAN Guo et al. (2017)</td><td>0.84</td><td>0.65</td><td>0.44</td><td>0.27</td><td>0.94</td><td>0.82</td><td>0.67</td><td>0.51</td></tr><tr><td>MLE(α=1.25-1)</td><td>0.93</td><td>0.74</td><td>0.51</td><td>0.32</td><td>0.93</td><td>0.78</td><td>0.59</td><td>0.41</td></tr></table>
+
+<table><tr><td></td><td colspan="4">BLEU</td><td colspan="4">Self-BLEU</td></tr><tr><td></td><td>2</td><td>3</td><td>4</td><td>5</td><td>2</td><td>3</td><td>4</td><td>5</td></tr><tr><td>Training Data</td><td>0.74</td><td>0.53</td><td>0.34</td><td>0.22</td><td>0.90</td><td>0.75</td><td>0.58</td><td>0.42</td></tr><tr><td>SeqGAN Yu et al. (2017)</td><td>0.75</td><td>0.50</td><td>0.29</td><td>0.18</td><td>0.95</td><td>0.84</td><td>0.67</td><td>0.49</td></tr><tr><td>MaliGAN Che et al. (2017)</td><td>0.67</td><td>0.43</td><td>0.26</td><td>0.16</td><td>0.92</td><td>0.78</td><td>0.61</td><td>0.44</td></tr><tr><td>RankGAN Lin et al. (2017)</td><td>0.74</td><td>0.47</td><td>0.26</td><td>0.16</td><td>0.96</td><td>0.88</td><td>0.76</td><td>0.62</td></tr><tr><td>TextGAN Zhang et al. (2017)</td><td>0.59</td><td>0.46</td><td>0.28</td><td>0.21</td><td>0.94</td><td>0.93</td><td>0.80</td><td>0.75</td></tr><tr><td>LeakGAN Guo et al. (2017)</td><td>0.74</td><td>0.52</td><td>0.33</td><td>0.21</td><td>0.93</td><td>0.82</td><td>0.66</td><td>0.51</td></tr><tr><td>MLE</td><td>0.74</td><td>0.52</td><td>0.33</td><td>0.21</td><td>0.89</td><td>0.72</td><td>0.54</td><td>0.38</td></tr></table>
+
+Table 5: BLEU (left) and Self-BLEU (right) on test data of Image COCO. (Higher BLEU and lower Self-BLEU is better).
+
+# F ISSUES OF VARYING TEMPERATURE DURING TRAINING
+
+As a penultimate experiment, we analyze the effect of changing the temperature at training instead of inference. Guo et al. (2017) suggested that increasing the temperature at training time leads to more diverse samples. However, we argue that this procedure leads to the opposite outcome as a model can adapt to the temperature change. This would have the net result of lowering the entropy at test time. To examine this, we trained 30 GANs maintaining everything constant except training temperature. Negative BLEU-5 against SBLEU-5 are plotted in Figure 7. The darker the dot, the higher the $\alpha$ and consequently the temperature. As we hypothesize, models trained with increased temperature at training time adapted to the change and the net result was a colder temperature at inference (hence reduced diversity). We therefore recommend only adjusting the temperature at inference. One should consider other techniques to facilitate exploration during training.
+
+Table 6: Three randomly sampled sentences from our model with closest BLEU scores to the training set’s. The sentences have poor semantics or global coherence. They are also not perfect grammatically speaking.   
+
+<table><tr><td>MLE</td><td>(1) He explained that the Government’s plan to cut tax on unemployment was 3 . 3 percent lower than forecast for the first increase of 16 percent in 2Oi5 ,the fastest rate in the state since 2004.</td></tr><tr><td>α 1.05-1</td><td>(2) On the policy,it’s no more than the amount of money we have of the decades and Senate of our assets .</td></tr><tr><td></td><td>(3) They say it was possible supporting the Scottish government to make the changes as secret free environment based on competition .</td></tr></table>
+
+![](images/91b6caa2e7dc167f7da5fd190947e5c3a2f25d7bbaf797c357f76e4c98efcc61.jpg)  
+Figure 7: Negative BLEU-5 on test data against SBLEU5 for models with different temperature applied at training time. The redder the dot, the higher the $\alpha$ i.e. more pressure to increase entropy. From these results, it is evident that one should not increase the temperature at training time as the models adapts and the net results is mode collapse.
+
+# G DISCRIMINATOR REJECTION SAMPLING
+
+We experimented with a rejection sampling technique base on the Discriminator’s signal. For this method, we train a Discriminator on the Generator’s samples without ever updating the Generator. Next, we accept/reject samples in a similar fashion to Generator Rejection Sampling however now the score is determined by the Discriminator. The higher the threshold, the more confident the Discriminator needs to be about the realness of the data. This should increase the quality of the samples with the usual downside of reducing diversity. We show results with a Discriminator having the same architecture as the Generator (Discriminator Rejection) and the best Discriminator found with an hyper parameter search of 100 trials (Best Discriminator Rejection. Results are shown in Figure 8. Note that the domain of the figure is much smaller that in Figure 4b. The reason is that this approach can’t move the models further in quality-diversity space. For this reason, we do not advocate for the use of this approach as a means to obtain high quality samples.
+
+# H MODULATING QUALITITY/DIVERSITY FOR FM-GAN
+
+For FM-GAN, we observed that lowering the temperature to 0 didn’t completely remove all the stochasticity in the generations. This is because FM-GAN samples noise prior to sampling the first word. This is similar to how image generation GANs are trained. Precisely, $z \sim N ( 0 , \bar { 1 } )$ is sampled once and concatenated to every token of a generated sentence. Because temperature tuning wasn’t covering enough of the quality/diversity space, we also reduced the variance of the noise as quality modulating tool. Results are show in Figure 9.
+
+![](images/e309e212e69aaa8ed47938ec5c4c3ac817921d20d1d13903fecbf9d018e29679.jpg)  
+Figure 8: Discriminator Rejection Sampling is not a great tool to navigate in quality-diversity space.
+
+![](images/1173e4bf4ab67af100500e2503dc2e9212adadab335f4a7bf267867888552e58.jpg)  
+Figure 9: Different strategies to modulate the quality/diversity trade-off in FM-GAN.
+
+# I RL-GAN VERSUS MLE WITH OTHER DECODING MECHANISMS
+
+![](images/839e61acf369a8825f1638bcac105d7ee77b6571c9cf07311ec9f339ee16922f.jpg)  
+Figure 10: MLE still outperforms RL-GAN under different decoding mechanisms.
+
+# J EMNLP 2017 NEWS SAMPLES
+
+We present additional samples for EMNLP 2017 News dataset.
+
+EMNLP2017 News   
+Table 7: Samples from SeqGAN taken from Guo et al. (2017).   
+
+<table><tr><td>SeqGAN through . I wanted to be made you decided to have a crisis that way up and get some sort of weapon , not much to give birth to for an American room . She had been fined almost 2Oo, OOO with couple of asylum seekers in Syria and Iraq . Perhaps not,in looking for,housing offcials would help the frustration of Government , with an FBI shortly before 2020 . Once we got to real show for the young man since I m sure she went to love it just , whether to be late later last year . But ,after a holiday period we might have to go on a total - out debate like that could have</td><td>You only certainly might not rush it down for those circumstances where we are when they were the heads ,and when she s name . I think you should really really leave for because we hadn t been busy ，where it goes to one，he wrote . All the study knew was that they are ,so they continue to provide support service and it doesn texist . It can say become up with nothing sales have reached the charge for the other any evidence that been virtually well below the $ 800 . Three times before the start of the season is much early on 2O15 we are in the third training every year . That s the idea of strength that decision they said, we haven t already lost four or seven, or Liverpool s team. That is not the time for the cost of changing the system and it was pushing for $2O million We had to take it a good day for a military,but nearly 6 , OOO ] and prepare for them through . I actually didn t tell the background check the difference after my hour was to be recalled ... and it was great . We are thinking about 4O, OOO and jobs in what is wrong in the coming and you know . That is out how working you can t set out some pretty tight... or what I m going</td></tr></table>
+
+Table 8: Samples from LeakGAN taken from Guo et al. (2017).   
+
+<table><tr><td>LeakGAN</td><td>A man has been arrested at age 28 ,a resident in Seattle ，which was widely reported in 2007. I also think that s a good place for us ,I m sure that this would be a good opportunity for me to get in touch . What is the biggest problem for Clinton is that Donald Trump will be in the race and he s unlikely to be the nominee . We re going to do and we re going to put it out and get the ball， he said . I would be afraid to blame the girls to go back but I was just disappointed with the race , he said. I m not going to work together with a different role and we can win the game，he added The couple s lives are still missing and they have been killed in the city s way to play against them ,and because Icame out there . For the last three years ,we ve got a lot of things that we need to do with this is based on the financial markets . Don t ask me ,but I know ,if I ll be able to be out of Hillary Clinton ,I think it s being</td></tr></table>
+
+Table 9: Samples from our MLE with temperature to match BLEU scores reported in Guo et al. (2017)   
+
+<table><tr><td>MLE conservative . economy . police officer . coming weeks. game . for president . The US economy grew at a record low of 1 .6 percent in 2O14 ,and the unemployment rate has fallen by O .9 percent . The new rules are put into the hands of a member of the police ,and the public is not aware of the situation The World Health Organization said a number of people were killed in the attack ,according to the Pentagon . The study also found that women who are not particularly vulnerable to women ’s health</td><td>The UN Security Council is a major concern for the U . S . government , as well as a NATO ally in the Syrian civil war . A spokesman for the Met Ofice said the death toll was only slightly higher than the previous year,according to the report . But I hope that at the end of the day,I’ m going to give her the best chance to go to the gym and go out and play . The man,who cannot be named,said that he had never had sex with him,and he didn ’t want to see him . And it ’s just one of those things that I have to say ,I’m a Democrat ，and I’m a The bank is now the fastest growing market in the world and it is a significant change in the The two men ，aged 2O and 22 ，were arrested and charged with the murder of a man ， a The company will be able to provide a post Brexit strategy ，which will be published in the She said she had been on the wrong side of the road and was finally caught in a car accident and was taken to hospital . I don ’ t think he ’ s even a good player ,he said ,but he ’ s got a good chance to win the I don ’t know what the future holds but I’m sure it will be a good thing . It’ s a very important step forward ,and we ’ re going to be able to get the right results . The driver of the vehicle，who was inside the vehicle ，was taken to hospital for treatment , but said he was not aware of the incident . The leak was obtained by a Freedom of Information request ,which is based on the number of people claiming to be a victim of fraud . The former secretary of state has made a major speech in New York , where she ’ s running</td></tr></table>

parse/train/BJgza6VtPB/BJgza6VtPB_content_list.json

@@ -0,0 +1,1442 @@
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+    {
+        "type": "text",
+        "text": "LANGUAGE GANS FALLING SHORT ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Massimo Caccia∗ Mila, Universite de Montr´ eal´ massimo.p.caccia@gmail.com ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Lucas Caccia∗   \nMila, McGill University   \nlucas.page-caccia@mail.mcgill.ca ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "William Fedus Mila, Universite de Montr ´ eal ´ Google Brain, Montreal ´ ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Hugo Larochelle Google Brain, Montreal´ Mila, Universite de Montr ´ eal ´ Canada CIFAR AI Chair ",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Joelle Pineau ¨ Mila, McGill University Facebook AI Research, Montreal´ Canada CIFAR AI Chair ",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Laurent Charlin Mila, HEC Montreal´ Canada CIFAR AI Chair ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "ABSTRACT ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Traditional natural language generation (NLG) models are trained using maximum likelihood estimation (MLE) which differs from the sample generation inference procedure. During training the ground truth tokens are passed to the model, however, during inference, the model instead reads its previously generated samples - a phenomenon coined exposure bias. Exposure bias was hypothesized to be a root cause of poor sample quality and thus many generative adversarial networks (GANs) were proposed as a remedy since they have identical training and inference. However, many of the ensuing GAN variants validated sample quality improvements but ignored loss of sample diversity. This work reiterates the fallacy of quality-only metrics and clearly demonstrate that the well-established technique of reducing softmax temperature can outperform GANs on a quality-only metric. Further, we establish a definitive quality-diversity evaluation procedure using temperature tuning over local and global sample metrics. Under this, we find that MLE models consistently outperform the proposed GAN variants over the whole quality-diversity space. Specifically, we find that 1) exposure bias appears to be less of an issue than the complications arising from non-differentiable, sequential GAN training; 2) MLE trained models provide a better quality/diversity tradeoff compared to their GAN counterparts, all while being easier to train, easier to cross-validate, and less computationally expensive.1 ",
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+    {
+        "type": "text",
+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Generating fluent natural language is a central aim in Natural Language Processing (NLP). Transformer architectures (Vaswani et al., 2017) with hundreds of millions or billions of parameters regularly reestablish state-of-the-art on held-out validation perplexities, however, the generated samples can still often lack coherence. It was hypothesized that exposure bias, differences in the training and inference procedures, is the root cause for poor sample quality. Therefore, numerous GANs (Goodfellow et al., 2014) for text generation were proposed since they do not suffer from exposure bias due a training objective that directly seeks to improve sample quality (to a learned critic). ",
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+    {
+        "type": "text",
+        "text": "While many of the early GAN variants demonstrated improvements in sample quality (Yu et al., 2017; Guo et al., 2017), they often ignored loss of sample diversity. This is not only a theoretical concern because it is well-documented that GANs exhibit mode collapse (Che et al., 2016; Salimans et al., 2016) where the generator produces a subset of the ”modes” in the training data, reducing diversity. Evaluating generated samples remains challenging (Liu et al., 2016; Zhao et al., 2017), but C´ıfka et al. (2018) recommends assessing generated samples along two dimensions: 1) the quality of each sentence; 2) the diversity across sentences. However, this too is problematic because now the assessment relies on two measures which can make it difficult to compare models. Without further information about the relative trade-off between the two dimensions it is impossible to claim which is superior (Figure 1, left subplot). ",
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+    {
+        "type": "image",
+        "img_path": "images/1f29a04568f394bf533ee075c77fc1d4392323e684e74043cba15e4eda162d36.jpg",
+        "image_caption": [
+            "Figure 1: The importance of temperature for evaluating NLG models on quality and diversity. Each sub-figure plots inverse quality against inverse diversity (lower is better for both metrics). Left: current way of comparing NLG models. In this case, it is impossible to come to any meaningful conclusions about which model (red or blue) dominates the other. Middle: With our proposed NLG evaluation framework, the temperature sweep shines a light on the relative performance of the models: the red model should be used for high-diversity samples and the blue model for high-quality samples. Right: A second simulated scenario (consistent with the left Figure) where the temperature sweep reveals that the blue model dominates the red. That is, for any desired diversity-level, there is a temperature for which the blue model outperforms the red in terms of quality (and vice versa). "
+        ],
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+    {
+        "type": "text",
+        "text": "In this work, we build on the natural relationship between a model’s softmax temperature and the resultant quality-diversity trade-off: lower temperatures generate less diverse, higher-quality samples; higher temperatures increase the entropy of the distribution and produce more diverse, lower-quality samples. We propose a temperature sweep as a computationally efficient method to characterize the quality-diversity trade-off of different models. By explicitly controlling the temperature we remove a potential source of bias (models may have different ”implicit” temperatures) and obtain a more complete understanding of each model’s behavior (Figure 1 middle and right). ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Additionally, we address that temperature modulation changes the entropy of the conditional distributions, as opposed to changing the entropy of the joint distribution. We explore other ways to navigate the quality-diversity space with less bias, including stochastic beam search and generator rejection. Although these methods provide small gains in the quality-diversity trade-off they have other computational limitations. ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Despite the dizzying array of text-GAN variants and algorithms (Yu et al., 2017; Che et al., 2017; Lin et al., 2017; Zhang et al., 2017; Guo et al., 2017; Fedus et al., 2018; Lu et al., 2018a; Shi et al., 2018; Xu et al., 2018; Chen et al., 2018; Nie et al., 2019; d’Autume et al., 2019) our conclusions using temperature sweeps are clear: MLE models still dominate GANs. According to all metrics we studied, changing the temperature of MLE models at generation time leads to a better qualitydiversity trade-off compared to GANs. This evaluation technique provides a definitive boundary for future GAN research and our hope is that it will help the NLP community accurately assess natural-language generation progress. ",
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+    {
+        "type": "text",
+        "text": "2 ADVERSARIAL TEXT GENERATION ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 1
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+    {
+        "type": "text",
+        "text": "GANs are implicit generative models learned via a competition between a generator network $G _ { \\theta }$ and a discriminator network $D _ { \\phi }$ . The generator network $G _ { \\theta }$ produces samples from a probability distribution $p _ { m o d e l } ( x )$ . The discriminator $D _ { \\phi } ( x )$ attempts to distinguish whether an input value $x$ is real (training data) or generated. Mathematically, the GAN objective can be formulated as a minimax game ",
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+    {
+        "type": "equation",
+        "img_path": "images/d55c79a1d1f9f898c849cce8e0d43792c67bfe8c58e44f0ab5463aca67fa5bae.jpg",
+        "text": "$$\n\\mathcal { L } = \\underset { \\theta } { m i n } \\ : m a x \\ : \\mathbb { E } _ { { x } \\sim { p _ { d a t a } } } [ \\log D _ { \\phi } ( x ) ] + \\mathbb { E } _ { { x } \\sim { G _ { \\theta } } } [ 1 - \\log D _ { \\phi } ( x ) ]\n$$",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "GANs were first proposed for continuous domains since their training procedure differentiates through the discriminator into the generator. However, modeling text, which is both discrete and typically modeled sequentially requires a challenging adaptation for GANs which, in their original formulation, were built upon “one-shot” continuous data. Discrete (sequential) data require an alternative approach. Yu et al. (2017) estimate the gradient to the generator via REINFORCE policy gradients (Williams, 1992). In their formulation, the discriminator evaluates full sequences. Therefore, to provide error attribution earlier for incomplete sequences and to reduce the variance of gradients, they perform $k$ Monte-Carlo rollouts until the sentence is completed. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Yu et al. (2017) advertise their model using two tasks which we argue (with hindsight) are flawed. First, they introduce a synthetic evaluation procedure where the underlying data distribution $P$ is known and can be queried. By representing $P$ with an LSTM (referred to as an oracle in the literature), they directly compute the likelihood of samples drawn from a generative model $G _ { \\theta }$ . The issue is that they benchmark models against each other on this likelihood alone, i.e., the diagnostic is entirely blind to diversity. For example, a model that always outputs the same highly likely sequence would easily outperform other potentially superior models. For real data, there was no agreed-upon metric to evaluate the quality of unconditional NLG at the time. This led the authors to propose a new metric, Corpus-level BLEU, which computes the fraction of n-grams in a sample that appears in a reference corpus. Again, this metric is agnostic to diversity. Generating a single good sentence over and over will give a perfect BLEU score. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "This paper sparked a stream of works that adopt their evaluation framework. Notably, RankGAN (Lin et al., 2017), MaliGAN (Che et al., 2017), TextGAN (Zhang et al., 2017), LeakGAN (Guo et al., 2017) and IRL-GAN (Shi et al., 2018) were proposed soon after. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "All but one of the aforementioned papers evaluate sample quality alone. As a remedy, Zhu et al. (2018) propose a metric that compares a generated sentence with a corpus of generated sentences, called Self-BLEU. They, along with Lu et al. (2018b), provide an extensive comparison of GANs using quality (negative BLEU) and diversity (Self-Bleu). However, it is not clear which algorithm is superior, as evidenced by Figure 2, because no model simultaneously outperforms the other on both metrics. It is now standard for language GANs to evaluate simultaneously quality and diversity. ",
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+    {
+        "type": "text",
+        "text": "GANs Trained without RL Reinforcement Learning (RL) is often difficult to optimize, unstable, and sensitive to hyperparameters. Because of this, GAN-variants have recently been ",
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+    {
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+        "img_path": "images/1266ec0367a09686c0920c0bbaec46286e697474e8954caf2cf263765da54f5c.jpg",
+        "image_caption": [
+            "Figure 2: Negative BLEU-5 versus SBLEU5 (lower is better for both metrics) on the EMNLP2017 News dataset taken from (Lu et al., 2018b) and this work (train data and FM-GAN). These scatter plots do not clearly show which algorithm is preferred since none strictly dominates on both metrics simultaneously. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "proposed that eschew RL-techniques in favor of fully-differentiable objectives. Cooperative training (CoT) (Lu et al., 2018a) and feature mover GAN (FM-GAN) Chen et al. (2018) are notable approaches. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Research in both RL and non-RL GANs is still very active (e.g., Xu et al. (2018); Nie et al. (2019); d’Autume et al. (2019); Li et al. (2019); Gagnon-Marchand et al. (2019)) and so our review is not exhaustive. ",
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3 TEMPERATURE SWEEP: TOWARDS ROBUST NLG EVALUATION ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "During natural language generation, a single spurious sampled token can lead to an overall lowquality and incoherent sequence. In other words, a high-entropy conditional distribution may result in poor sample quality at inference. To address this problem, one can modulate the entropy of $G _ { \\theta } \\mathbf { \\bar { ( } } x _ { t } \\mid x _ { 1 : t - 1 } \\mathbf { \\bar { ) } }$ with a Boltzmann temperature parameter $\\alpha$ (Ackley et al., 1988). If $o _ { t }$ is the generator’s pre-logit activation and $W$ is the word embedding matrix, then the conditional distribution of the generator is given by $G _ { \\theta } ( x _ { t } \\mid x _ { 1 : t - 1 } ) = \\operatorname { s o f t m a x } ( o _ { t } \\cdot W / \\alpha )$ . Decreasing $\\alpha$ below 1.0 will increase $o _ { t }$ and thus decrease the entropy of $G$ ’s conditional probability. Temperature tuning naturally moves the model in quality/diversity space. We demonstrate this in Table 1. ",
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+    {
+        "type": "text",
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "α Samples ",
+        "text_level": 1,
+        "bbox": [
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+            196
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "table",
+        "img_path": "images/7df6d3e94db16971ba70d4471797207693e054a0f66b11d6fd2ca5b90ef078dc.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td colspan=\"2\">2.0 (1) If you go at watch crucial characters putting awareness in Washington ,forget there are now unique developments organized personally then why charge .</td></tr><tr><td></td><td>(2)Front wants zero house blood number places than above spin 5 provide school projects which youth particularly teenager temporary dollars plenty of investors enjoy headed Japan about if federal assets own,at 41 .</td></tr><tr><td>1.0 this point .</td><td>(1) Researchers are expected to comment on where a scheme is sold , but it is no longer this big name at (2) We know you ’re going to build the kind of home you ’re going to be expecting it can give us a better understanding of what ground test we’re on this year ,he explained .</td></tr><tr><td>0.7</td><td>(1) The other witnesses are believed to have been injured ,the police said in a statement ,adding that there was no immediate threat to any other witnesses . (2) The company ’ s net income fell to 5 .29 billion ,or 2 cents per share ,on the same period last year .</td></tr><tr><td>0.0</td><td>(1) The company’s shares rose 1.5 percent to 1.81 percent,the highest since the end of the year. (2) The company ’s shares rose 1 . 5 percent to 1 .81 percent,the highest since the end of the year .</td></tr></table>",
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+        "type": "text",
+        "text": "Table 1: The effect of temperature on samples from an language model trained via MLE on the EMNLP17 News dataset. At a temperature of $\\alpha = 1 . 0$ the samples are syntactically correct but often lack in global coherence. The sample quality varies predictably with temperature. At $\\alpha > 1 . 0$ , the syntax breaks down and at $\\alpha = 0 . 0$ the model always outputs the same sequence. At $\\alpha = 0 . 7$ the samples are both of high quality and of sufficient diversity. ",
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+        "type": "text",
+        "text": "The evaluation protocol for NLG explained in Section 2 is to compare models with respect to both quality and diversity metrics. Often this results in a situation where it is impossible to tell which model is superior, as shown in Figure 2 and further exemplified in Figure 1 (Left). One can then control the quality-diversity trade-off of autoregressive text generators using temperature. We can leverage this tool to design a new evaluation framework that shines a light on the real performance of each model. More precisely, we propose to generate samples at s temperatures for each model in order to compute temperature curves in quality-diversity space. This is exemplified in Figure 1. We refer to this procedure as temperature sweep. This new way of evaluating NLG models allows practitioners to answer questions such as: which model to use if interested in high quality (or diversity) samples? Does a new model improve upon others in the quality/diversity space or is it just reducing the entropy of the distribution? It could also be leveraged as a cross-validation tool e.g., early-stop once the best temperature curve is achieved according to a heuristic. ",
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+        "text": "In the next section we show, using temperature sweep, that MLE models consistently outperform the new proposed GAN variants everywhere in the quality-diversity space. MLE performs equally on synthetic data to CoT and outperforms it on real data, whilst being computationally and algorithmically less complicated. Our results are further validated in independent follow-up works (d’Autume et al., 2019; Alihosseini et al., 2019)where temperature sweeps show MLE outperforming GANs. ",
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+        "type": "text",
+        "text": "To implement temperature sweep we have taken advantage of the fact that our model factorizes the joint distribution over an observation as a product of conditional distributions over single tokens given all previous tokens (this is a property of most autoregressive neural networks). We change the temperature of these conditionals, which is straightforward to implement. However, this is different from changing the temperature of the joint probability distribution. The samples generated in this way are biased towards having lower entropy at the beginning of sentences compared to samples obtained by changing the entropy of the joint distribution. Changing the entropy of the joint distribution quickly becomes intractable with respect to vocabulary size and/or the total number of timesteps. We show below some entropy reducing techniques are less biased than changing the temperature of the conditionals and might achieve a better quality-diversity trade-off. However, we argue that theses methods aren’t suitable for our evaluation protocol due to computational inefficiency (see Section 5.4). ",
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+        "type": "text",
+        "text": "Stochastic Beam Search is a popular approximate decoding technique. It is computationally expensive but leads to higher-likelihood samples than greedy decoding. Here, we focus on its stochastic version (not to be confused with the locally optimal one local beam search). In Stochastic beam search with beam size $k$ , the $k$ most likely hypotheses (sampled so far) are kept at every decoding steps. In Appendix A, we detail this technique and explain how it is less biased than temperature tuning regarding the reduction of the joint distribution’s entropy. Finally, the more traditional local (deterministic) beam search removes all sample diversity and is not useful in our setting. ",
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+        "text": "Generator Rejection Sampling works as follow: generate some sentences; compute their likelihood under the generator’s own distribution; accept/reject the sample given a threshold. The threshold enables the practitioner to modulate the quality-diversity trade-off. In Appendix B, we explain how it is less biased than temperature tuning, why it is computationally expensive, and how the discriminator can be used in rejection sampling. ",
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+        "text": "4 RELATED WORK ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Concurrent with our work, Semeniuta et al. (2018) demonstrated the issues of local n-gram metrics. Their extensive empirical evaluation of GAN models and language models (LM) did not result in evidence of GAN-trained models outperforming on the new and improved global metrics from C´ıfka et al. (2018). Our analysis further explores this path by examining the performance of these models under a sweep of temperatures. We believe this difference to be of utmost importance, as it is the necessary ingredient towards definitively showing MLE models outperform current GAN variants on quality-diversity global metrics. Work from Ott et al. (2018) thoroughly examines the local beam search strategy for neural machine translation. In their analysis, the authors compare local beam search and generator rejection sampling and find the beam search is quite effective at finding highlikelihood regions. However, their work focuses on conditional text generation, where quality-only metrics measures performance. ",
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+        "type": "text",
+        "text": "Guo et al. (2017) suggest that increasing the temperature at training time leads to more diverse samples. However, we argue that this procedure leads to the opposite outcome as a model can adapt to the temperature change. This would have the net result of lowering the entropy at test time. We discuss this issue and propose a study in Appendix F. ",
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+    {
+        "type": "text",
+        "text": "5 EMPIRICAL RESULTS ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Using our evaluation approach (Section 3), we examine several recent GAN text generation models and compare against an MLE baseline. The experiments consist of two parts: synthetic data generation and long-text generation. We provide strong empirical evidence for both types of data that MLE trained models reliably outperform textual GANs in the quality-diversity space. For these experiments, we only use temperature tuning, as it is the only technique that gives a smooth control over said trade-off whilst being computationally efficient (see Section 5.4). ",
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+    {
+        "type": "text",
+        "text": "5.1 EXPERIMENTAL DETAILS ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "The ever-growing body of RL trained language GANs makes writing, running hyperparameter searches and cross-validations on all the variants prohibitively expensive.2 We implemented our own language GAN, including improvements/functionalities proposed in several text GAN papers. We ensure that each functionality can be toggled during training. Then for each dataset, we ran a hyperparameter search of 300 trials encompassing all possible combinations of said functionalities. We refer to this model as RL-GAN. It is based on SeqGAN (Yu et al., 2017) with additional improvements shown to be useful including: MLE pretraining (Yu et al., 2017), leaky discriminator (Guo et al., 2017), step-level loss instead of sequence level (Fedus et al., 2018), learned baseline to reduce variance (Fedus et al., 2018), regularizing REINFORCE with a maximum-entropy loss (Williams & Peng, 1991) and alternating adversarial loss with MLE loss (Guo et al., 2017). ",
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+    },
+    {
+        "type": "text",
+        "text": "Through comparisons with previously reported results and results obtained via running the official repositories, we show that RL-GAN is the state-of-the-art RL trained GAN. Our MLE model is trained with the same codebase (adversarial training turned off) and only one-sixth of the trials. Moreover, we report SeqGAN and LeakGAN results in the synthetic data experiment. These were obtained with the official repositories that we modified in order to obtain samples at different temperatures. Finally, the SeqGAN, LeakGAN, RankGAN, and MaliGAN results in Figure 4a are taken from (Lu et al., 2018b), which was written by the authors of SeqGAN and LeakGAN. ",
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+    {
+        "type": "text",
+        "text": "Finally, we conducted experiments differently for non-RL GANs. The CoT (Lu et al., 2018a) results are obtained with the official repository via a careful hyperparameter search guided by a discussion with the authors. The FM-GAN (Chen et al., 2018) results were obtained with the best performing model that was provided by the authors. ",
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+    {
+        "type": "text",
+        "text": "Selecting temperature sweep range. We describe how we selected the range of temperatures in the temperate sweeps. We found that in practice, both the quality and the diversity axes induce bounds beyond which results are non-informative. On the diversity dimension, we found no value in increasing the entropy of the MLE model because minimizing the forward KL does not lead to an underestimation of the real data entropy. Hence, we decreased the temperatures of the other models until a similar diversity to the MLE model was reached. On the quality dimension, we decreased the temperatures to $\\alpha = 0$ but did not report the complete curves for the following reasons. First, with synthetic data (Figure 3) the $N L L _ { t e s t }$ explodes when diversity is decreased too much, so we reduce the temperature of the MLE model until the difference in performance compared to the GAN results was evident. Second, in the real data in Figure $^ { 4 \\mathrm { b } }$ , we stopped decreasing the temperature when the models achieved a Reverse LM score equal to the perplexity achieved by a 1-gram (unigram) model. This means that the generated dataset is almost non-informative for the (Reverse) language model to learn on i.e., it is as informative as counting tokens. This also coincides with severe mode collapse and a temperature of $< 0 . 5$ for the MLE model. In Figure 4a, we once more decreased the temperature until the difference in performance of MLE with respect to the other models is unambiguous. ",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/7bce730181fe5aaafba34bd3ad5e2f996accb734a698be7bbbbd739eb3aeccb8.jpg",
+        "table_caption": [
+            "Table 2: NLLoracle measured on the synthetic task (lower is better). All results are taken from their respective papers. An MLE-trained model with reduced temperature easily improves upon these GAN variants, producing the highest quality sample. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>NLLoracle</td></tr><tr><td>SeqGAN(Yu et al., 2017) RankGAN (Lin et al., 2017) LeakGAN (Guo et al., 2017)</td><td>8.74 8.25 7.04</td></tr><tr><td>IRL (Shi et al., 2018)</td><td>6.91</td></tr><tr><td>MLE(α = 1.0) MLE (α = 0.4)</td><td>9.40</td></tr><tr><td>MLE (α = 0.001)</td><td>5.50 4.58</td></tr></table>",
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+    },
+    {
+        "type": "image",
+        "img_path": "images/89a710e6ced3625a11e248fec87dfeea71ca3e21b27c78876d09e52ce012345c.jpg",
+        "image_caption": [
+            "Figure 3: Effect of temperature tuning on the global metrics (lower is better for both metrics) for the synthetic task. "
+        ],
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+    {
+        "type": "text",
+        "text": "5.2 SYNTHETIC DATA EXPERIMENT ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "In the synthetic experiment, we learn a generative model of data produced from a fixed LSTM oracle Yu et al. (2017) with a hidden dimension of 32 with parameters drawn from a standard normal distribution. This allows us to compute a perfect quality metric, the likelihood under the Oracle $\\mathrm { N L L } _ { o r a c l e }$ . In Table 2, we see that artificially reducing the temperature at inference achieves stateof-the-art as evaluated by the ${ \\mathrm { N L L } } _ { o r a c l e }$ . As we and others have argued, evaluating quality alone is misleading. The MLE-trained model with extremely low temperature will repeatedly output only a single sequence. It is therefore essential to evaluate the resulting sample diversity which we evaluate using the log-likelihood that a generator assigns to held-out data $( N L L _ { t e s t } )$ ). We report the result of a temperature sweep in Figure 3. ",
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+    },
+    {
+        "type": "image",
+        "img_path": "images/f993cd4f5146404c29140048f94bea8ae21c0b90b29d10bb16d319d9b644b653.jpg",
+        "image_caption": [
+            "Figure 4: Results on the EMNLP 2017 News dataset. (lower is better for all metrics). MLE under a temperature sweep achieves better quality-diversity trade-off compared to the GAN approaches. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Our RL-GAN benchmark is superior to the official SeqGAN and LeakGAN implementations. Nonetheless, MLE outperforms GANs everywhere in the quality-diversity space. Semeniuta et al. (2018) suggest that the best-performing GANs tend to stay close to the solution given by maximumlikelihood training. We find support for this conclusion, as the best performing RL-GAN models have the smallest learning rate and a considerable amount of pretraining. CoT achieves similar performance to MLE, but with dramatically increased algorithmic complexity. This is unsurprising as their objectives are somewhat similar (see Section 4). Alihosseini et al. (2019) replicated this experiment on synthetic data and arrived at the same conclusions. ",
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+    {
+        "type": "text",
+        "text": "5.3 LONG-TEXT GENERATION ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Next, we study long-text generation using EMNLP News 2017. We first compare an MLE model to the reported GAN results on the local metrics Negative BLEU and Self-BLEU. Negative BLEU5 and SBLEU-5 are used for Figure 4a and results for (Self-)BLEU-2 to (Self-)BLEU-4 are reported in Appendix D. Again, the conclusions are the same: MLE outperforms all RL GANs considered in the quality-diversity trade-off. Moreover, MLE outperforms FM-GAN, the state-of-the-art non-RL Language GAN. Note that the FM-GAN results were obtained with a combination of temperature tuning and noise reduction in order to achieve the best possible results. We provide additional details in Appendix H. We compare MLE to GANs using recently proposed global metrics, the Language Model score (quality) and Reverse Language Model score (diversity+quality) (C´ıfka et al., 2018; Semeniuta et al., 2018). See Figure 4b for a comparison of the training scheme in quality-diversity space. The conclusion is the same as with BLEU and Self-BLEU: MLE outperforms all GANs everywhere in the quality-diversity space. Further results on this dataset as well as on the IMDB movie reviews (Maas et al., 2011) and WikiText-103 (Merity et al., 2016) datasets are presented in independent follow-up works (d’Autume et al., 2019; Alihosseini et al., 2019) where MLE is also shown to outperform GANs using temperature sweeps. ",
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+    {
+        "type": "text",
+        "text": "5.4 EMPIRICAL REMARKS ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "These findings are illustrative: a body of research is predicated on exposure bias as the culprit for poor sample quality. Therefore, under this hypothesis, MLE should be at its weakest on long-text generation tasks. However, our results are evidence that exposure bias is less of an issue than optimization problems arising from GAN training combined with the non-differentiability of the original objective function. There is also another way to interpret these results. It seems that MLE (pre)training leaves the generator with a better policy according to quality-diversity. However, because GAN training removes entropy from the learned distribution (see Fig. 5 in Appendix ??), which results in high-quality samples, it can lead one to believe that GAN trained models are superior. ",
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+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/03979eb1832a55dff2d4982a15dfaed1b86a25a7cf279b10f11963b5118f22fa.jpg",
+        "image_caption": [
+            "Figure 6: Analysis of decoding methods. (lower is better for all metrics). Left: Less biased methods provided a better quality/diversity trade-off. Right: However, they are computationally much more expensive. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Methods to approximately reduce the entropy of the joint distribution We analyze the different decoding mechanisms as tools to move in the quality-diversity space and as an alternative to temperature sweep. We evaluate these tools by decoding from the best performing MLE model on the EMNLP2017 News dataset. We also consider the different properties of these tools, including their ability to provide smooth control over the quality-diversity trade-off and their computational efficiency. The purpose of this experiment is thus not to find the best performing strategy i.e., a model combined with a decoding method but rather to compare decoding methods. Further, a comparison between MLE and RL-GAN using these approaches is in Appendix I and it supports our prior results. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Figure 6a compares three methods for navigating the quality (Language Model, LM) diversity (Reverse LM) space: temperature sweep, generator rejection,3 and beam search. We first note that temperature tuning and generator rejection sampling yield a similar trade-off in the high-diversity regime. However, as the bias incurred by temperature tuning grows, so does the gap between both methods. An important finding is that generation rejection sampling gets exponentially slower as the threshold increases (see Figure 6b). It is for this reason that the generator rejection sampling curve doesn’t span further in the high-quality part of the space. ",
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+    {
+        "type": "text",
+        "text": "Beam search, a less biased method, also seems to offer a better trade-off compared to temperature sweep. However, beam search has a major drawback: unitary increases in beam size leads to drastic leaps in qualitydiversity space. In Figure 6a we report beam sizes of 1 (right dot), 2 (middle dot), and 3 (left dot). This study shows that although the less biased methods seem to offer at least small gains in the quality-diversity space, temperature tuning still has important advantages to assess a model’s quality-diversity trade-off efficiently. The discreteness of beam search and the computational inefficacy of generator rejection sampling are important drawbacks. However, if one’s goal is to obtain the best samples possible, we advocate for their use. ",
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+    {
+        "type": "text",
+        "text": "GAN Training Reduces Entropy Figure 5 shows the evolution of a generator’s entropy with respect to epochs. We observe that as soon as adversarial training starts, a drastic entropy reduction occurs. Future work investigates if GAN training changes the learned distribution or simply reduces the entropy in an ineffective way with respect to the quality-diversity trade-off. ",
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+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/5f48d48a79b42b8cd8328a508fb1fd72a229c158d24512ded9834936e2917fa1.jpg",
+        "image_caption": [
+            "Figure 5: Dotted line indicates the start of GAN training. We notice a clear drop in entropy (spike in $\\mathrm { N L L } _ { t e s t . }$ ) when moving from maximum-likelihood to adversarial updates. "
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "6 DISCUSSION ",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "We demonstrate that well-adjusted language models are a strong baseline and that temperature sweeping can provide an unambiguous characterization of model performance in terms of quality and diversity. A well-adjusted language model outperforms the considered GAN variants as evaluated on both local, and more surprisingly, global metrics of quality and diversity. Our temperature sweeping framework shares characteristics with a Receiver Operating Curve. Analogously, if one needed a single scalar to compare NLG models, one could compute the area under the curve and seek the model with the smallest value (lower is better for our considered metrics). ",
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+    {
+        "type": "text",
+        "text": "GAN-based generative models have been proven effective on real-valued data. However, there exist many difficult pernicious issues involved in moving to discrete data. These issues must be overcome before they will improve over the strong MLE baselines for unconditional language generation. On the datasets and tasks considered, potential issues caused by exposure bias were less severe than the ones arising from adversarial training combined with learning the non-differentiability of the original objective function. GAN training may prove fruitful eventually, but this research lays forth clear boundaries that it must first surpass. ",
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+    {
+        "type": "text",
+        "text": "REFERENCES ",
+        "text_level": 1,
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
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+        "text": "Lantao Yu, Weinan Zhang, Jun Wang, and Yong Yu. Seqgan: Sequence generative adversarial nets with policy gradient. 2017. ",
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+        "text": "Yizhe Zhang, Zhe Gan, Kai Fan, Zhi Chen, Ricardo Henao, Dinghan Shen, and Lawrence Carin. Adversarial feature matching for text generation. arXiv preprint arXiv:1706.03850, 2017. ",
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+        "text": "Junbo Jake Zhao, Yoon Kim, Kelly Zhang, Alexander M Rush, and Yann LeCun. Adversarially regularized autoencoders for generating discrete structures. CoRR, abs/1706.04223, 2017. ",
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+        "text": "Yaoming Zhu, Sidi Lu, Lei Zheng, Jiaxian Guo, Weinan Zhang, Jun Wang, and Yong Yu. Texygen: A benchmarking platform for text generation models. SIGIR, 2018. ",
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+    {
+        "type": "text",
+        "text": "A STOCHASTIC BEAM SEARCH. ",
+        "text_level": 1,
+        "bbox": [
+            178,
+            102,
+            452,
+            117
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Beam search is a popular approximate decoding technique. It is computationally expensive but usually leads to higher-likelihood samples than greedy decoding. Here, we focus on its stochastic version, not to be confused with the locally optimal one, Local Beam Search. In Stochastic Beam Search with beam size $k$ , words are sampled sequentially starting from the first one. At the first timestep $k$ words are sampled, each represents a hypothesis. At subsequent timesteps, $k$ next words are sampled conditioned on each of the $k$ current hypotheses, resulting in $k ^ { 2 }$ hypotheses. The $k$ most likely are kept and so on. Because an increase in beam size results in higher-likelihood samples, beam size can be leveraged to modulate the quality-diversity trade-off. Moreover, an infinite beam size would result in sampling the most likely sentences under the generator’s distribution. This is not what we can expect from setting the temperature to 0, which is equivalent to greedy decoding. For this reason, we can hypothesize that Stochastic Beam Search is less biased regarding the reduction of the joint distribution’s entropy. However, unlike temperature tuning, one cannot smoothly trade quality for diversity, as the beam size is a discrete parameter. The more traditional local (deterministic) beam search removes all sample diversity. Thus, it is not useful in our setting. ",
+        "bbox": [
+            174,
+            135,
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+            328
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "B GENERATOR REJECTION SAMPLING. ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            351,
+            513,
+            366
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Generator Rejection Sampling works as follow: generate some sentences; compute their likelihood under the Generator’s own distribution; accept/reject the sample given a threshold. The threshold enables the practitioner to modulate the quality-diversity trade-off. Similar to Stochastic Beam Search, increasing the threshold to a maximum level would result in always sampling the most likely sentence. We can again hypothesize that this method achieves a better quality-diversity trade-off compared to temperature tuning, since it is not biased towards having sentences with a lower entropy prefix. However, the running time of this procedure increases significantly as the acceptance threshold lowers, as discussed in Section 5.4. We also experimented with a rejection sampling scheme where the score is determined by a discriminator but it did not provide any additional insights. ",
+        "bbox": [
+            174,
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+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "C QUALITATIVE ANALYSIS OF THE SAMPLES",
+        "text_level": 1,
+        "bbox": [
+            174,
+            531,
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+            546
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "For completeness, we show samples of SeqGAN, LeakGAN, and MLE from both datasets in Table 3. In this experiment, we used the Image COCO dataset (Lin et al., 2014) in order to generate shorter sentences as well. In this case, the samples of all models appear similar. This is because generating captions is a relatively easier task. For the EMNLP2017 News dataset, we would like to point out interesting facts from our samples. In our first sample (1), the model generates the sequence “post Brexit strategy”. This is n-gram is not present in the training set. In our second sample (2), the token “leak” and the n-gram “Freedom of Information request” never appear together in the training dataset. The extrapolations show that the model learns a certain level of generalization beyond the training set. Additional samples are presented further in Appendix J. ",
+        "bbox": [
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+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "D FULL BLEU AND SELF-BLEU RESULTS ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            710,
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+            727
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Full BLEU and Self-BLEU results are shown in Table 4. ",
+        "bbox": [
+            173,
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+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "E THE LIMITATIONS OF BLEU ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            779,
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+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "In this section, we want to highlight an important flaw in using BLEU as a proxy for quality. We tuned the temperature in order to find a MLE model with BLEU score equal to the training data’s. We show three randomly sampled sentences from the model in Table 6. Although sometimes grammatically correct, the samples lack in semantic and/or global coherence. It seems the generated text has poor information content. Surprisingly, in order to get great samples on a consistent basis, the temperature needs to be reduced to a level where BLEU-5 is twice as large as the training data’s. Thus, it seems like BLEU is not always a good proxy of sample quality. Again, we think it is of utmost importance to develop better metrics and modernize NLG’s canonical evaluation framework. ",
+        "bbox": [
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+        "page_idx": 11
+    },
+    {
+        "type": "table",
+        "img_path": "images/7783ec756cfca81f2f71dfaf99af0fd7cd6e0e60c09c85be046439ff58612863.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Datasets</td><td>imageCOCO</td><td>EMNLP2017NeWs</td></tr><tr><td rowspan=\"2\">SeqGAN</td><td>(1)A woman is riding a bike on the street next to a bus.</td><td>(1) You only certainly might not rush it down for those circumstances where we are when they were the heads, and when she&#x27;s name.</td></tr><tr><td>(2)A silver stove,the refrigera- tor, sitting in a kitchen.</td><td>(2) I think you should really really leave for because we hadn&#x27;t been busy, where it goes to one,&quot;he wrote.</td></tr><tr><td rowspan=\"2\">LeakGAN</td><td>(1）A woman holding an um- brella while standing against the sidewalk.</td><td>(1)A man has been arrested at age 28,a resident in Seattle,which was widely reported in 2007.</td></tr><tr><td>(2) A bathroom with a toilet and sink and mirror (1）A narrow kitchenwith</td><td>(2) I also think that&#x27;s a good place for us,I&#x27;m sure that this would be a good opportunity for me to get in touch.</td></tr><tr><td rowspan=\"2\">MLE</td><td>woodencabinetsandwhite appliances .</td><td>(1） The company will be able to provide a post Brexit strategy,which will be published in the coming weeks</td></tr><tr><td>(2） There are several bikes parked in front of a tall building with four cars .</td><td>(2) The leak was obtained by a Freedom of Informa- tion request，which is based on the number of people claiming to be a victim of fraud .</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "table",
+        "img_path": "images/a41f8fdd0bb43f4aff4235d9f271b726d2fd4e85e871b25add79430078e4f5f2.jpg",
+        "table_caption": [
+            "Table 3: Samples from the different models on Image COCO and EMNLP2017 WMT News. For SeqGAN and LeakGAN, samples were taken from (Guo et al., 2017). It’s the first two samples found in their appendix. For our samples, we reduced the temperature of the model till we achieved similar BLEU scores to the ones reported in (Guo et al., 2017) in order to keep comparison fair. ",
+            "Table 4: BLEU (left) and Self-BLEU (right) on test data of EMNLPNEWS 2017. (Higher BLEU and lower Self-BLEU is better). "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td colspan=\"4\">BLEU</td><td colspan=\"4\">Self-BLEU</td></tr><tr><td></td><td>2</td><td>3</td><td>4</td><td>5</td><td>2</td><td>3</td><td>4</td><td>5</td></tr><tr><td>Training Data</td><td>0.86</td><td>0.61</td><td>0.38</td><td>0.23</td><td>0.86</td><td>0.62</td><td>0.38</td><td>0.24</td></tr><tr><td>SeqGAN Yu et al. (2017)</td><td>0.72</td><td>0.42</td><td>0.18</td><td>0.09</td><td>0.91</td><td>0.70</td><td>0.46</td><td>0.27</td></tr><tr><td>MaliGAN Che et al. (2017)</td><td>0.76</td><td>0.44</td><td>0.17</td><td>0.08</td><td>0.91</td><td>0.72</td><td>0.47</td><td>0.25</td></tr><tr><td>RankGAN Lin et al. (2017)</td><td>0.69</td><td>0.39</td><td>0.18</td><td>0.09</td><td>0.90</td><td>0.68</td><td>0.45</td><td>0.30</td></tr><tr><td>TextGAN Zhang et al. (2017)</td><td>0.21</td><td>0.17</td><td>0.15</td><td>0.13</td><td>1.00</td><td>0.98</td><td>0.97</td><td>0.96</td></tr><tr><td>LeakGAN Guo et al. (2017)</td><td>0.84</td><td>0.65</td><td>0.44</td><td>0.27</td><td>0.94</td><td>0.82</td><td>0.67</td><td>0.51</td></tr><tr><td>MLE(α=1.25-1)</td><td>0.93</td><td>0.74</td><td>0.51</td><td>0.32</td><td>0.93</td><td>0.78</td><td>0.59</td><td>0.41</td></tr></table>",
+        "bbox": [
+            197,
+            411,
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+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "table",
+        "img_path": "images/46129c38741476da1199214ef20fdc72b1efe38fee8ffa4ff9377da0724eebca.jpg",
+        "table_caption": [],
+        "table_footnote": [
+            "Table 5: BLEU (left) and Self-BLEU (right) on test data of Image COCO. (Higher BLEU and lower Self-BLEU is better). "
+        ],
+        "table_body": "<table><tr><td></td><td colspan=\"4\">BLEU</td><td colspan=\"4\">Self-BLEU</td></tr><tr><td></td><td>2</td><td>3</td><td>4</td><td>5</td><td>2</td><td>3</td><td>4</td><td>5</td></tr><tr><td>Training Data</td><td>0.74</td><td>0.53</td><td>0.34</td><td>0.22</td><td>0.90</td><td>0.75</td><td>0.58</td><td>0.42</td></tr><tr><td>SeqGAN Yu et al. (2017)</td><td>0.75</td><td>0.50</td><td>0.29</td><td>0.18</td><td>0.95</td><td>0.84</td><td>0.67</td><td>0.49</td></tr><tr><td>MaliGAN Che et al. (2017)</td><td>0.67</td><td>0.43</td><td>0.26</td><td>0.16</td><td>0.92</td><td>0.78</td><td>0.61</td><td>0.44</td></tr><tr><td>RankGAN Lin et al. (2017)</td><td>0.74</td><td>0.47</td><td>0.26</td><td>0.16</td><td>0.96</td><td>0.88</td><td>0.76</td><td>0.62</td></tr><tr><td>TextGAN Zhang et al. (2017)</td><td>0.59</td><td>0.46</td><td>0.28</td><td>0.21</td><td>0.94</td><td>0.93</td><td>0.80</td><td>0.75</td></tr><tr><td>LeakGAN Guo et al. (2017)</td><td>0.74</td><td>0.52</td><td>0.33</td><td>0.21</td><td>0.93</td><td>0.82</td><td>0.66</td><td>0.51</td></tr><tr><td>MLE</td><td>0.74</td><td>0.52</td><td>0.33</td><td>0.21</td><td>0.89</td><td>0.72</td><td>0.54</td><td>0.38</td></tr></table>",
+        "bbox": [
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+            597,
+            800,
+            729
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "F ISSUES OF VARYING TEMPERATURE DURING TRAINING ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            794,
+            671,
+            810
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "As a penultimate experiment, we analyze the effect of changing the temperature at training instead of inference. Guo et al. (2017) suggested that increasing the temperature at training time leads to more diverse samples. However, we argue that this procedure leads to the opposite outcome as a model can adapt to the temperature change. This would have the net result of lowering the entropy at test time. To examine this, we trained 30 GANs maintaining everything constant except training temperature. Negative BLEU-5 against SBLEU-5 are plotted in Figure 7. The darker the dot, the higher the $\\alpha$ and consequently the temperature. As we hypothesize, models trained with increased temperature at training time adapted to the change and the net result was a colder temperature at inference (hence reduced diversity). We therefore recommend only adjusting the temperature at inference. One should consider other techniques to facilitate exploration during training. ",
+        "bbox": [
+            174,
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+            825,
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+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "table",
+        "img_path": "images/9a5cef161d9d8d9009c424aa2d14ac6e8e7752528ebe264d3187a33cdde8425d.jpg",
+        "table_caption": [
+            "Table 6: Three randomly sampled sentences from our model with closest BLEU scores to the training set’s. The sentences have poor semantics or global coherence. They are also not perfect grammatically speaking. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>MLE</td><td>(1) He explained that the Government’s plan to cut tax on unemployment was 3 . 3 percent lower than forecast for the first increase of 16 percent in 2Oi5 ,the fastest rate in the state since 2004.</td></tr><tr><td>α 1.05-1</td><td>(2) On the policy,it’s no more than the amount of money we have of the decades and Senate of our assets .</td></tr><tr><td></td><td>(3) They say it was possible supporting the Scottish government to make the changes as secret free environment based on competition .</td></tr></table>",
+        "bbox": [
+            176,
+            101,
+            825,
+            202
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            174,
+            277,
+            823,
+            319
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "image",
+        "img_path": "images/91b6caa2e7dc167f7da5fd190947e5c3a2f25d7bbaf797c357f76e4c98efcc61.jpg",
+        "image_caption": [
+            "Figure 7: Negative BLEU-5 on test data against SBLEU5 for models with different temperature applied at training time. The redder the dot, the higher the $\\alpha$ i.e. more pressure to increase entropy. From these results, it is evident that one should not increase the temperature at training time as the models adapts and the net results is mode collapse. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            336,
+            333,
+            661,
+            510
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "G DISCRIMINATOR REJECTION SAMPLING ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            606,
+            542,
+            622
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "We experimented with a rejection sampling technique base on the Discriminator’s signal. For this method, we train a Discriminator on the Generator’s samples without ever updating the Generator. Next, we accept/reject samples in a similar fashion to Generator Rejection Sampling however now the score is determined by the Discriminator. The higher the threshold, the more confident the Discriminator needs to be about the realness of the data. This should increase the quality of the samples with the usual downside of reducing diversity. We show results with a Discriminator having the same architecture as the Generator (Discriminator Rejection) and the best Discriminator found with an hyper parameter search of 100 trials (Best Discriminator Rejection. Results are shown in Figure 8. Note that the domain of the figure is much smaller that in Figure 4b. The reason is that this approach can’t move the models further in quality-diversity space. For this reason, we do not advocate for the use of this approach as a means to obtain high quality samples. ",
+        "bbox": [
+            174,
+            636,
+            825,
+            790
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "H MODULATING QUALITITY/DIVERSITY FOR FM-GAN ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            809,
+            648,
+            825
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "For FM-GAN, we observed that lowering the temperature to 0 didn’t completely remove all the stochasticity in the generations. This is because FM-GAN samples noise prior to sampling the first word. This is similar to how image generation GANs are trained. Precisely, $z \\sim N ( 0 , \\bar { 1 } )$ is sampled once and concatenated to every token of a generated sentence. Because temperature tuning wasn’t covering enough of the quality/diversity space, we also reduced the variance of the noise as quality modulating tool. Results are show in Figure 9. ",
+        "bbox": [
+            174,
+            840,
+            825,
+            924
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "image",
+        "img_path": "images/e309e212e69aaa8ed47938ec5c4c3ac817921d20d1d13903fecbf9d018e29679.jpg",
+        "image_caption": [
+            "Figure 8: Discriminator Rejection Sampling is not a great tool to navigate in quality-diversity space. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            338,
+            103,
+            658,
+            270
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "image",
+        "img_path": "images/1173e4bf4ab67af100500e2503dc2e9212adadab335f4a7bf267867888552e58.jpg",
+        "image_caption": [
+            "Figure 9: Different strategies to modulate the quality/diversity trade-off in FM-GAN. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            336,
+            315,
+            658,
+            481
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "I RL-GAN VERSUS MLE WITH OTHER DECODING MECHANISMS ",
+        "text_level": 1,
+        "bbox": [
+            171,
+            534,
+            736,
+            551
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "image",
+        "img_path": "images/839e61acf369a8825f1638bcac105d7ee77b6571c9cf07311ec9f339ee16922f.jpg",
+        "image_caption": [
+            "Figure 10: MLE still outperforms RL-GAN under different decoding mechanisms. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            338,
+            571,
+            658,
+            748
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "J EMNLP 2017 NEWS SAMPLES ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            102,
+            464,
+            118
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "We present additional samples for EMNLP 2017 News dataset. ",
+        "bbox": [
+            173,
+            133,
+            588,
+            148
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "table",
+        "img_path": "images/10914e69247b6ef94c6969048906cf221d6ee9c071284e2da721b3a1bd8f5107.jpg",
+        "table_caption": [
+            "EMNLP2017 News ",
+            "Table 7: Samples from SeqGAN taken from Guo et al. (2017). "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>SeqGAN through . I wanted to be made you decided to have a crisis that way up and get some sort of weapon , not much to give birth to for an American room . She had been fined almost 2Oo, OOO with couple of asylum seekers in Syria and Iraq . Perhaps not,in looking for,housing offcials would help the frustration of Government , with an FBI shortly before 2020 . Once we got to real show for the young man since I m sure she went to love it just , whether to be late later last year . But ,after a holiday period we might have to go on a total - out debate like that could have</td><td>You only certainly might not rush it down for those circumstances where we are when they were the heads ,and when she s name . I think you should really really leave for because we hadn t been busy ，where it goes to one，he wrote . All the study knew was that they are ,so they continue to provide support service and it doesn texist . It can say become up with nothing sales have reached the charge for the other any evidence that been virtually well below the $ 800 . Three times before the start of the season is much early on 2O15 we are in the third training every year . That s the idea of strength that decision they said, we haven t already lost four or seven, or Liverpool s team. That is not the time for the cost of changing the system and it was pushing for $2O million We had to take it a good day for a military,but nearly 6 , OOO ] and prepare for them through . I actually didn t tell the background check the difference after my hour was to be recalled ... and it was great . We are thinking about 4O, OOO and jobs in what is wrong in the coming and you know . That is out how working you can t set out some pretty tight... or what I m going</td></tr></table>",
+        "bbox": [
+            173,
+            176,
+            857,
+            595
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "table",
+        "img_path": "images/a5f5c1310fb139989b6308747ee70b69487e92be5d687cf13cbcaa9e9b223637.jpg",
+        "table_caption": [
+            "Table 8: Samples from LeakGAN taken from Guo et al. (2017). "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>LeakGAN</td><td>A man has been arrested at age 28 ,a resident in Seattle ，which was widely reported in 2007. I also think that s a good place for us ,I m sure that this would be a good opportunity for me to get in touch . What is the biggest problem for Clinton is that Donald Trump will be in the race and he s unlikely to be the nominee . We re going to do and we re going to put it out and get the ball， he said . I would be afraid to blame the girls to go back but I was just disappointed with the race , he said. I m not going to work together with a different role and we can win the game，he added The couple s lives are still missing and they have been killed in the city s way to play against them ,and because Icame out there . For the last three years ,we ve got a lot of things that we need to do with this is based on the financial markets . Don t ask me ,but I know ,if I ll be able to be out of Hillary Clinton ,I think it s being</td></tr></table>",
+        "bbox": [
+            178,
+            290,
+            857,
+            722
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "table",
+        "img_path": "images/b7064b3d792aa487cdb86e124aab6b0d4fd2ed0a5011f7737363b8aa1204e761.jpg",
+        "table_caption": [
+            "Table 9: Samples from our MLE with temperature to match BLEU scores reported in Guo et al. (2017) "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>MLE conservative . economy . police officer . coming weeks. game . for president . The US economy grew at a record low of 1 .6 percent in 2O14 ,and the unemployment rate has fallen by O .9 percent . The new rules are put into the hands of a member of the police ,and the public is not aware of the situation The World Health Organization said a number of people were killed in the attack ,according to the Pentagon . The study also found that women who are not particularly vulnerable to women ’s health</td><td>The UN Security Council is a major concern for the U . S . government , as well as a NATO ally in the Syrian civil war . A spokesman for the Met Ofice said the death toll was only slightly higher than the previous year,according to the report . But I hope that at the end of the day,I’ m going to give her the best chance to go to the gym and go out and play . The man,who cannot be named,said that he had never had sex with him,and he didn ’t want to see him . And it ’s just one of those things that I have to say ,I’m a Democrat ，and I’m a The bank is now the fastest growing market in the world and it is a significant change in the The two men ，aged 2O and 22 ，were arrested and charged with the murder of a man ， a The company will be able to provide a post Brexit strategy ，which will be published in the She said she had been on the wrong side of the road and was finally caught in a car accident and was taken to hospital . I don ’ t think he ’ s even a good player ,he said ,but he ’ s got a good chance to win the I don ’t know what the future holds but I’m sure it will be a good thing . It’ s a very important step forward ,and we ’ re going to be able to get the right results . The driver of the vehicle，who was inside the vehicle ，was taken to hospital for treatment , but said he was not aware of the incident . The leak was obtained by a Freedom of Information request ,which is based on the number of people claiming to be a victim of fraud . The former secretary of state has made a major speech in New York , where she ’ s running</td></tr></table>",
+        "bbox": [
+            171,
+            250,
+            857,
+            750
+        ],
+        "page_idx": 17
+    }
+]

parse/train/ByOvsIqeg/ByOvsIqeg.md

@@ -0,0 +1,233 @@
+# REGULARIZING CNNS WITH LOCALLY CONSTRAINED DECORRELATIONS
+
+Pau Rodr´ıguez†, Jordi Gonzalez \` †,‡, Guillem Cucurull†, Josep M. Gonfaus‡, Xavier Roca†,‡ †Computer Vision Center - Univ. Autonoma de Barcelona (UAB), 08193 Bellaterra, Catalonia Spain \` ‡Visual Tagging Services, Campus UAB, 08193 Bellaterra, Catalonia Spain
+
+# ABSTRACT
+
+Regularization is key for deep learning since it allows training more complex models while keeping lower levels of overfitting. However, the most prevalent regularizations do not leverage all the capacity of the models since they rely on reducing the effective number of parameters. Feature decorrelation is an alternative for using the full capacity of the models but the overfitting reduction margins are too narrow given the overhead it introduces. In this paper, we show that regularizing negatively correlated features is an obstacle for effective decorrelation and present OrthoReg, a novel regularization technique that locally enforces feature orthogonality. As a result, imposing locality constraints in feature decorrelation removes interferences between negatively correlated feature weights, allowing the regularizer to reach higher decorrelation bounds, and reducing the overfitting more effectively. In particular, we show that the models regularized with OrthoReg have higher accuracy bounds even when batch normalization and dropout are present. Moreover, since our regularization is directly performed on the weights, it is especially suitable for fully convolutional neural networks, where the weight space is constant compared to the feature map space. As a result, we are able to reduce the overfitting of state-of-the-art CNNs on CIFAR-10, CIFAR-100, and SVHN.
+
+# 1 INTRODUCTION
+
+Neural networks perform really well in numerous tasks even when initialized randomly and trained with Stochastic Gradient Descent (SGD) (see Krizhevsky et al. (2012)). Deeper models, like Googlenet (Szegedy et al. (2015)) and Deep Residual Networks (Szegedy et al. (2015); He et al. (2015a)) are released each year, providing impressive results and even surpassing human performances in well-known datasets such as the Imagenet (Russakovsky et al. (2015)). This would not have been possible without the help of regularization and initialization techniques which solve the overfitting and convergence problems that are usually caused by data scarcity and the growth of the architectures.
+
+From the literature, two different regularization strategies can be defined. The first ones consist in reducing the complexity of the model by (i) reducing the effective number of parameters with weight decay (Nowlan & Hinton (1992)), and (ii) randomly dropping activations with Dropout (Srivastava et al. (2014)) or dropping weights with DropConnect (Wan et al. (2013)) so as to prevent feature co-adaptation. Due to their nature, although this set of strategies have proved to be very effective, they do not leverage all the capacity of the models they regularize.
+
+The second group of regularizations is those which improve the effectiveness and generality of the trained model without reducing its capacity. In this second group, the most relevant approaches decorrelate the weights or feature maps, e.g. Bengio & Bergstra (2009) introduced a new criterion so as to learn slow decorrelated features while pre-training models. In the same line Bao et al. (2013) presented ”incoherent training”, a regularizer for reducing the decorrelation of the network activations or feature maps in the context of speech recognition. Although regularizations in the second group are promising and have already been used to reduce the overfitting in different tasks, even with the presence of Dropout (as shown by Cogswell et al. (2016)), they are seldom used in the large scale image recognition domain because of the small improvement margins they provide together with the computational overhead they introduce.
+
+<table><tr><td></td><td>Base</td><td>DeCov</td><td>OrthoReg</td></tr><tr><td>MLP</td><td>8.1108</td><td>5.21010</td><td>9.7109</td></tr><tr><td>ResNet-110</td><td>6.51010</td><td>3.4 1014</td><td>3.4 108</td></tr></table>
+
+Table 1: Count of the Flops for the models used in this paper: the 3-hidden-layer MLP and the 110- layer ResNet we use later in the experiments section when not regularized, using DeCov (Cogswell et al. (2016)) and using OrthoReg. Batch size is set to 128, the same we use to train the ResNet. Regularizing weights is orders of magnitude faster than regularizing activations.
+
+Although they are not directly presented as regularizers, there are other strategies to reduce the overfitting such as Batch Normalization (Ioffe & Szegedy (2015)), which decreases the overfitting by reducing the internal covariance shift. In the same line, initialization strategies such as ”Xavier” (Glorot & Bengio (2010)) or ”He” (He et al. (2015b)), also keep the same variance at both input and output of the layers in order to preserve propagated signals in deep neural networks. Orthogonal initialization techniques are another family which set the weights in a decorrelated initial state so as to condition the network training to converge into better representations. For instance, Mishkin & Matas (2016) propose to initialize the network with decorrelated features using orthonormal initialization (Saxe et al. (2013)) while normalizing the variance of the outputs as well.
+
+In this work we hypothesize that regularizing negatively correlated features is an obstacle for achieving better results and we introduce OrhoReg, a novel regularization technique that addresses the performance margin issue by only regularizing positively correlated feature weights. Moreover, OrthoReg is computationally efficient since it only regularizes the feature weights, which makes it very suitable for the latest CNN models. We verify our hypothesis through a series of experiments: first using MNIST as a proof of concept, secondly we regularize wide residual networks on CIFAR-10, CIFAR-100, and SVHN (Netzer et al. (2011)) achieving the lowest error rates in the dataset to the best of our knowledge.
+
+# 2 DEALING WITH WEIGHT REDUNDANCIES
+
+Deep Neural Networks (DNN) are very expressive models which can usually have millions of parameters. However, with limited data, they tend to overfit. There is an abundant number of techniques in order to deal with this problem, from L1 and L2 regularizations (Nowlan & Hinton (1992)), early-stopping, Dropout or DropConnect. Models presenting high levels of overfitting usually have a lot of redundancy in their feature weights, capturing similar patterns with slight differences which usually correspond to noise in the training data. A particular case where this is evident is in AlexNet (Krizhevsky et al. (2012)), which presents very similar convolution filters and even ”dead” ones, as it was remarked by Zeiler & Fergus (2014).
+
+In fact, given a set of parameters $\theta _ { I , j }$ connecting a set of inputs $I = \{ i _ { 1 } , i _ { 2 } , . . . , i _ { n } \}$ to a neuron $h _ { j }$ , two neurons $\{ h _ { j } , \bar { h } _ { k } \}$ , $j \neq k$ will be positively correlated, and thus fire always together if $\bar { \theta _ { I , j } } = \theta _ { I , k }$ and negatively correlated if $\theta _ { I , j } = - \theta _ { I , k }$ . In other words, two neurons with the same or slightly different weights will produce very similar outputs. In order to reduce the redundancy present in the network parameters, one should maximize the amount of information encoded by each neuron. From an information theory point of view, this means one should not be able to predict the output of a neuron given the output of the rest of the neurons of the layer. However, this measure requires batch statistics, huge joint probability tables, and it would have a high computational cost.
+
+In this paper, we will focus on the weights correlation rather than activation independence since it still is an open problem in many neural network models and it can be addressed without introducing too much overhead, see Table 1. Then, we show that models generalize better when different feature detectors are enforced to be dissimilar. Although it might seem contradictory, CNNs can benefit from having repeated filter weights with different biases, as shown by Li et al. (2016). However, those repeated filters must be shared copies and adding too many unshared filter weights to CNNs increases overfitting and the need for stronger regularization (Zagoruyko & Komodakis (May 2016)). Thus, our proposed method and multi-bias neural networks are complementary since they jointly increase the representation power of the network with fewer parameters.
+
+In order to find a good target to optimize so as to reduce the correlation between weights, it is first required to find a metric to measure it. In this paper, we propose to use the cosine similarity between feature detectors to express how strong is their relationship. Note that the cosine similarity is equivalent to the Pearson correlation for mean-centered normalized vectors, but we will use the term correlation for the sake of clarity.
+
+# 2.1 ORTHOGONAL WEIGHT REGULARIZATION
+
+This section introduces the orthogonal weight regularization, a regularization technique that aims to reduce feature detector correlation enforcing local orthogonality between all pairs of weight vectors. In order to keep the magnitudes of the detectors unaffected, we have chosen the cosine similarity between the vector pairs in order to solely focus on the vectors angle $\beta \in [ - \pi , \pi ]$ . Then, given any pair of feature vectors of the same size $\theta _ { 1 } , \theta _ { 2 }$ the cosine of their relative angle is:
+
+$$
+\cos ( \theta _ { 1 } , \theta _ { 2 } ) = \frac { \langle \theta _ { 1 } , \theta _ { 2 } \rangle } { | | \theta _ { 1 } | | | | \theta _ { 2 } | | }
+$$
+
+Where $\left. \theta _ { 1 } , \theta _ { 2 } \right.$ denotes the inner product between $\theta _ { 1 }$ and $\theta _ { 2 }$ . We then square the cosine similarity in order to define a regularization cost function for steepest descent that has its local minima when vectors are orthogonal:
+
+$$
+C ( \theta ) = \frac { 1 } { 2 } \sum _ { i = 1 } ^ { n } \sum _ { \substack { j = 1 , j \neq i } } ^ { n } \cos ^ { 2 } ( \theta _ { i } , \theta _ { j } ) = \frac { 1 } { 2 } \sum _ { \substack { i = 1 } } ^ { n } \sum _ { \substack { j = 1 , j \neq i } } ^ { n } \left( \frac { \langle \theta _ { i } , \theta _ { j } \rangle } { | | \theta _ { i } | | | | \theta _ { j } | | } \right) ^ { 2 }
+$$
+
+Where $\theta _ { i }$ are the weights connecting the output of the layer $l - 1$ to the neuron $i$ of the layer $l$ , which has $n$ hidden units. Interestingly, minimizing this cost function relates to the minimization of the Frobenius norm of the cross-covariance matrix without the diagonal. This cost will be added to the global cost of the model $J ( \theta ; X , y )$ , where $X$ are the inputs and $y$ are the labels or targets, obtaining $\tilde { J } ( \theta ; X , y ) = J ( \theta ; X , y ) + \gamma C ( \theta )$ . Note that $\gamma$ is an hyperparameter that weights the relative contribution of the regularization term. We can now define the gradient with respect to the parameters:
+
+$$
+\frac { \delta } { \delta \theta _ { ( i , j ) } } C ( \theta ) = \sum _ { k = 1 , k \neq i } ^ { n } \frac { \theta _ { ( k , j ) } \langle \theta _ { i } , \theta _ { k } \rangle } { \langle \theta _ { i } , \theta _ { i } \rangle \langle \theta _ { k } , \theta _ { k } \rangle } - \frac { \theta _ { ( i , j ) } \langle \theta _ { i } , \theta _ { k } \rangle ^ { 2 } } { \langle \theta _ { i } , \theta _ { i } \rangle ^ { 2 } \langle \theta _ { k } , \theta _ { k } \rangle }
+$$
+
+The second term is introduced by the magnitude normalization. As magnitudes are not relevant for the vector angle problem, this equation can be simplified just by assuming normalized feature detectors:
+
+$$
+{ \frac { \delta } { \delta \theta _ { ( i , j ) } } } C ( \theta ) = \sum _ { k = 1 , k \neq i } ^ { n } \theta _ { ( k , j ) } \langle \theta _ { i } , \theta _ { k } \rangle
+$$
+
+We then add eq. 4 to the backpropagation gradient:
+
+$$
+\Delta \theta _ { ( i , j ) } = - \alpha \Big ( \nabla J _ { \theta _ { ( i , j ) } } + \gamma \sum _ { k = 1 , k \neq i } ^ { n } \theta _ { ( k , j ) } \langle \theta _ { i } , \theta _ { k } \rangle \Big )
+$$
+
+Where $\alpha$ is the global learning rate coefficient, $J$ any target loss function for the backpropagation algorithm.
+
+Although this update can be done sequentially for each feature-detector pair, it can be vectorized to speedup computations. Let $\Theta$ be a matrix where each row is a feature detector $\theta _ { ( I , j ) }$ corresponding to the normalized weights connecting the whole input $I$ of the layer to the neuron $j$ . Then, $\Theta \Theta ^ { t }$ contains the inner product of each pair of vectors $i$ and $j$ in each position $i , j$ . Subsequently, we
+
+# Algorithm 1 Orthogonal Regularization Step.
+
+Require: Layer parameter matrices $\Theta ^ { l }$ , regularization coefficient $\gamma$ , global learning rate $\alpha$
+
+1: for each layer $l$ to regularize do   
+2: $\eta _ { 1 } = n o r m \_ r o w s ( \Theta ^ { l } )$   
+3: $\Theta _ { 1 } ^ { l } = d i v \_ r o w s ( \Theta ^ { l } , \eta _ { 1 } )$ .   
+4: in $\AA \ i e r P r o d M a t = \Theta _ { 1 } ^ { l } t r a n s p o s e ( \Theta _ { 1 } ^ { l } )$   
+5: ∇Θl1 = $\models \gamma ( i n n e r P r o d M a t - d i a g ( i n n e r P r o d M a t ) ) \Theta _ { 1 } ^ { l }$   
+6: $\Delta \Theta ^ { l } = - \alpha ( \nabla J _ { \Theta ^ { l } } + \gamma \nabla \Theta _ { 1 } ^ { l } )$   
+7: end for
+
+. Second term in eq. 6 . Complete eq. 6.
+
+![](images/065bfaab774f5e272775601e0ded5149b3d4f916d5211a8b0b9d7bedee67b1a6.jpg)  
+Figure 1: Comparison between the two loss functions represented by eq.2 and 7. (a) is the original loss, (b) is the new loss that discards negative correlations given for different $\lambda$ values. It can be seen $\lambda = 1 0$ reaches a plateau when approximating to $\frac { \pi } { 2 }$ . (c) and (d) shows the directions of the gradients for the two loss functions above. For instance, a red arrow coming from a green ball represents the gradient of the loss between the red and green balls with respect to the green one. In (d) most of the arrows disappear since the loss in (b) only applies to angles smaller than $\frac { \pi } { 2 }$ .
+
+![](images/c8412b5ab42884c6f586a1bd08e2e7c84bef80594ea863fcd89db80465ea9b10.jpg)  
+(d) Direction of gradients for loss in (b).
+
+(c) Direction of gradients for the loss in (a).
+
+subtract the diagonal so as to ignore the angle from each feature with respect to itself and multiply by $\Theta$ to compute the final value corresponding to the sum in eq. 5:
+
+$$
+\Delta \Theta = - \alpha \Big ( \nabla J _ { \Theta } + \gamma \big ( \Theta \Theta ^ { t } - d i a g ( \Theta \Theta ^ { t } ) \big ) \Theta \Big )
+$$
+
+Where the second term is $\nabla C _ { \Theta }$ . Algorithm 1 summarizes the steps in order to apply OrthoReg.
+
+# 2.2 NEGATIVE CORRELATIONS
+
+Note that the presented algorithm, based on the cosine similarity, penalizes any kind of correlation between all pairs of feature detectors, i.e. the positive and the negative correlations, see Figure 1a. However, negative correlations are related to inhibitory connections, competitive learning, and self-organization. In fact, there is evidence that negative correlations can help a neural population to increase the signal-to-noise ratio (Chelaru & Dragoi (2016)) in the V1. In order to find out the advantages of keeping negative correlations, we propose to use an exponential to squash the gradients for angles greater than $\frac { \pi } { 2 }$ (orthogonal):
+
+$$
+C ( \theta ) = \sum _ { i = 1 } ^ { n } \sum _ { j = 1 , j \neq i } ^ { n } \log ( 1 + e ^ { \lambda ( c o s ( \theta _ { i } , \theta _ { j } ) - 1 ) } ) = \log ( 1 + e ^ { \lambda ( \langle \theta _ { i } , \theta _ { j } \rangle - 1 ) } ) , \ | | \theta _ { i } | | = | | \theta _ { j } | | = 1
+$$
+
+Where $\lambda$ is a coefficient that controls the minimum angle-of-influence of the regularizer, i.e. the minimum angle between two feature weights so that there exists a gradient pushing them apart, see Figure 1b. We empirically found that the regularizer worked well for $\lambda = 1 0$ , see Figure 2b. Note that when $\lambda \simeq 1 0$ the loss and the gradients approximate to zero when vectors are at more than $\textstyle { \frac { \pi } { 2 } }$ (orthogonal). As a result of incorporating the squashing function on the cosine similarity, negatively correlated feature weights will not be regularized. This is different from all previous approaches and the loss presented in eq. 2, where all pairs of weight vectors influence each other. Thus, from now on, the loss in eq. 2 is named as global loss and the loss in eq. 7 is named as local loss.
+
+The derivative of eq. 7 is:
+
+$$
+{ \frac { \delta } { \delta \theta _ { ( i , j ) } } } C ( \theta ) = \sum _ { k = 1 , k \neq i } ^ { n } \lambda { \frac { e ^ { \lambda \langle \theta _ { i } , \theta _ { k } \rangle } \theta _ { ( k , j ) } } { e ^ { \lambda \langle \theta _ { i } , \theta _ { k } \rangle } + e ^ { \lambda } } }
+$$
+
+Then, given the element-wise exponential operator exp, we define the following expression in order to simplify the formulas:
+
+$$
+\hat { \Theta } = \exp ( \lambda ( \Theta \Theta ^ { t } ) )
+$$
+
+and thus, the $\Delta$ in vectorial form can be formulated as:
+
+$$
+\nabla C _ { \Theta } = \lambda \frac { ( \hat { \Theta } - d i a g ( \hat { \Theta } ) ) \Theta } { \hat { \Theta } - d i a g ( \hat { \Theta } ) + e ^ { \lambda } }
+$$
+
+In order to provide a visual example, we have created a $2 D$ toy dataset and used the previous equations for positive and negative $\gamma$ values, see Figure 2. As expected, it can be seen that the angle between all pairs of adjacent feature weights becomes more uniform after regularization. Note that Figure 2b shows that regularization with the global loss (eq. 2) results in less uniform angles than using the local loss as shown in 2c (which corresponds to the local loss presented in eq. 7) because vectors in opposite quadrants still influence each other. This is why in Figure 2d, it can be seen that the mean nearest neighbor angle using the global loss (b) is more unstable than the local loss (c). As a proof of concept, we also performed gradient ascent, which minimizes the angle between the vectors. Thus, in Figures 2e and 2f, it can be seen that the locality introduced by the local loss reaches a stable configuration where feature weights with angle $\frac { \pi } { 2 }$ are too far to attract each other.
+
+The effects of global and local regularizations on Alexnet, VGG-16 and a 50-layer ResNet are shown on Figure 3. As it can be seen, OrthoReg reaches higher decorrelation bounds. Lower decorrelation peaks are still observed when the input dimensionality of the layers is smaller than the output since all vectors cannot be orthogonal at the same time. In this case, local regularization largely outperforms global regularization since it removes interferences caused by negatively correlated feature weights. This suggests why increasing fully connected layers’ size has not improved networks performance.
+
+# 3 EXPERIMENTS
+
+In this section we provide a set of experiments that verify that (i) training with the proposed regularization increases the performance of naive unregularized models, (ii) negatively correlated feature weights are useful, and (iii) the proposed regularization improves the performance of state-of-the-art models.
+
+![](images/34a3be8804f26a57d411d167237444d8d7958399d4ffb56568305dbab17fe2bf.jpg)
+
+![](images/274103e294a9b385d101077beda43ccb46196b1e4b5f4f46e0a2d67c28c9fbf0.jpg)  
+Figure 2: 2D toy dataset regularized with global loss (eq. 2) and local loss (eq. 7). (a) shows the initial 2D randomly generated dataset. (b) the dataset after 300 regularization steps using the global loss and (c) using the local loss. (d) the evolution of the mean nearest neighbor angle for the global loss (b) and the local loss (c). (e) and (f) correspond to (b) and (c) but using gradient ascent instead of gradient descent as a sanity-check.   
+Figure 3: Effects of local and global regularization on the Alexnet, VGG-16 and 50-layer-ResNet weights. The regularized versions reach higher decorrelation bounds (in terms of minimum angle) than the unregularized counterparts.
+
+# 3.1 VERIFICATION EXPERIMENTS
+
+As a sanity check, we first train a three-hidden-layer Multi-Layer Perceptron (MLP) with ReLU non-liniarities on the MNIST dataset (LeCun et al. (1998)). Our code is based in the train-a-digit-classifier example included in torch/demos1, which uses an upsampled version of the dataset $( 3 2 \times 3 2 )$ ). The only pre-processing applied to the data is a global standardization. The model is trained with SGD and a batch size of 200 during 200 epochs. No momentum neither weight decay was applied. By default, the magnitude of the weights of this experiments is recovered after each regularization step in order to prove the regularization only affects their angle.
+
+Sensitivity to hyperparameters. We train a three-hidden-layer MLP with 1024 hidden units, and different $\gamma$ and $\lambda$ values so as to verify how they affect the performance of the model. Figure 4a shows that the model effectively achieves the best error rate for the highest gamma value $( \gamma = 1 )$ ), thus proving the advantages of the regularization. On Figure 4b, we verify that higher regularization rates produce more general models. Figure 5a depicts the sensitivity of the model to $\lambda$ . As expected, the best value is found when lambda corresponds to Orthogonality $\lambda \simeq 1 0$ ).
+
+![](images/797a937a123e416d547a9590449fdc1933d1fd97d9b389860168faf07f3ea464.jpg)  
+Figure 4: (a) The evolution of the error rate on the MNIST validation set for different regularization magnitudes. It can be seen that for $\gamma = 1$ it reaches the best error rate $( 1 . 4 5 \% )$ while the unregularized counterpart $( \gamma = 0 )$ is $1 . 7 4 \%$ . (b) Measures the overfitting of the model for different $\gamma$ , confirming that higher regularization rates decrease overfitting.
+
+![](images/bd7b23b9c26025a4c3a4beaaaa85011185c26e6e789f3f3cb62ff6e2a71dbbdc.jpg)  
+Figure 5: (a) Shows the minimum error rate for different $\lambda$ values. (b) Classification error on MNIST for different loss functions. Not regularizing negative correlated feature weights (eq. 7) results in better test error than regularizing them (eq.2).
+
+Negative Correlations. Figure 5b highlights the difference between regularizing with the global or the local regularizer. Although both regularizations reach better error rates than the unregularized counterpart, the local regularization is better than the global. This confirms the hypothesis that negative correlations are useful and thus, performance decreases when we reduce them.
+
+Compatibility with initialization and dropout. To demonstrate the proposed regularization can help even when other regularizations are present, we trained a CNN with (i) dropout $( \mathtt { c 3 2 - c \bar { 6 } 4 - 1 5 1 2 - d 0 . 5 - 1 1 0 } ) ^ { 2 }$ or (ii) LSUV initialization (Mishkin & Matas (2016)). In Table 2, we show that best results are obtained when orthogonal regularization is present. The results are consistent with the hypothesis that OrthoReg, as well as Dropout and LSUV, focuses on reducing the model redundancy. Thus, when one of them is present, the margin of improvement for the others is reduced.
+
+<table><tr><td>OrthoReg</td><td>Base</td><td>Base+Dropout</td><td>Base+LSUV</td></tr><tr><td>None</td><td>0.92</td><td>0.70 ± 0.01</td><td>0.86</td></tr><tr><td>Conv Layers</td><td>0.75</td><td>0.69 ± 0.03</td><td>0.83</td></tr><tr><td>All Layers</td><td>0.75</td><td>0.66 ± 0.03</td><td>0.79</td></tr></table>
+
+Table 2: Error rates for a small CNN trained with the MNIST dataset. OrthoReg leads to much better results when no other improvements such as Dropout and LSUV are present but it can still make small accuracy increments when these two techniques are present.
+
+![](images/d5c89f137ebdad2f4302c5935ff362f628cfc870fd05c573b7a9e6ca4094c997.jpg)  
+Figure 6: Wide ResNet error rate on Cifar10 and Cifar100. OrthoReg shows better performance than the base regularizer (all feature maps), and the unregularized counterparts.
+
+# 3.2 REGULARIZATION ON CIFAR-10 AND CIFAR-100
+
+We show that the proposed OrthoReg can help to improve the performance of state-of-the-art models such as deep residual networks (He et al. (2015a)). In order to show the regularization is suitable for deep CNNs, we successfuly regularize a 110-layer ResNet3 on CIFAR-10, decreasing its error from $6 . 5 5 \%$ to $6 . 2 9 \%$ without data augmentation.
+
+In order to compare with the most recent state-of-the-art, we train a wide residual network (Zagoruyko & Komodakis (November 2016)) on CIFAR-10 and CIFAR-100. The experiment is based on a torch implementation of the 28-layer and 10th width factor wide deep residual model, for which the median error rate on CIFAR-10 is $3 . 8 9 \%$ and $1 8 . 8 5 \%$ on CIFAR- $1 0 0 ^ { 4 }$ . As it can be seen in Figure 6, regularizing with OrthoReg yields the best test error rates compared to the baselines.
+
+The regularization coefficient $\gamma$ was chosen using grid search although similar values were found for all the experiments, specially if regularization gradients are normalized before adding them to the weights. The regularization was equally applied to all the convolution layers of the (wide) ResNet. We found that, although the regularized models were already using weight decay, dropout, and batch normalization, best error rates were always achieved with OrthoReg.
+
+Table 3 compares the performance of the regularized models with other state-of-the-art results. As it can be seen the regularized model surpasses the state of the art, with a $5 . 1 \%$ relative error improvement on CIFAR-10, and a $1 . 5 \%$ relative error improvement on CIFAR-100.
+
+# 3.3 REGULARIZATION ON SVHN
+
+For SVHN we follow the procedure depicted in Zagoruyko & Komodakis (May 2016), training a wide residual network of depth $^ { \underline { { { \ O } } } } = 2 8$ , width $= 4$ , and dropout. Results are shown in Table 4. As it
+
+Table 3: Comparison with other CNNs on CIFAR-10 and CIFAR-100 (Test error $\%$ ). Orthogonally regularized residual networks achieve the best results to the best of our knowldege. Only single-crop results are reported for fairness of comparison. \*Median over 5 runs as reported by Zagoruyko & Komodakis (November 2016).   
+
+<table><tr><td>Network</td><td>CIFAR-10</td><td>CIFAR-100</td><td>Augmented</td></tr><tr><td>Maxout (Goodfellow et al. (2013))</td><td>9.38</td><td>38.57</td><td>YES</td></tr><tr><td>NiN (Lin et al. (2014))</td><td>8.81</td><td>35.68</td><td>YES</td></tr><tr><td>DSN (Lee et al. (2015))</td><td>7.97</td><td>34.57</td><td>YES</td></tr><tr><td>Highway Network (Srivastava et al. (2015))</td><td>7.60</td><td>32.24</td><td>YES</td></tr><tr><td>All-CNN (Springenberg et al. (2015))</td><td>7.25</td><td>33.71</td><td>NO</td></tr><tr><td>110-Layer ResNet (He et al. (2015a))</td><td>6.61</td><td>28.4</td><td>NO</td></tr><tr><td>ELU-Network (Clevert et al. (2016))</td><td>6.55</td><td>24.28</td><td>NO</td></tr><tr><td>OrthoReg on 110-Layer ResNet*</td><td>6.29 ± 0.19</td><td>28.33 ± 0.5</td><td>NO</td></tr><tr><td>LSUV (Mishkin &amp; Matas (2016))</td><td>5.84</td><td>1</td><td>YES</td></tr><tr><td>Fract.Max-Pooling (Graham (2014))</td><td>4.50</td><td>27.62</td><td>YES</td></tr><tr><td>Wide ResNet v1 (Zagoruyko &amp; Komodakis (May 2016))*</td><td>4.37</td><td>20.40</td><td>YES</td></tr><tr><td>OrthoReg on Wide ResNet v1 (May 2016)*</td><td>4.32 ± 0.05</td><td>19.50 ± 0.03</td><td>YES</td></tr><tr><td>Wide ResNet v2 (Zagoruyko &amp; Komodakis (November 2016))*</td><td>3.89</td><td>18.85</td><td>YES</td></tr><tr><td>OrthoReg on Wide ResNet v2 (November 2016)*</td><td>3.69 ± 0.01</td><td>18.56 ± 0.12</td><td>YES</td></tr></table>
+
+Table 4: Comparison with other CNNs on SVHN. Wide Resnets regularized with OrthoReg show better performance.   
+
+<table><tr><td>Model</td><td>Error rate</td></tr><tr><td>NiN (Lin et al. (2014))</td><td>2.35</td></tr><tr><td>DSN (Lee et al. (2015))</td><td>1.92</td></tr><tr><td>Stochastic Depth ResNet (Huang et al. (2016))</td><td>1.75</td></tr><tr><td>Wide Resnet (Zagoruyko &amp; Komodakis (May 2016))</td><td>1.64</td></tr><tr><td>OrthoReg on Wide Resnet</td><td>1.54</td></tr></table>
+
+can be seen, we reduce the error rate from $1 . 6 4 \%$ to $1 . 5 4 \%$ , which is the lowest value reported on this dataset to the best of our knowledge.
+
+# 4 DISCUSSION
+
+Regularization by feature decorrelation can reduce Neural Networks overfitting even in the presence of other kinds of regularizations. However, especially when the number of feature detectors is higher than the input dimensionality, its decorrelation capacity is limited due to the effects of negatively correlated features. We showed that imposing locality constraints in feature decorrelation removes interferences between negatively correlated feature weights, allowing regularizers to reach higher decorrelation bounds, and reducing the overfitting more effectively.
+
+In particular, we show that the models regularized with the constrained regularization present lower overfitting even when batch normalization and dropout are present. Moreover, since our regularization is directly performed on the weights, it is especially suitable for fully convolutional neural networks, where the weight space is constant compared to the feature map space. As a result, we are able to reduce the overfitting of 110-layer ResNets and wide ResNets on CIFAR-10, CIFAR-100, and SVHN improving their performance. Note that despite OrthoReg consistently improves state of the art ReLU networks, the choice of the activation function could affect regularizers like the one presented in this work. In this sense, the effect of asymmetrical activations on feature correlations and regularizers should be further investigated in the future.
+
+# ACKNOWLEDGEMENTS
+
+Authors acknowledge the support of the Spanish project TIN2015-65464-R (MINECO/FEDER), the 2016FI B 01163 grant of Generalitat de Catalunya, and the COST Action IC1307 iV&L Net (European Network on Integrating Vision and Language) supported by COST (European Cooperation in Science and Technology). We also gratefully acknowledge the support of NVIDIA Corporation with the donation of a Tesla K40 GPU and a GTX TITAN GPU, used for this research.
+
+# REFERENCES
+
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+Yoshua Bengio and James S Bergstra. Slow, decorrelated features for pretraining complex cell-like networks. In NIPS, pp. 99–107, 2009.   
+Mircea I Chelaru and Valentin Dragoi. Negative correlations in visual cortical networks. Cerebral Cortex, 26(1):246–256, 2016.   
+Djork-Arn Clevert, Thomas Unterthiner, and Sepp Hochreiter. Fast and accurate deep network learning by exponential linear units (ELUs). ICLR, 2016.   
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+Olga Russakovsky, Jia Deng, Hao Su, Jonathan Krause, Sanjeev Satheesh, Sean Ma, Zhiheng Huang, Andrej Karpathy, Aditya Khosla, Michael Bernstein, et al. Imagenet large scale visual recognition challenge. IJCV, 115(3):211–252, 2015.   
+Andrew M. Saxe, James L. McClelland, and Surya Ganguli. Exact solutions to the nonlinear dynamics of learning in deep linear neural networks. arXiv:1312.6120, December 2013.   
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parse/train/ByOvsIqeg/ByOvsIqeg_content_list.json

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+    {
+        "type": "text",
+        "text": "REGULARIZING CNNS WITH LOCALLY CONSTRAINED DECORRELATIONS ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Pau Rodr´ıguez†, Jordi Gonzalez \\` †,‡, Guillem Cucurull†, Josep M. Gonfaus‡, Xavier Roca†,‡ †Computer Vision Center - Univ. Autonoma de Barcelona (UAB), 08193 Bellaterra, Catalonia Spain \\` ‡Visual Tagging Services, Campus UAB, 08193 Bellaterra, Catalonia Spain ",
+        "bbox": [
+            183,
+            169,
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "ABSTRACT ",
+        "text_level": 1,
+        "bbox": [
+            454,
+            250,
+            544,
+            265
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Regularization is key for deep learning since it allows training more complex models while keeping lower levels of overfitting. However, the most prevalent regularizations do not leverage all the capacity of the models since they rely on reducing the effective number of parameters. Feature decorrelation is an alternative for using the full capacity of the models but the overfitting reduction margins are too narrow given the overhead it introduces. In this paper, we show that regularizing negatively correlated features is an obstacle for effective decorrelation and present OrthoReg, a novel regularization technique that locally enforces feature orthogonality. As a result, imposing locality constraints in feature decorrelation removes interferences between negatively correlated feature weights, allowing the regularizer to reach higher decorrelation bounds, and reducing the overfitting more effectively. In particular, we show that the models regularized with OrthoReg have higher accuracy bounds even when batch normalization and dropout are present. Moreover, since our regularization is directly performed on the weights, it is especially suitable for fully convolutional neural networks, where the weight space is constant compared to the feature map space. As a result, we are able to reduce the overfitting of state-of-the-art CNNs on CIFAR-10, CIFAR-100, and SVHN. ",
+        "bbox": [
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+        "page_idx": 0
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+    {
+        "type": "text",
+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Neural networks perform really well in numerous tasks even when initialized randomly and trained with Stochastic Gradient Descent (SGD) (see Krizhevsky et al. (2012)). Deeper models, like Googlenet (Szegedy et al. (2015)) and Deep Residual Networks (Szegedy et al. (2015); He et al. (2015a)) are released each year, providing impressive results and even surpassing human performances in well-known datasets such as the Imagenet (Russakovsky et al. (2015)). This would not have been possible without the help of regularization and initialization techniques which solve the overfitting and convergence problems that are usually caused by data scarcity and the growth of the architectures. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "From the literature, two different regularization strategies can be defined. The first ones consist in reducing the complexity of the model by (i) reducing the effective number of parameters with weight decay (Nowlan & Hinton (1992)), and (ii) randomly dropping activations with Dropout (Srivastava et al. (2014)) or dropping weights with DropConnect (Wan et al. (2013)) so as to prevent feature co-adaptation. Due to their nature, although this set of strategies have proved to be very effective, they do not leverage all the capacity of the models they regularize. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "The second group of regularizations is those which improve the effectiveness and generality of the trained model without reducing its capacity. In this second group, the most relevant approaches decorrelate the weights or feature maps, e.g. Bengio & Bergstra (2009) introduced a new criterion so as to learn slow decorrelated features while pre-training models. In the same line Bao et al. (2013) presented ”incoherent training”, a regularizer for reducing the decorrelation of the network activations or feature maps in the context of speech recognition. Although regularizations in the second group are promising and have already been used to reduce the overfitting in different tasks, even with the presence of Dropout (as shown by Cogswell et al. (2016)), they are seldom used in the large scale image recognition domain because of the small improvement margins they provide together with the computational overhead they introduce. ",
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+    {
+        "type": "table",
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+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>Base</td><td>DeCov</td><td>OrthoReg</td></tr><tr><td>MLP</td><td>8.1108</td><td>5.21010</td><td>9.7109</td></tr><tr><td>ResNet-110</td><td>6.51010</td><td>3.4 1014</td><td>3.4 108</td></tr></table>",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Table 1: Count of the Flops for the models used in this paper: the 3-hidden-layer MLP and the 110- layer ResNet we use later in the experiments section when not regularized, using DeCov (Cogswell et al. (2016)) and using OrthoReg. Batch size is set to 128, the same we use to train the ResNet. Regularizing weights is orders of magnitude faster than regularizing activations. ",
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+    {
+        "type": "text",
+        "text": "Although they are not directly presented as regularizers, there are other strategies to reduce the overfitting such as Batch Normalization (Ioffe & Szegedy (2015)), which decreases the overfitting by reducing the internal covariance shift. In the same line, initialization strategies such as ”Xavier” (Glorot & Bengio (2010)) or ”He” (He et al. (2015b)), also keep the same variance at both input and output of the layers in order to preserve propagated signals in deep neural networks. Orthogonal initialization techniques are another family which set the weights in a decorrelated initial state so as to condition the network training to converge into better representations. For instance, Mishkin & Matas (2016) propose to initialize the network with decorrelated features using orthonormal initialization (Saxe et al. (2013)) while normalizing the variance of the outputs as well. ",
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+    {
+        "type": "text",
+        "text": "In this work we hypothesize that regularizing negatively correlated features is an obstacle for achieving better results and we introduce OrhoReg, a novel regularization technique that addresses the performance margin issue by only regularizing positively correlated feature weights. Moreover, OrthoReg is computationally efficient since it only regularizes the feature weights, which makes it very suitable for the latest CNN models. We verify our hypothesis through a series of experiments: first using MNIST as a proof of concept, secondly we regularize wide residual networks on CIFAR-10, CIFAR-100, and SVHN (Netzer et al. (2011)) achieving the lowest error rates in the dataset to the best of our knowledge. ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2 DEALING WITH WEIGHT REDUNDANCIES",
+        "text_level": 1,
+        "bbox": [
+            174,
+            530,
+            545,
+            544
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Deep Neural Networks (DNN) are very expressive models which can usually have millions of parameters. However, with limited data, they tend to overfit. There is an abundant number of techniques in order to deal with this problem, from L1 and L2 regularizations (Nowlan & Hinton (1992)), early-stopping, Dropout or DropConnect. Models presenting high levels of overfitting usually have a lot of redundancy in their feature weights, capturing similar patterns with slight differences which usually correspond to noise in the training data. A particular case where this is evident is in AlexNet (Krizhevsky et al. (2012)), which presents very similar convolution filters and even ”dead” ones, as it was remarked by Zeiler & Fergus (2014). ",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In fact, given a set of parameters $\\theta _ { I , j }$ connecting a set of inputs $I = \\{ i _ { 1 } , i _ { 2 } , . . . , i _ { n } \\}$ to a neuron $h _ { j }$ , two neurons $\\{ h _ { j } , \\bar { h } _ { k } \\}$ , $j \\neq k$ will be positively correlated, and thus fire always together if $\\bar { \\theta _ { I , j } } = \\theta _ { I , k }$ and negatively correlated if $\\theta _ { I , j } = - \\theta _ { I , k }$ . In other words, two neurons with the same or slightly different weights will produce very similar outputs. In order to reduce the redundancy present in the network parameters, one should maximize the amount of information encoded by each neuron. From an information theory point of view, this means one should not be able to predict the output of a neuron given the output of the rest of the neurons of the layer. However, this measure requires batch statistics, huge joint probability tables, and it would have a high computational cost. ",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In this paper, we will focus on the weights correlation rather than activation independence since it still is an open problem in many neural network models and it can be addressed without introducing too much overhead, see Table 1. Then, we show that models generalize better when different feature detectors are enforced to be dissimilar. Although it might seem contradictory, CNNs can benefit from having repeated filter weights with different biases, as shown by Li et al. (2016). However, those repeated filters must be shared copies and adding too many unshared filter weights to CNNs increases overfitting and the need for stronger regularization (Zagoruyko & Komodakis (May 2016)). Thus, our proposed method and multi-bias neural networks are complementary since they jointly increase the representation power of the network with fewer parameters. ",
+        "bbox": [
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+            797,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In order to find a good target to optimize so as to reduce the correlation between weights, it is first required to find a metric to measure it. In this paper, we propose to use the cosine similarity between feature detectors to express how strong is their relationship. Note that the cosine similarity is equivalent to the Pearson correlation for mean-centered normalized vectors, but we will use the term correlation for the sake of clarity. ",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2.1 ORTHOGONAL WEIGHT REGULARIZATION",
+        "text_level": 1,
+        "bbox": [
+            176,
+            190,
+            503,
+            205
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "This section introduces the orthogonal weight regularization, a regularization technique that aims to reduce feature detector correlation enforcing local orthogonality between all pairs of weight vectors. In order to keep the magnitudes of the detectors unaffected, we have chosen the cosine similarity between the vector pairs in order to solely focus on the vectors angle $\\beta \\in [ - \\pi , \\pi ]$ . Then, given any pair of feature vectors of the same size $\\theta _ { 1 } , \\theta _ { 2 }$ the cosine of their relative angle is: ",
+        "bbox": [
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+            217,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/532babe973466204da2fb90352d3b6f63c2648dd29dfdae42be577e68034a5cf.jpg",
+        "text": "$$\n\\cos ( \\theta _ { 1 } , \\theta _ { 2 } ) = \\frac { \\langle \\theta _ { 1 } , \\theta _ { 2 } \\rangle } { | | \\theta _ { 1 } | | | | \\theta _ { 2 } | | }\n$$",
+        "text_format": "latex",
+        "bbox": [
+            415,
+            304,
+            583,
+            338
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Where $\\left. \\theta _ { 1 } , \\theta _ { 2 } \\right.$ denotes the inner product between $\\theta _ { 1 }$ and $\\theta _ { 2 }$ . We then square the cosine similarity in order to define a regularization cost function for steepest descent that has its local minima when vectors are orthogonal: ",
+        "bbox": [
+            174,
+            349,
+            826,
+            391
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/3e90e297d40d13ac2c2c0f92c4a8912832f7195d585c7a38dba64bb879631e3a.jpg",
+        "text": "$$\nC ( \\theta ) = \\frac { 1 } { 2 } \\sum _ { i = 1 } ^ { n } \\sum _ { \\substack { j = 1 , j \\neq i } } ^ { n } \\cos ^ { 2 } ( \\theta _ { i } , \\theta _ { j } ) = \\frac { 1 } { 2 } \\sum _ { \\substack { i = 1 } } ^ { n } \\sum _ { \\substack { j = 1 , j \\neq i } } ^ { n } \\left( \\frac { \\langle \\theta _ { i } , \\theta _ { j } \\rangle } { | | \\theta _ { i } | | | | \\theta _ { j } | | } \\right) ^ { 2 }\n$$",
+        "text_format": "latex",
+        "bbox": [
+            281,
+            407,
+            715,
+            452
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Where $\\theta _ { i }$ are the weights connecting the output of the layer $l - 1$ to the neuron $i$ of the layer $l$ , which has $n$ hidden units. Interestingly, minimizing this cost function relates to the minimization of the Frobenius norm of the cross-covariance matrix without the diagonal. This cost will be added to the global cost of the model $J ( \\theta ; X , y )$ , where $X$ are the inputs and $y$ are the labels or targets, obtaining $\\tilde { J } ( \\theta ; X , y ) = J ( \\theta ; X , y ) + \\gamma C ( \\theta )$ . Note that $\\gamma$ is an hyperparameter that weights the relative contribution of the regularization term. We can now define the gradient with respect to the parameters: ",
+        "bbox": [
+            173,
+            462,
+            826,
+            563
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/5bb071228d1b1a3361886f1d42e183e8d7cdb652a6a568d1501eee2f17856527.jpg",
+        "text": "$$\n\\frac { \\delta } { \\delta \\theta _ { ( i , j ) } } C ( \\theta ) = \\sum _ { k = 1 , k \\neq i } ^ { n } \\frac { \\theta _ { ( k , j ) } \\langle \\theta _ { i } , \\theta _ { k } \\rangle } { \\langle \\theta _ { i } , \\theta _ { i } \\rangle \\langle \\theta _ { k } , \\theta _ { k } \\rangle } - \\frac { \\theta _ { ( i , j ) } \\langle \\theta _ { i } , \\theta _ { k } \\rangle ^ { 2 } } { \\langle \\theta _ { i } , \\theta _ { i } \\rangle ^ { 2 } \\langle \\theta _ { k } , \\theta _ { k } \\rangle }\n$$",
+        "text_format": "latex",
+        "bbox": [
+            305,
+            579,
+            691,
+            622
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The second term is introduced by the magnitude normalization. As magnitudes are not relevant for the vector angle problem, this equation can be simplified just by assuming normalized feature detectors: ",
+        "bbox": [
+            174,
+            632,
+            825,
+            674
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/db865c1c4220222c1b67b84f3fc30d5f890ebdc3f6c3b02c90ac2cc04ef04939.jpg",
+        "text": "$$\n{ \\frac { \\delta } { \\delta \\theta _ { ( i , j ) } } } C ( \\theta ) = \\sum _ { k = 1 , k \\neq i } ^ { n } \\theta _ { ( k , j ) } \\langle \\theta _ { i } , \\theta _ { k } \\rangle\n$$",
+        "text_format": "latex",
+        "bbox": [
+            379,
+            690,
+            619,
+            734
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "We then add eq. 4 to the backpropagation gradient: ",
+        "bbox": [
+            174,
+            746,
+            509,
+            761
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/20b6b25c909fc2eab03fabb2140b9d7206f3e02335eba49cfafba5a5b33360b6.jpg",
+        "text": "$$\n\\Delta \\theta _ { ( i , j ) } = - \\alpha \\Big ( \\nabla J _ { \\theta _ { ( i , j ) } } + \\gamma \\sum _ { k = 1 , k \\neq i } ^ { n } \\theta _ { ( k , j ) } \\langle \\theta _ { i } , \\theta _ { k } \\rangle \\Big )\n$$",
+        "text_format": "latex",
+        "bbox": [
+            330,
+            776,
+            666,
+            820
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Where $\\alpha$ is the global learning rate coefficient, $J$ any target loss function for the backpropagation algorithm. ",
+        "bbox": [
+            171,
+            830,
+            823,
+            859
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Although this update can be done sequentially for each feature-detector pair, it can be vectorized to speedup computations. Let $\\Theta$ be a matrix where each row is a feature detector $\\theta _ { ( I , j ) }$ corresponding to the normalized weights connecting the whole input $I$ of the layer to the neuron $j$ . Then, $\\Theta \\Theta ^ { t }$ contains the inner product of each pair of vectors $i$ and $j$ in each position $i , j$ . Subsequently, we ",
+        "bbox": [
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+            866,
+            825,
+            924
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Algorithm 1 Orthogonal Regularization Step. ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            103,
+            475,
+            118
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Require: Layer parameter matrices $\\Theta ^ { l }$ , regularization coefficient $\\gamma$ , global learning rate $\\alpha$ ",
+        "bbox": [
+            166,
+            125,
+            771,
+            140
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "1: for each layer $l$ to regularize do   \n2: $\\eta _ { 1 } = n o r m \\_ r o w s ( \\Theta ^ { l } )$   \n3: $\\Theta _ { 1 } ^ { l } = d i v \\_ r o w s ( \\Theta ^ { l } , \\eta _ { 1 } )$ .   \n4: in $\\AA \\ i e r P r o d M a t = \\Theta _ { 1 } ^ { l } t r a n s p o s e ( \\Theta _ { 1 } ^ { l } )$   \n5: ∇Θl1 = $\\models \\gamma ( i n n e r P r o d M a t - d i a g ( i n n e r P r o d M a t ) ) \\Theta _ { 1 } ^ { l }$   \n6: $\\Delta \\Theta ^ { l } = - \\alpha ( \\nabla J _ { \\Theta ^ { l } } + \\gamma \\nabla \\Theta _ { 1 } ^ { l } )$   \n7: end for ",
+        "bbox": [
+            178,
+            140,
+            606,
+            236
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": ". Second term in eq. 6 . Complete eq. 6. ",
+        "bbox": [
+            671,
+            194,
+            823,
+            223
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/065bfaab774f5e272775601e0ded5149b3d4f916d5211a8b0b9d7bedee67b1a6.jpg",
+        "image_caption": [
+            "Figure 1: Comparison between the two loss functions represented by eq.2 and 7. (a) is the original loss, (b) is the new loss that discards negative correlations given for different $\\lambda$ values. It can be seen $\\lambda = 1 0$ reaches a plateau when approximating to $\\frac { \\pi } { 2 }$ . (c) and (d) shows the directions of the gradients for the two loss functions above. For instance, a red arrow coming from a green ball represents the gradient of the loss between the red and green balls with respect to the green one. In (d) most of the arrows disappear since the loss in (b) only applies to angles smaller than $\\frac { \\pi } { 2 }$ . "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            181,
+            257,
+            472,
+            568
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/c8412b5ab42884c6f586a1bd08e2e7c84bef80594ea863fcd89db80465ea9b10.jpg",
+        "image_caption": [
+            "(d) Direction of gradients for loss in (b). "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            506,
+            256,
+            792,
+            568
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "(c) Direction of gradients for the loss in (a). ",
+        "bbox": [
+            209,
+            573,
+            465,
+            587
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "subtract the diagonal so as to ignore the angle from each feature with respect to itself and multiply by $\\Theta$ to compute the final value corresponding to the sum in eq. 5: ",
+        "bbox": [
+            173,
+            710,
+            823,
+            739
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/8167e8f760a41cbdc639d32db33dd260c6f4fafb739369db75799c5e05fa99d1.jpg",
+        "text": "$$\n\\Delta \\Theta = - \\alpha \\Big ( \\nabla J _ { \\Theta } + \\gamma \\big ( \\Theta \\Theta ^ { t } - d i a g ( \\Theta \\Theta ^ { t } ) \\big ) \\Theta \\Big )\n$$",
+        "text_format": "latex",
+        "bbox": [
+            344,
+            756,
+            651,
+            784
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Where the second term is $\\nabla C _ { \\Theta }$ . Algorithm 1 summarizes the steps in order to apply OrthoReg. ",
+        "bbox": [
+            171,
+            795,
+            795,
+            810
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "2.2 NEGATIVE CORRELATIONS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            827,
+            401,
+            842
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Note that the presented algorithm, based on the cosine similarity, penalizes any kind of correlation between all pairs of feature detectors, i.e. the positive and the negative correlations, see Figure 1a. However, negative correlations are related to inhibitory connections, competitive learning, and self-organization. In fact, there is evidence that negative correlations can help a neural population to increase the signal-to-noise ratio (Chelaru & Dragoi (2016)) in the V1. In order to find out the advantages of keeping negative correlations, we propose to use an exponential to squash the gradients for angles greater than $\\frac { \\pi } { 2 }$ (orthogonal): ",
+        "bbox": [
+            174,
+            853,
+            825,
+            924
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            171,
+            103,
+            825,
+            133
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/70aca7fdc358c77aa9410f4a211e33cdb81f3f50e010e29449d3abfb234d9d2b.jpg",
+        "text": "$$\nC ( \\theta ) = \\sum _ { i = 1 } ^ { n } \\sum _ { j = 1 , j \\neq i } ^ { n } \\log ( 1 + e ^ { \\lambda ( c o s ( \\theta _ { i } , \\theta _ { j } ) - 1 ) } ) = \\log ( 1 + e ^ { \\lambda ( \\langle \\theta _ { i } , \\theta _ { j } \\rangle - 1 ) } ) , \\ | | \\theta _ { i } | | = | | \\theta _ { j } | | = 1\n$$",
+        "text_format": "latex",
+        "bbox": [
+            194,
+            156,
+            784,
+            200
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Where $\\lambda$ is a coefficient that controls the minimum angle-of-influence of the regularizer, i.e. the minimum angle between two feature weights so that there exists a gradient pushing them apart, see Figure 1b. We empirically found that the regularizer worked well for $\\lambda = 1 0$ , see Figure 2b. Note that when $\\lambda \\simeq 1 0$ the loss and the gradients approximate to zero when vectors are at more than $\\textstyle { \\frac { \\pi } { 2 } }$ (orthogonal). As a result of incorporating the squashing function on the cosine similarity, negatively correlated feature weights will not be regularized. This is different from all previous approaches and the loss presented in eq. 2, where all pairs of weight vectors influence each other. Thus, from now on, the loss in eq. 2 is named as global loss and the loss in eq. 7 is named as local loss. ",
+        "bbox": [
+            173,
+            213,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The derivative of eq. 7 is: ",
+        "bbox": [
+            174,
+            332,
+            343,
+            347
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/877c7b33e2d9d9821c556d990f6295780dbc89c1b5a332b34e506d15ebfc62df.jpg",
+        "text": "$$\n{ \\frac { \\delta } { \\delta \\theta _ { ( i , j ) } } } C ( \\theta ) = \\sum _ { k = 1 , k \\neq i } ^ { n } \\lambda { \\frac { e ^ { \\lambda \\langle \\theta _ { i } , \\theta _ { k } \\rangle } \\theta _ { ( k , j ) } } { e ^ { \\lambda \\langle \\theta _ { i } , \\theta _ { k } \\rangle } + e ^ { \\lambda } } }\n$$",
+        "text_format": "latex",
+        "bbox": [
+            369,
+            363,
+            629,
+            406
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Then, given the element-wise exponential operator exp, we define the following expression in order to simplify the formulas: ",
+        "bbox": [
+            174,
+            416,
+            823,
+            445
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/49a3962fd72029ede29506440d7b9686e912007c445ec6dd483281d28db3427a.jpg",
+        "text": "$$\n\\hat { \\Theta } = \\exp ( \\lambda ( \\Theta \\Theta ^ { t } ) )\n$$",
+        "text_format": "latex",
+        "bbox": [
+            434,
+            462,
+            563,
+            483
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "and thus, the $\\Delta$ in vectorial form can be formulated as: ",
+        "bbox": [
+            173,
+            492,
+            534,
+            507
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/c1da0033dc46d5adef4d5dec2a33c9429bbd293b5beb236f6b474a97c5fb1c7d.jpg",
+        "text": "$$\n\\nabla C _ { \\Theta } = \\lambda \\frac { ( \\hat { \\Theta } - d i a g ( \\hat { \\Theta } ) ) \\Theta } { \\hat { \\Theta } - d i a g ( \\hat { \\Theta } ) + e ^ { \\lambda } }\n$$",
+        "text_format": "latex",
+        "bbox": [
+            398,
+            523,
+            599,
+            563
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "In order to provide a visual example, we have created a $2 D$ toy dataset and used the previous equations for positive and negative $\\gamma$ values, see Figure 2. As expected, it can be seen that the angle between all pairs of adjacent feature weights becomes more uniform after regularization. Note that Figure 2b shows that regularization with the global loss (eq. 2) results in less uniform angles than using the local loss as shown in 2c (which corresponds to the local loss presented in eq. 7) because vectors in opposite quadrants still influence each other. This is why in Figure 2d, it can be seen that the mean nearest neighbor angle using the global loss (b) is more unstable than the local loss (c). As a proof of concept, we also performed gradient ascent, which minimizes the angle between the vectors. Thus, in Figures 2e and 2f, it can be seen that the locality introduced by the local loss reaches a stable configuration where feature weights with angle $\\frac { \\pi } { 2 }$ are too far to attract each other. ",
+        "bbox": [
+            173,
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+            825,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The effects of global and local regularizations on Alexnet, VGG-16 and a 50-layer ResNet are shown on Figure 3. As it can be seen, OrthoReg reaches higher decorrelation bounds. Lower decorrelation peaks are still observed when the input dimensionality of the layers is smaller than the output since all vectors cannot be orthogonal at the same time. In this case, local regularization largely outperforms global regularization since it removes interferences caused by negatively correlated feature weights. This suggests why increasing fully connected layers’ size has not improved networks performance. ",
+        "bbox": [
+            174,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3 EXPERIMENTS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            835,
+            326,
+            852
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "In this section we provide a set of experiments that verify that (i) training with the proposed regularization increases the performance of naive unregularized models, (ii) negatively correlated feature weights are useful, and (iii) the proposed regularization improves the performance of state-of-the-art models. ",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/34a3be8804f26a57d411d167237444d8d7958399d4ffb56568305dbab17fe2bf.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
+            192,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/274103e294a9b385d101077beda43ccb46196b1e4b5f4f46e0a2d67c28c9fbf0.jpg",
+        "image_caption": [
+            "Figure 2: 2D toy dataset regularized with global loss (eq. 2) and local loss (eq. 7). (a) shows the initial 2D randomly generated dataset. (b) the dataset after 300 regularization steps using the global loss and (c) using the local loss. (d) the evolution of the mean nearest neighbor angle for the global loss (b) and the local loss (c). (e) and (f) correspond to (b) and (c) but using gradient ascent instead of gradient descent as a sanity-check. ",
+            "Figure 3: Effects of local and global regularization on the Alexnet, VGG-16 and 50-layer-ResNet weights. The regularized versions reach higher decorrelation bounds (in terms of minimum angle) than the unregularized counterparts. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "3.1 VERIFICATION EXPERIMENTS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            737,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "As a sanity check, we first train a three-hidden-layer Multi-Layer Perceptron (MLP) with ReLU non-liniarities on the MNIST dataset (LeCun et al. (1998)). Our code is based in the train-a-digit-classifier example included in torch/demos1, which uses an upsampled version of the dataset $( 3 2 \\times 3 2 )$ ). The only pre-processing applied to the data is a global standardization. The model is trained with SGD and a batch size of 200 during 200 epochs. No momentum neither weight decay was applied. By default, the magnitude of the weights of this experiments is recovered after each regularization step in order to prove the regularization only affects their angle. ",
+        "bbox": [
+            174,
+            763,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Sensitivity to hyperparameters. We train a three-hidden-layer MLP with 1024 hidden units, and different $\\gamma$ and $\\lambda$ values so as to verify how they affect the performance of the model. Figure 4a shows that the model effectively achieves the best error rate for the highest gamma value $( \\gamma = 1 )$ ), thus proving the advantages of the regularization. On Figure 4b, we verify that higher regularization rates produce more general models. Figure 5a depicts the sensitivity of the model to $\\lambda$ . As expected, the best value is found when lambda corresponds to Orthogonality $\\lambda \\simeq 1 0$ ). ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/797a937a123e416d547a9590449fdc1933d1fd97d9b389860168faf07f3ea464.jpg",
+        "image_caption": [
+            "Figure 4: (a) The evolution of the error rate on the MNIST validation set for different regularization magnitudes. It can be seen that for $\\gamma = 1$ it reaches the best error rate $( 1 . 4 5 \\% )$ while the unregularized counterpart $( \\gamma = 0 )$ is $1 . 7 4 \\%$ . (b) Measures the overfitting of the model for different $\\gamma$ , confirming that higher regularization rates decrease overfitting. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            186,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/bd7b23b9c26025a4c3a4beaaaa85011185c26e6e789f3f3cb62ff6e2a71dbbdc.jpg",
+        "image_caption": [
+            "Figure 5: (a) Shows the minimum error rate for different $\\lambda$ values. (b) Classification error on MNIST for different loss functions. Not regularizing negative correlated feature weights (eq. 7) results in better test error than regularizing them (eq.2). "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            186,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+            678,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Negative Correlations. Figure 5b highlights the difference between regularizing with the global or the local regularizer. Although both regularizations reach better error rates than the unregularized counterpart, the local regularization is better than the global. This confirms the hypothesis that negative correlations are useful and thus, performance decreases when we reduce them. ",
+        "bbox": [
+            173,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Compatibility with initialization and dropout. To demonstrate the proposed regularization can help even when other regularizations are present, we trained a CNN with (i) dropout $( \\mathtt { c 3 2 - c \\bar { 6 } 4 - 1 5 1 2 - d 0 . 5 - 1 1 0 } ) ^ { 2 }$ or (ii) LSUV initialization (Mishkin & Matas (2016)). In Table 2, we show that best results are obtained when orthogonal regularization is present. The results are consistent with the hypothesis that OrthoReg, as well as Dropout and LSUV, focuses on reducing the model redundancy. Thus, when one of them is present, the margin of improvement for the others is reduced. ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/b80fa05b0669ea58488acd80091c8a2cc7afbf5e245d4e715d465ba566ef1ac6.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>OrthoReg</td><td>Base</td><td>Base+Dropout</td><td>Base+LSUV</td></tr><tr><td>None</td><td>0.92</td><td>0.70 ± 0.01</td><td>0.86</td></tr><tr><td>Conv Layers</td><td>0.75</td><td>0.69 ± 0.03</td><td>0.83</td></tr><tr><td>All Layers</td><td>0.75</td><td>0.66 ± 0.03</td><td>0.79</td></tr></table>",
+        "bbox": [
+            316,
+            101,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Table 2: Error rates for a small CNN trained with the MNIST dataset. OrthoReg leads to much better results when no other improvements such as Dropout and LSUV are present but it can still make small accuracy increments when these two techniques are present. ",
+        "bbox": [
+            176,
+            186,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/d5c89f137ebdad2f4302c5935ff362f628cfc870fd05c573b7a9e6ca4094c997.jpg",
+        "image_caption": [
+            "Figure 6: Wide ResNet error rate on Cifar10 and Cifar100. OrthoReg shows better performance than the base regularizer (all feature maps), and the unregularized counterparts. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            181,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "3.2 REGULARIZATION ON CIFAR-10 AND CIFAR-100 ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            507,
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+            522
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "We show that the proposed OrthoReg can help to improve the performance of state-of-the-art models such as deep residual networks (He et al. (2015a)). In order to show the regularization is suitable for deep CNNs, we successfuly regularize a 110-layer ResNet3 on CIFAR-10, decreasing its error from $6 . 5 5 \\%$ to $6 . 2 9 \\%$ without data augmentation. ",
+        "bbox": [
+            174,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "In order to compare with the most recent state-of-the-art, we train a wide residual network (Zagoruyko & Komodakis (November 2016)) on CIFAR-10 and CIFAR-100. The experiment is based on a torch implementation of the 28-layer and 10th width factor wide deep residual model, for which the median error rate on CIFAR-10 is $3 . 8 9 \\%$ and $1 8 . 8 5 \\%$ on CIFAR- $1 0 0 ^ { 4 }$ . As it can be seen in Figure 6, regularizing with OrthoReg yields the best test error rates compared to the baselines. ",
+        "bbox": [
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+            598,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "The regularization coefficient $\\gamma$ was chosen using grid search although similar values were found for all the experiments, specially if regularization gradients are normalized before adding them to the weights. The regularization was equally applied to all the convolution layers of the (wide) ResNet. We found that, although the regularized models were already using weight decay, dropout, and batch normalization, best error rates were always achieved with OrthoReg. ",
+        "bbox": [
+            174,
+            688,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Table 3 compares the performance of the regularized models with other state-of-the-art results. As it can be seen the regularized model surpasses the state of the art, with a $5 . 1 \\%$ relative error improvement on CIFAR-10, and a $1 . 5 \\%$ relative error improvement on CIFAR-100. ",
+        "bbox": [
+            174,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "3.3 REGULARIZATION ON SVHN ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            827,
+            416,
+            840
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "For SVHN we follow the procedure depicted in Zagoruyko & Komodakis (May 2016), training a wide residual network of depth $^ { \\underline { { { \\ O } } } } = 2 8$ , width $= 4$ , and dropout. Results are shown in Table 4. As it ",
+        "bbox": [
+            174,
+            853,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/20bec678b951e9e7b03641aaf3c857d7cd8341e4ec34efc02f724b5578fe113b.jpg",
+        "table_caption": [
+            "Table 3: Comparison with other CNNs on CIFAR-10 and CIFAR-100 (Test error $\\%$ ). Orthogonally regularized residual networks achieve the best results to the best of our knowldege. Only single-crop results are reported for fairness of comparison. \\*Median over 5 runs as reported by Zagoruyko & Komodakis (November 2016). "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Network</td><td>CIFAR-10</td><td>CIFAR-100</td><td>Augmented</td></tr><tr><td>Maxout (Goodfellow et al. (2013))</td><td>9.38</td><td>38.57</td><td>YES</td></tr><tr><td>NiN (Lin et al. (2014))</td><td>8.81</td><td>35.68</td><td>YES</td></tr><tr><td>DSN (Lee et al. (2015))</td><td>7.97</td><td>34.57</td><td>YES</td></tr><tr><td>Highway Network (Srivastava et al. (2015))</td><td>7.60</td><td>32.24</td><td>YES</td></tr><tr><td>All-CNN (Springenberg et al. (2015))</td><td>7.25</td><td>33.71</td><td>NO</td></tr><tr><td>110-Layer ResNet (He et al. (2015a))</td><td>6.61</td><td>28.4</td><td>NO</td></tr><tr><td>ELU-Network (Clevert et al. (2016))</td><td>6.55</td><td>24.28</td><td>NO</td></tr><tr><td>OrthoReg on 110-Layer ResNet*</td><td>6.29 ± 0.19</td><td>28.33 ± 0.5</td><td>NO</td></tr><tr><td>LSUV (Mishkin &amp; Matas (2016))</td><td>5.84</td><td>1</td><td>YES</td></tr><tr><td>Fract.Max-Pooling (Graham (2014))</td><td>4.50</td><td>27.62</td><td>YES</td></tr><tr><td>Wide ResNet v1 (Zagoruyko &amp; Komodakis (May 2016))*</td><td>4.37</td><td>20.40</td><td>YES</td></tr><tr><td>OrthoReg on Wide ResNet v1 (May 2016)*</td><td>4.32 ± 0.05</td><td>19.50 ± 0.03</td><td>YES</td></tr><tr><td>Wide ResNet v2 (Zagoruyko &amp; Komodakis (November 2016))*</td><td>3.89</td><td>18.85</td><td>YES</td></tr><tr><td>OrthoReg on Wide ResNet v2 (November 2016)*</td><td>3.69 ± 0.01</td><td>18.56 ± 0.12</td><td>YES</td></tr></table>",
+        "bbox": [
+            173,
+            101,
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+            324
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "table",
+        "img_path": "images/491d5d56bda3cbf9480511a3c0a3e95cb5510759803f8c107a3f374476de40d5.jpg",
+        "table_caption": [
+            "Table 4: Comparison with other CNNs on SVHN. Wide Resnets regularized with OrthoReg show better performance. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>Error rate</td></tr><tr><td>NiN (Lin et al. (2014))</td><td>2.35</td></tr><tr><td>DSN (Lee et al. (2015))</td><td>1.92</td></tr><tr><td>Stochastic Depth ResNet (Huang et al. (2016))</td><td>1.75</td></tr><tr><td>Wide Resnet (Zagoruyko &amp; Komodakis (May 2016))</td><td>1.64</td></tr><tr><td>OrthoReg on Wide Resnet</td><td>1.54</td></tr></table>",
+        "bbox": [
+            246,
+            428,
+            750,
+            526
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "can be seen, we reduce the error rate from $1 . 6 4 \\%$ to $1 . 5 4 \\%$ , which is the lowest value reported on this dataset to the best of our knowledge. ",
+        "bbox": [
+            174,
+            604,
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "4 DISCUSSION ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            667,
+            310,
+            684
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Regularization by feature decorrelation can reduce Neural Networks overfitting even in the presence of other kinds of regularizations. However, especially when the number of feature detectors is higher than the input dimensionality, its decorrelation capacity is limited due to the effects of negatively correlated features. We showed that imposing locality constraints in feature decorrelation removes interferences between negatively correlated feature weights, allowing regularizers to reach higher decorrelation bounds, and reducing the overfitting more effectively. ",
+        "bbox": [
+            174,
+            708,
+            825,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "In particular, we show that the models regularized with the constrained regularization present lower overfitting even when batch normalization and dropout are present. Moreover, since our regularization is directly performed on the weights, it is especially suitable for fully convolutional neural networks, where the weight space is constant compared to the feature map space. As a result, we are able to reduce the overfitting of 110-layer ResNets and wide ResNets on CIFAR-10, CIFAR-100, and SVHN improving their performance. Note that despite OrthoReg consistently improves state of the art ReLU networks, the choice of the activation function could affect regularizers like the one presented in this work. In this sense, the effect of asymmetrical activations on feature correlations and regularizers should be further investigated in the future. ",
+        "bbox": [
+            174,
+            797,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "ACKNOWLEDGEMENTS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            103,
+            367,
+            117
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Authors acknowledge the support of the Spanish project TIN2015-65464-R (MINECO/FEDER), the 2016FI B 01163 grant of Generalitat de Catalunya, and the COST Action IC1307 iV&L Net (European Network on Integrating Vision and Language) supported by COST (European Cooperation in Science and Technology). We also gratefully acknowledge the support of NVIDIA Corporation with the donation of a Tesla K40 GPU and a GTX TITAN GPU, used for this research. ",
+        "bbox": [
+            174,
+            133,
+            825,
+            203
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "REFERENCES ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Yebo Bao, Hui Jiang, Lirong Dai, and Cong Liu. Incoherent training of deep neural networks to de-correlate bottleneck features for speech recognition. In 2013 IEEE ICASSP, pp. 6980–6984. IEEE, 2013.   \nYoshua Bengio and James S Bergstra. Slow, decorrelated features for pretraining complex cell-like networks. In NIPS, pp. 99–107, 2009.   \nMircea I Chelaru and Valentin Dragoi. Negative correlations in visual cortical networks. Cerebral Cortex, 26(1):246–256, 2016.   \nDjork-Arn Clevert, Thomas Unterthiner, and Sepp Hochreiter. Fast and accurate deep network learning by exponential linear units (ELUs). ICLR, 2016.   \nMichael Cogswell, Faruk Ahmed, Ross Girshick, Larry Zitnick, and Dhruv Batra. Reducing overfitting in deep networks by decorrelating representations. ICLR, 2016.   \nXavier Glorot and Yoshua Bengio. Understanding the difficulty of training deep feedforward neural networks. In AISTATS, 2010.   \nIan Goodfellow, David Warde-Farley, Mehdi Mirza, Aaron Courville, and Yoshua Bengio. Maxout networks. In ICML, pp. 1319–1327, 2013.   \nBenjamin Graham. Fractional max-pooling. arXiv preprint arXiv:1412.6071, 2014.   \nKaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recognition. arXiv preprint arXiv:1512.03385, 2015a.   \nKaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Delving deep into rectifiers: Surpassing human-level performance on imagenet classification. In ICCV, pp. 1026–1034, 2015b.   \nGao Huang, Yu Sun, Zhuang Liu, Daniel Sedra, and Kilian Weinberger. Deep networks with stochastic depth. arXiv preprint arXiv:1603.09382, 2016.   \nSergey Ioffe and Christian Szegedy. Batch normalization: Accelerating deep network training by reducing internal covariate shift. In ICML, pp. 448–456, 2015.   \nAlex Krizhevsky, Ilya Sutskever, and Geoffrey E. Hinton. ImageNet Classification with Deep Convolutional Neural Networks. In NIPS, pp. 1106–1114, 2012.   \nYann LeCun, Leon Bottou, Yoshua Bengio, and Patrick Haffner. Gradient-based learning applied to ´ document recognition. Proceedings of the IEEE, 86(11):2278–2324, 1998.   \nChen-Yu Lee, Saining Xie, Patrick W. Gallagher, Zhengyou Zhang, and Zhuowen Tu. Deeplysupervised nets. In Guy Lebanon and S. V. N. Vishwanathan (eds.), AISTATS, volume 38 of JMLR Proceedings. JMLR.org, 2015.   \nHongyang Li, Wanli Ouyang, and Xiaogang Wang. Multi-bias non-linear activation in deep neural networks. arXiv preprint arXiv:1604.00676, 2016.   \nMin Lin, Qiang Chen, and Shuicheng Yan. Network in network. arXiv preprint arXiv:1312.4400, March 2014. ",
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+]

parse/train/BybtVK9lg/BybtVK9lg.md

@@ -0,0 +1,293 @@
+# AUTOENCODING VARIATIONAL INFERENCE FOR TOPIC MODELS
+
+Akash Srivastava   
+Informatics Forum, University of Edinburgh   
+10, Crichton St   
+Edinburgh, EH89AB, UK   
+akash.srivastava@ed.ac.uk   
+Charles Sutton∗   
+Informatics Forum, University of Edinburgh   
+10, Crichton St   
+Edinburgh, EH89AB, UK   
+csutton@inf.ed.ac.uk
+
+# ABSTRACT
+
+Topic models are one of the most popular methods for learning representations of text, but a major challenge is that any change to the topic model requires mathematically deriving a new inference algorithm. A promising approach to address this problem is autoencoding variational Bayes (AEVB), but it has proven difficult to apply to topic models in practice. We present what is to our knowledge the first effective AEVB based inference method for latent Dirichlet allocation (LDA), which we call Autoencoded Variational Inference For Topic Model (AVITM). This model tackles the problems caused for AEVB by the Dirichlet prior and by component collapsing. We find that AVITM matches traditional methods in accuracy with much better inference time. Indeed, because of the inference network, we find that it is unnecessary to pay the computational cost of running variational optimization on test data. Because AVITM is black box, it is readily applied to new topic models. As a dramatic illustration of this, we present a new topic model called ProdLDA, that replaces the mixture model in LDA with a product of experts. By changing only one line of code from LDA, we find that ProdLDA yields much more interpretable topics, even if LDA is trained via collapsed Gibbs sampling.
+
+# 1 INTRODUCTION
+
+Topic models (Blei, 2012) are among the most widely used models for learning unsupervised representations of text, with hundreds of different model variants in the literature, and have have found applications ranging from the exploration of the scientific literature (Blei & Lafferty, 2007) to computer vision (Fei-Fei & Perona, 2005), bioinformatics (Rogers et al., 2005), and archaeology (Mimno, 2009). A major challenge in applying topic models and developing new models is the computational cost of computing the posterior distribution. Therefore a large body of work has considered approximate inference methods, the most popular methods being variational methods, especially mean field methods, and Markov chain Monte Carlo, particularly methods based on collapsed Gibbs sampling.
+
+Both mean-field and collapsed Gibbs have the drawback that applying them to new topic models, even if there is only a small change to the modeling assumptions, requires re-deriving the inference methods, which can be mathematically arduous and time consuming, and limits the ability of practitioners to freely explore the space of different modeling assumptions. This has motivated the development of black-box inference methods (Ranganath et al., 2014; Mnih & Gregor, 2014; Kucukelbir et al., 2016; Kingma & Welling, 2014) which require only very limited and easy to compute information from the model, and hence can be applied automatically to new models given a simple declarative specification of the generative process.
+
+Autoencoding variational Bayes (AEVB) (Kingma & Welling, 2014; Rezende et al., 2014) is a particularly natural choice for topic models, because it trains an inference network (Dayan et al., 1995), a neural network that directly maps a document to an approximate posterior distribution, without the need to run further variational updates. This is intuitively appealing because in topic models, we expect the mapping from documents to posterior distributions to be well behaved, that is, that a small change in the document will produce only a small change in topics. This is exactly the type of mapping that a universal function approximator like a neural network should be good at representing. Essentially, the inference network learns to mimic the effect of probabilistic inference, so that on test data, we can enjoy the benefits of probabilistic modeling without paying a further cost for inference.
+
+However, despite some notable successes for latent Gaussian models, black box inference methods are significantly more challenging to apply to topic models. For example, in initial experiments, we tried to apply ADVI (Kucukelbir et al., 2016), a recent black-box variational method, but it was difficult to obtain any meaningful topics. Two main challenges are: first, the Dirichlet prior is not a location scale family, which hinders reparameterisation, and second, the well known problem of component collapsing (Dinh & Dumoulin, 2016), in which the inference network becomes stuck in a bad local optimum in which all topics are identical.
+
+In this paper, we present what is, to our knowledge, the first effective AEVB inference method for topic models, which we call Autoencoded Variational Inference for Topic Models or AVITM1. On several data sets, we find that AVITM yields topics of equivalent quality to standard mean-field inference, with a large decrease in training time. We also find that the inference network learns to mimic the process of approximate inference highly accurately, so that it is not necessary to run variational optimization at all on test data.
+
+But perhaps more important is that AVITM is a black-box method that is easy to apply to new models. To illustrate this, we present a new topic model, called ProdLDA, in which the distribution over individual words is a product of experts rather than the mixture model used in LDA. We find that ProdLDA consistently produces better topics than standard LDA, whether measured by automatically determined topic coherence or qualitative examination. Furthermore, because we perform probabilistic inference using a neural network, we can fit a topic model on roughly a one million documents in under 80 minutes on a single GPU, and because we are using a black box inference method, implementing ProdLDA requires a change of only one line of code from our implementation of standard LDA.
+
+To summarize, the main advantages of our methods are:
+
+1. Topic coherence: ProdLDA returns consistently better topics than LDA, even when LDA is trained using Gibbs sampling.   
+2. Computational efficiency: Training AVITM is fast and efficient like standard mean-field. On new data, AVITM is much faster than standard mean field, because it requires only one forward pass through a neural network.   
+3. Black box: AVITM does not require rigorous mathematical derivations to handle changes in the model, and can be easily applied to a wide range of topic models.
+
+Overall, our results suggest that AVITM is ready to take its place alongside mean field and collapsed Gibbs as one of the workhorse inference methods for topic models.
+
+# 2 BACKGROUND
+
+To fix notation, we begin by describing topic modelling and AVITM.
+
+# 2.1 LATENT DIRICHLET ALLOCATION
+
+We describe the most popular topic model, latent Dirichlet allocation (LDA). In LDA, each document of the collection is represented as a mixture of topics, where each topic $\beta _ { k }$ is a probability distribution over the vocabulary. We also use $\beta$ to denote the matrix $\beta = \left( \beta _ { 1 } \ldots \beta _ { K } \right)$ . The generative process is then as described in Algorithm 1. Under this generative model, the marginal likelihood of
+
+for each document w do Draw topic distribution $\theta \sim$ Dirichlet $( \alpha )$ ; for each word at position $n$ do Sample topic $z _ { n } \sim$ Multinomial $( 1 , \theta )$ ; Sample word $w _ { n } \sim$ Multinomia $( 1 , \beta _ { z _ { n } } )$ ; end   
+end
+
+Algorithm 1: LDA as a generative model.
+
+a document w is
+
+$$
+p ( \mathbf { w } | \alpha , \beta ) = \int _ { \boldsymbol { \theta } } \left( \prod _ { n = 1 } ^ { N } \sum _ { z _ { n } = 1 } ^ { k } p ( w _ { n } | z _ { n } , \beta ) p ( z _ { n } | \boldsymbol { \theta } ) \right) p ( \boldsymbol { \theta } | \alpha ) d \boldsymbol { \theta } .
+$$
+
+Posterior inference over the hidden variables $\theta$ and $z$ is intractable due to the coupling between the $\theta$ and $\beta$ under the multinomial assumption (Dickey, 1983).
+
+# 2.2 MEAN FIELD AND AEVB
+
+A popular approximation for efficient inference in topic models is mean field variational inference, which breaks the coupling between $\theta$ and $z$ by introducing free variational parameters $\gamma$ over $\theta$ and $\phi$ over $z$ and dropping the edges between them. This results in an approximate variational posterior $\begin{array} { r } { q ( \theta , z | \gamma , \phi ) \stackrel { \_ } { = } q _ { \gamma } \bar { ( \theta ) } \prod _ { n } \bar { q _ { \phi } } ( z _ { n } ) } \end{array}$ , which is optimized to best approximate the true posterior $p ( \boldsymbol { \theta } , z | \mathbf { w } , \alpha , \beta )$ . The optimization problem is to minimize
+
+$$
+\begin{array} { r } { L ( \gamma , \phi \mid \alpha , \beta ) = D _ { K L } \left[ q ( \theta , z \vert \gamma , \phi ) \vert \vert p ( \theta , z \vert \mathbf { w } , \alpha , \beta ) \right] - \log p ( \mathbf { w } \vert \alpha , \beta ) . } \end{array}
+$$
+
+In fact the above equation is a lower bound to the marginal log likelihood, sometimes called an evidence lower bound $( E L B O )$ , a fact which can be easily verified by multiplying and dividing (1) by the variational posterior and then applying Jensen’s inequality on its logarithm. Note that the mean field method optimizes over an independent set of variational parameters for each document. To emphasize this, we will refer to this standard method by the non-standard name of Decoupled Mean-Field Variational Inference (DMFVI).
+
+For LDA, this optimization has closed form coordinate descent equations due to the conjugacy between the Dirichlet and multinomial distributions. Although this is a computationally convenient aspect of DMFVI, it also limits its flexibility. Applying DMFVI to new models relies on the practitioner’s ability to derive the closed form updates, which can be impractical and sometimes impossible.
+
+AEVB (Kingma & Welling, 2014; Rezende et al., 2014) is one of several recent methods that aims at “black box” inference methods to sidestep this issue. First, rewrite the ELBO as
+
+$$
+L ( \gamma , \phi \mid \alpha , \beta ) = - D _ { K L } \left[ q ( \theta , z | \gamma , \phi ) | | p ( \theta , z | \alpha ) \right] + \mathbb { E } _ { q ( \theta , z | \gamma , \phi ) } [ \log p ( \mathbf { w } | z , \theta , \alpha , \beta ) ]
+$$
+
+This form is intuitive. The first term attempts to match the variational posterior over latent variables to the prior on the latent variables, while the second term ensures that the variational posterior favors values of the latent variables that are good at explaining the data. By analogy to autoencoders, this second term is referred to as a reconstruction term.
+
+What makes this method “Autoencoding,” and in fact the main difference from DMFVI, is the parameterization of the variational distribution. In AEVB, the variational parameters are computed by using a neural network called an inference network that takes the observed data as input. For example, if the model prior $p ( \theta )$ were Gaussian, we might define the inference network as a feedforward neural network $( \mu ( \mathbf { w } ) , \mathbf { v } ( \mathbf { w } ) ) = f ( \mathbf { w } , \gamma )$ , where $\mu ( \mathbf { w } )$ and $\mathbf { v } ( \mathbf { w } )$ are both vectors of length $k$ , and $\gamma$ are the network’s parameters. Then we might choose a Gaussian variational distribution $q _ { \gamma } ( \theta ) = N ( \theta ; \mu ( \mathbf { w } ) , \mathrm { d i a g } ( \bar { \mathbf { v } ( \mathbf { w } ) } ) )$ , where $\mathrm { d i a g ( \cdot \cdot \cdot ) }$ produces a diagonal matrix from a column vector. The variational parameters $\gamma$ can then be chosen by optimizing the ELBO (3). Note that we have now, unlike DMFVI, coupled the variational parameters for different documents because they are all computed from the same neural network. To compute the expectations with respect to $q$ in (3), Kingma & Welling (2014); Rezende et al. (2014) use a Monte Carlo estimator which they call the “reparameterization trick” (RT; appears also in Williams (1992)). In the RT, we define a variate $U$ with a simple distribution that is independent of all variational parameters, like a uniform or standard normal, and a reparameterization function $F$ such that $F ( U , \gamma )$ has distribution $q _ { \gamma }$ . This is always possible, as we could choose $F$ to be the inverse cumulative distribution function of $q _ { \gamma }$ , although we will additionally want $F$ to be easy to compute and differentiable. If we can determine a suitable $F$ , then we can approximate (3) by taking Monte Carlo samples of $U$ , and optimize $\gamma$ using stochastic gradient descent.
+
+# 3 AUTOENCODING VARIATIONAL BAYES IN LATENT DIRICHLET ALLOCATION
+
+Although simple conceptually, applying AEVB to topic models raises several practical challenges. The first is the need to determine a reparameterization function for $q ( \theta )$ and $q ( z _ { n } )$ to use the RT. The $z _ { n }$ are easily dealt with, but $\theta$ is more difficult; if we choose $q ( \theta )$ to be Dirichlet, it is difficult to apply the RT, whereas if we choose $q$ to be Gaussian or logistic normal, then the KL divergence in (3) becomes more problematic. The second issue is the well known problem of component collapsing (Dinh & Dumoulin, 2016), which a type of bad local optimum that is particularly endemic to AEVB and similar methods. We describe our solutions to each of those problems in the next few subsections.
+
+# 3.1 COLLAPSING z’S
+
+Dealing with discrete variables like $\mathbf { z }$ using reparameterization can be problematic, but fortunately in LDA the variable $\mathbf { z }$ can be conveniently summed out. By collapsing $\mathbf { z }$ we are left with having to sample from $\theta$ only, reducing (1) to
+
+$$
+p ( \mathbf { w } | \alpha , \beta ) = \int _ { \theta } \left( \prod _ { n = 1 } ^ { N } p ( w _ { n } | \beta , \theta ) \right) p ( \theta | \alpha ) d \theta .
+$$
+
+where the distribution of $w _ { n } | \beta , \theta$ is Multinomial(1, $\beta \theta ,$ ), recalling that $\beta$ denotes the matrix of all topic-word probability vectors.
+
+# 3.2 WORKING WITH DIRICHLET BELIEFS: LAPLACE APPROXIMATION
+
+LDA gets its name from the Dirichlet prior on the topic proportions $\theta$ , and the choice of Dirichlet prior is important to obtaining interpretable topics (Wallach et al., 2009). But it is difficult to handle the Dirichlet within AEVB because it is difficult to develop an effective reparameterization function for the RT. Fortunately, a RT does exist for the Gaussian distribution and has been shown to perform quite well in the context of variational autoencoder (VAE) (Kingma & Welling, 2014).
+
+We resolve this issue by constructing a Laplace approximation to the Dirichlet prior. Following MacKay (1998), we do so in the softmax basis instead of the simplex. There are two benefits of this choice. First, Dirichlet distributions are unimodal in the softmax basis with their modes coinciding with the means of the transformed densities. Second, the softmax basis also allows for carrying out unconstrained optimization of the cost function without the simplex constraints. The Dirichlet probability density function in this basis over the softmax variable $\mathbf { h }$ is given by
+
+$$
+P ( \theta ( \mathbf { h } ) | \alpha ) = \frac { \Gamma ( \sum _ { k } \alpha _ { k } ) } { \prod _ { k } \Gamma ( \alpha _ { k } ) } \prod _ { k } \theta _ { k } ^ { \alpha _ { k } } g ( \mathbf { 1 } ^ { T } \mathbf { h } ) .
+$$
+
+Here $\theta = \sigma ( { \bf h } )$ , where $\sigma ( . )$ represents the softmax function. Recall that the Jacobian of $\sigma$ is proportional to $\textstyle \prod _ { k } \theta _ { k }$ and $g ( \cdot )$ is an arbitrary density that ensures integrability by constraining the redundant degree of freedom. We use the Laplace approximation of Hennig et al. (2012), which
+
+has the property that the covariance matrix becomes diagonal for large $k$ (number of topics). This approximation to the Dirichlet prior $p ( \theta | \alpha )$ is results in the distribution over the softmax variables h as a multivariate normal with mean $\mu _ { 1 }$ and covariance matrix $\Sigma _ { 1 }$ where
+
+$$
+\begin{array} { c l } { \displaystyle \mu _ { 1 k } = \log \alpha _ { k } - \frac 1 K \sum _ { i } \log \alpha _ { i } } \\ { \displaystyle \sum _ { 1 k k } = \frac 1 { \alpha _ { k } } \left( 1 - \frac 2 K \right) + \frac 1 { K ^ { 2 } } \sum _ { i } \frac 1 { \alpha _ { k } } . } \end{array}
+$$
+
+Finally, we approximate $p ( \theta | \alpha )$ in the simplex basis with $\hat { p } ( \theta | \mu _ { 1 } , \Sigma _ { 1 } ) = \mathcal { L N } ( \theta | \mu _ { 1 } , \Sigma _ { 1 } )$ where $\mathcal { L N }$ is a logistic normal distribution with parameters $\mu _ { 1 } , \Sigma _ { 1 }$ . Although we approximate the Dirichlet prior in LDA with a logistic normal, this is not the same idea as a correlated topic model (Blei & Lafferty, 2006), because we use a diagonal covariance matrix. Rather, it is an approximation to standard LDA.
+
+# 3.3 VARIATIONAL OBJECTIVE
+
+Now we can write the modified variational objective function. We use a logistic normal variational distribution over $\theta$ with diagonal covariance. More precisely, we define two inference networks as feed forward neural networks $f _ { \mu }$ and $f _ { \Sigma }$ with parameters $\delta$ ; the output of each network is a vector in $\mathbb { R } ^ { K }$ . Then for a document w, we define $q ( \theta )$ to be logistic normal with mean $\mu _ { 0 } = f _ { \mu } ( \mathbf { w } , \pmb \delta )$ and diagonal covariance $\pmb { \Sigma } _ { 0 } = \mathrm { d i a g } ( f _ { \Sigma } ( \mathbf { w } , \pmb { \delta } ) )$ , where diag converts a column vector to a diagonal matrix. Note that we can generate samples from $q ( \theta )$ by sampling $\epsilon \sim \mathcal { N } ( 0 , I )$ and computing $\theta = \sigma ( \pmb { \mu } _ { 0 } + \pmb { \Sigma } _ { 0 } ^ { 1 / 2 } \pmb { \epsilon } ) .$ .
+
+We can now write the ELBO as
+
+$$
+\begin{array} { r } { L ( \boldsymbol { \Theta } ) = \displaystyle \sum _ { d = 1 } ^ { D } \Bigg [ - \left( \frac { 1 } { 2 } \Big \{ t r ( \boldsymbol { \Sigma } _ { 1 } ^ { - 1 } \boldsymbol { \Sigma } _ { 0 } ) + ( \boldsymbol { \mu } _ { 1 } - \boldsymbol { \mu } _ { 0 } ) ^ { T } \boldsymbol { \Sigma } _ { 1 } ^ { - 1 } ( \boldsymbol { \mu } _ { 1 } - \boldsymbol { \mu } _ { 0 } ) - K + \log \frac { | \boldsymbol { \Sigma } _ { 1 } | } { | \boldsymbol { \Sigma } _ { 0 } | } \Big \} \right) } \\ { + \mathbb { E } _ { \epsilon \sim \mathcal { N } ( 0 , I ) } \Bigg [ \mathbf { w } _ { d } ^ { \top } \log \Big ( \sigma ( \boldsymbol { \beta } ) \sigma ( \boldsymbol { \mu } _ { 0 } + \boldsymbol { \Sigma } _ { 0 } ^ { 1 / 2 } \boldsymbol { \epsilon } ) \Big ) \Bigg ] \Bigg ] , } \end{array}
+$$
+
+where $\Theta$ represents the set of all the model and variational parameters and $\mathbf { w } _ { 1 } \ldots \mathbf { w } _ { D }$ are the documents in the corpus. The first line in this equation arises from the KL divergence between the two logistic normal distributions $q$ and $\hat { p }$ , while the second line is the reconstruction error.
+
+In order to impose the simplex constraint on the $\beta$ matrix during the optimization, we apply the softmax transformation. That is, each topic $\beta _ { k } \in \mathbb { R } ^ { V }$ is unconstrained, and the notation $\sigma ( \beta )$ means to apply the softmax function separately to each column of the matrix $\beta$ . Note that the mixture of multinomials for each word $w _ { n }$ can then be written as $p ( w _ { n } | \beta , \theta ) = [ \sigma ( \beta ) \theta ] _ { w _ { n } }$ , which explains the ndot product in (7). To optimize (7), we use stochastic gradient descent using Monte Carlo samples from , following the Law of the Unconscious Statistician.
+
+# 3.4 TRAINING AND PRACTICAL CONSIDERATIONS: DEALING WITH COMPONENT COLLAPSING
+
+AEVB is prone to component collapsing (Dinh & Dumoulin, 2016), which is a particular type of local optimum very close to the prior belief, early on in the training. As the latent dimensionality of the model is increased, the KL regularization in the variational objective dominates, so that the outgoing decoder weights collapse for the components of the latent variable that reach close to the prior and do not show any posterior divergence. In our case, the collapsing specifically occurs because of the inclusion of the softmax transformation to produce $\theta$ . The result is that the $k$ inferred topics are identical as shown in table 7.
+
+We were able to resolve this issue by tweaking the optimization. Specifically, we train the network with the ADAM optimizer (Kingma & Ba, 2015) using high moment weight $( \beta 1 )$ and learning rate $( \eta )$ . Through training at higher rates, early peaks in the functional space can be easily avoided. The problem is that momentum based training coupled with higher learning rate causes the optimizer to diverge. While explicit gradient clipping helps to a certain extent, we found that batch normalization (Ioffe & Szegedy, 2015) does even better by smoothing out the functional space and hence curbing sudden divergence.
+
+Finally, we also found an increase in performance with dropout units when applied to $\theta$ to force the network to use more of its capacity.
+
+While more prominent in the AEVB framework, the collapsing can also occurs in DMFVI if the learning offset (referred to as the $\tau$ parameter (Hofmann, 1999)) is not set properly. Interestingly, a similar learning offset or annealing based approach can also be used to down-weight the KL term in early iterations of the training to avoid local optima.
+
+# 4 PRODLDA: LATENT DIRICHLET ALLOCATION WITH PRODUCTS OF EXPERTS
+
+In LDA, the distribution $p ( \mathbf { w } | \theta , \beta )$ is a mixture of multinomials. A problem with this assumption is that it can never make any predictions that are sharper than the components that are being mixed (Hinton & Salakhutdinov, 2009). This can result in some topics appearing that are poor quality and do not correspond well with human judgment. One way to resolve this issue is to replace this word-level mixture with a weighted product of experts which by definition is capable of making sharper predictions than any of the constituent experts (Hinton, 2002). In this section we present a novel topic model PRODLDA that replaces the mixture assumption at the word-level in LDA with a weighted product of experts, resulting in a drastic improvement in topic coherence. This is a good illustration of the benefits of a black box inference method, like AVITM, to allow exploration of new models.
+
+# 4.1 MODEL
+
+The PRODLDA model can be simply described as latent Dirichlet allocation where the word-level mixture over topics is carried out in natural parameter space, i.e. the topic matrix is not constrained to exist in a multinomial simplex prior to mixing. In other words, the only changes from LDA are that $\beta$ is unnormalized, and that the conditional distribution of $w _ { n }$ is defined as $w _ { n } | \beta , \theta \ \sim$ Multinomia $( 1 , \sigma ( \beta \theta ) )$ .
+
+The connection to a product of experts is straightforward, as for the multinomial, a mixture of natural parameters corresponds to a weighted geometric average of the mean parameters. That is, consider two $N$ dimensional multinomials parametrized by mean vectors $\mathbf { p }$ and $\mathbf { q }$ . Define the corresponding natural parameters as $\mathbf { p } = \sigma ( \pmb { r } )$ and $\mathbf { q } = \sigma ( \pmb { \mathscr { s } } )$ , and let $\delta \in [ 0 , 1 ]$ . It is then easy to show that
+
+$$
+P \Big ( \mathbf { x } | \delta r + ( 1 - \delta ) \pmb { s } \Big ) \propto \prod _ { i = 1 } ^ { N } \sigma ( \delta r _ { i } + ( 1 - \delta ) s _ { i } ) ^ { x _ { i } } \propto \prod _ { i = 1 } ^ { N } [ r _ { i } ^ { \delta } \cdot s _ { i } ^ { ( 1 - \delta ) } ] ^ { x _ { i } } .
+$$
+
+So the PRODLDA model can be simply described as a product of experts, that is, $p ( w _ { n } | \theta , \beta ) \ \propto$ $\begin{array} { r } { \prod _ { k } p ( w _ { n } | z _ { n } = k , \beta ) ^ { \theta _ { k } } } \end{array}$ . PRODLDA is an instance of the exponential-family PCA (Collins et al., 2001) class, and relates to the exponential-family harmoniums (Welling et al., 2004) but with nonGaussian priors.
+
+# 5 RELATED WORK
+
+For an overview of topic modeling, see Blei (2012). There are several examples of topic models based on neural networks and neural variational inference (Hinton & Salakhutdinov, 2009; Larochelle & Lauly, 2012; Mnih & Gregor, 2014; Miao et al., 2016) but we are unaware of methods that apply AEVB generically to a topic model specified by an analyst, or even of a successful application of AEVB to the most widely used topic model, latent Dirichlet allocation.
+
+Recently, Miao et al. (2016) introduced a closely related model called the Neural Variational Document Model (NVDM). This method uses a latent Gaussian distribution over topics, like probabilistic latent semantic indexing, and averages over topic-word distributions in the logit space. However, they do not use either of the two key aspects of our work: explicitly approximating the Dirichlet prior using a Gaussian, or high-momentum training. In the experiments we show that these aspects lead to much improved training and much better topics.
+
+# 6 EXPERIMENTS AND RESULTS
+
+Qualitative evaluation of topic models is a challenging task and consequently a large body of work has developed automatic evaluation metrics that attempt to match human judgment of topic quality. Traditionally, perplexity has been used to measure the goodness-of-fit of the model but it has been repeatedly shown that perplexity is not a good metric for qualitative evaluation of topics (Newman et al., 2010). Several new metrics of topic coherence evaluation have thus been proposed; see Lau et al. (2014) for a comparative review. Lau et al. (2014) showed that among all the competing metrics, normalized pointwise mutual information (NPMI) between all the pairs of words in a set of topics matches human judgment most closely, so we adopt it in this work. We also report perplexity, primarily as a way of evaluating the capability of different optimizers. Following standard practice (Blei et al., 2003), for variational methods we use the ELBO to calculate perplexity. For AEVB methods, we calculate the ELBO using the same Monte Carlo approximation as for training.
+
+We run experiments on both the 20 Newsgroups (11,000 training instances with 2000 word vocabulary) and RCV1 Volume 2 ( 800K training instances with 10000 word vocabulary) datasets. Our preprocessing involves tokenization, removal of some non UTF-8 characters for 20 Newsgroups and English stop word removal. We first compare our AVITM inference method with the standard online mean-field variational inference (Hoffman et al., 2010) and collapsed Gibbs sampling (Griffiths & Steyvers, 2004) on the LDA model. We use standard implementations of both methods, scikit-learn for DMFVI and mallet (McCallum, 2002) for collapsed Gibbs. Then we compare two autoencoding inference methods on three different topic models: standard LDA, PRODLDA using our inference method and the Neural Variational Document Model (NVDM) (Miao et al., 2016), using the inference described in the paper.2
+
+Table 1: Average topic coherence on the 20 Newsgroups dataset. Higher is better.   
+
+<table><tr><td rowspan=1 colspan=1># topics</td><td rowspan=1 colspan=1>ProdLDAVAE</td><td rowspan=1 colspan=1>LDAVAE</td><td rowspan=1 colspan=1>LDADMFVI</td><td rowspan=1 colspan=1>LDACollapsed Gibbs</td><td rowspan=1 colspan=1>NVDM</td></tr><tr><td rowspan=1 colspan=1>50</td><td rowspan=1 colspan=1>0.24</td><td rowspan=1 colspan=1>0.11</td><td rowspan=1 colspan=1>0.11</td><td rowspan=1 colspan=1>0.17</td><td rowspan=1 colspan=1>0.08</td></tr><tr><td rowspan=1 colspan=1>200</td><td rowspan=1 colspan=1>0.19</td><td rowspan=1 colspan=1>0.11</td><td rowspan=1 colspan=1>0.06</td><td rowspan=1 colspan=1>0.14</td><td rowspan=1 colspan=1>0.06</td></tr></table>
+
+Tables 1 and 2 show the average topic coherence values for all the models for two different settings of $k$ , the number of topics. Comparing the different inference methods for LDA, we find that, consistent with previous work, collapsed Gibbs sampling yields better topics than mean-field methods. Among the variational methods, we find that VAE-LDA model (AVITM) 3 yields similar topic coherence and perplexity to the standard DMFVI (although in some cases, VAE-LDA yields significantly better topics). However, AVITM is significantly faster to train than DMFVI. It takes 46 seconds on 20 Newsgroup compared to 18 minutes for DMFVI. Whereas for a million document corpus of RCV1 it only under 1.5 hours while scikit-learn’s implementation of DMFVI failed to return any results even after running for 24 hours.4
+
+Comparing the new topic models than LDA, it is clear that PRODLDA finds significantly better topics than LDA, even when trained by collapsed Gibbs sampling. To verify this qualitatively, we display examples of topics from all the models in Table 6. The topics from ProdLDA appear visually more coherent than NVDM or LDA. Unfortunately, NVDM does not perform comparatively to LDA
+
+<table><tr><td rowspan=1 colspan=1># topics</td><td rowspan=1 colspan=1>ProdLDAVAE</td><td rowspan=1 colspan=1>LDAVAE</td><td rowspan=1 colspan=1>LDADMFVI</td><td rowspan=1 colspan=1>LDACollapsed Gibbs</td><td rowspan=1 colspan=1>NVDM</td></tr><tr><td rowspan=1 colspan=1>50</td><td rowspan=1 colspan=1>0.14</td><td rowspan=1 colspan=1>0.07</td><td rowspan=1 colspan=1>-</td><td rowspan=1 colspan=1>0.04</td><td rowspan=1 colspan=1>0.07</td></tr><tr><td rowspan=1 colspan=1>200</td><td rowspan=1 colspan=1>0.12</td><td rowspan=1 colspan=1>0.05</td><td rowspan=1 colspan=1>1</td><td rowspan=1 colspan=1>0.06</td><td rowspan=1 colspan=1>0.05</td></tr></table>
+
+Table 2: Average topic coherence on the RCV1 dataset. Higher is better. Results not reported for LDA DMFVI, as inference failed to converge in 24 hours.
+
+Table 3: Perplexity scores for 20 Newsgroups. Lower is better.   
+
+<table><tr><td rowspan=1 colspan=1># topics</td><td rowspan=1 colspan=1>ProdLDAVAE</td><td rowspan=1 colspan=1>LDAVAE</td><td rowspan=1 colspan=1>LDADMFVI</td><td rowspan=1 colspan=1>LDACollapsed Gibbs</td><td rowspan=1 colspan=1>NVDM</td></tr><tr><td rowspan=1 colspan=1>50</td><td rowspan=1 colspan=1>1172</td><td rowspan=1 colspan=1>1059</td><td rowspan=1 colspan=1>1046</td><td rowspan=1 colspan=1>728</td><td rowspan=1 colspan=1>837</td></tr><tr><td rowspan=1 colspan=1>200</td><td rowspan=1 colspan=1>1168</td><td rowspan=1 colspan=1>1128</td><td rowspan=1 colspan=1>1195</td><td rowspan=1 colspan=1>688</td><td rowspan=1 colspan=1>884</td></tr></table>
+
+for any value of $k$ . To avoid any training dissimilarities we train all the competing models until we reach the perplexities that were reported in previous work. These are reported in Table $3 ^ { 5 }$ .
+
+A major benefit of AVITM inference is that it does not require running variational optimization, which can be costly, for new data. Rather, the inference network can be used to obtain topic proportions for new documents for new data points without running any optimization. We evaluate whether this approximation is accurate, i.e. whether the neural network effectively learns to mimic probabilistic inference. We verify this by training the model on the training set, then on the test set, holding the topics $\beta$ matrix) fixed, and comparing the test perplexity if we obtain topic proportions by running the inference neural network directly, or by the standard method of variational optimization of the inference network on the test set. As shown in Table 4, the perplexity remains practically un-changed. The computational benefits of this are remarkable. On both the datasets, computing perplexity using the neural network takes well under a minute, while running the standard variational approximation takes $\sim 3$ minutes even on the smaller 20 Newsgroups data. Finally, we investigate the reasons behind the improved topic coherence in PRODLDA. First, Table 5 explores the effects of each of our two main ideas separately. In this table, “Dirichlet” means that the prior is the Laplace approximation to Dirichlet $\langle \alpha = 0 . 0 2 \rangle$ , while “Gaussian” indicates that we use a standard Gaussian as prior. ‘High Learning Rate” training means we use $\beta 1 > 0 . 8$ and $0 . 1 > \eta > 0 . 0 0 1 ^ { 6 }$ with batch normalization, whereas “Low Learning Rate” means $\beta 1 > 0 . 8$ and $0 . 0 0 0 9 > \eta > 0 . 0 0 0 0 9$ without batch normalization. (For both parameters, the precise value was chosen by Bayesian optimization. We found that these values in the ”with BN” cases were close to the default settings in the Adam optimizer.) We find that the high topic coherence that we achieve in this work is only possible if we use both tricks together. In fact the high learning rates with momentum is required to avoid local minima in the beginning of the training and batch-normalization is required to be able to train the network at these values without diverging. If trained at a lower momentum value or at a lower learning rate PRODLDA shows component collapsing. Interestingly, if we choose a Gaussian prior, rather than the logistic normal approximation used in ProdLDA or NVLDA, the model is easier to train even with low learning rate without any momentum or batch normalization.
+
+The main advantage of AVITM topic models as opposed to NVDM is that the Laplace approximation allows us to match a specific Dirichlet prior of interest. As pointed out by Wallach et al. (2009), the choice of Dirichlet hyperparameter is important to the topic quality of LDA. Following this reasoning, we hypothesize that AVITM topics are higher quality than those of NVDM because they are much more focused, i.e., apply to a more specific subset of documents of interest. We provide support for this hypothesis in Figure 1, by evaluating the sparsity of the posterior proportions over topics, that is, how many of the model’s topics are typically used to explain each document. In order to estimate the sparsity in topic proportions, we project samples from the Gaussian latent spaces of PRODLDA and NVDM in the simplex and average them across documents. We compare the topic sparsity for the standard Gaussian prior used by NVDM to the Laplace approximation of Dirichlet priors with different hyperparameters. Clearly the Laplace approximation to the Dirichlet prior significantly promotes sparsity, providing support for our hypothesis that preserving the Dirichlet prior explains the the increased topic coherence in our method.
+
+Table 4: Evaluation of inference network of VAE-LDA on 20 Newsgroups test set. “Inference network only” shows the test perplexity when the inference network is trained on the training set, but no variational optimization is performed on the test set. “Inference Network $^ +$ Optimization” shows the standard approach of optimizing the ELBO on the test set. The neural network effectively learns to approximate probabilistic inference effectively.   
+
+<table><tr><td rowspan=1 colspan=1># Topics</td><td rowspan=1 colspan=1>Inference Network Only</td><td rowspan=1 colspan=1>Inference Network + Optimization</td></tr><tr><td rowspan=1 colspan=1>50</td><td rowspan=1 colspan=1>1172</td><td rowspan=1 colspan=1>1162</td></tr><tr><td rowspan=1 colspan=1>200</td><td rowspan=1 colspan=1>1168</td><td rowspan=1 colspan=1>1151</td></tr></table>
+
+![](images/b2094ca292cd2e8de3ce313104a3413e9ae589d52d53d728144ce0132732c235.jpg)  
+Figure 1: Effect of prior assumptions on $\theta$ on sparsity of $\theta$ in neural topic models.
+
+<table><tr><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>Dirichlet+High Learning Rate</td><td rowspan=1 colspan=1>Dirichlet+Low Learning Rate</td><td rowspan=1 colspan=1>GaussianPrior+High Learning Rate</td><td rowspan=1 colspan=1>GaussianPrior+Low Learning Rate</td></tr><tr><td rowspan=1 colspan=1>Topic Coherence</td><td rowspan=1 colspan=1>0.24</td><td rowspan=1 colspan=1>0.016</td><td rowspan=1 colspan=1>0.08</td><td rowspan=1 colspan=1>0.08</td></tr></table>
+
+Table 5: Average topic coherence for different choices of prior and optimization strategies of PRODLDA on 20 Newsgroup for $k = 5 0$ .
+
+The inference network architecture can be found in figure 2 in the appendix.
+
+# 7 DISCUSSION AND FUTURE WORK
+
+We present what is to our knowledge the first effective AEVB inference algorithm for latent Dirichlet allocation. Although this combination may seem simple in principle, in practice this method is difficult to train because of the Dirichlet prior and because of the component collapsing problem. By addressing both of these problems, we presented a black-box inference method for topic models with the notable advantage that the neural network allows computing topic proportions for new documents without the need to run any variational optimization. As an illustration of the advantages of
+
+Table 6: Five randomly selected topics from all the models.   
+
+<table><tr><td rowspan=1 colspan=1>Model</td><td rowspan=1 colspan=1>Topics</td></tr><tr><td rowspan=1 colspan=1>ProdLDA</td><td rowspan=1 colspan=1>motherboard meg printer quadra hd windows processor vga mhz connectorarmenian genocide turks turkish muslim massacre turkey armenians armenia greekvoltage nec outlet circuit cable wiring wire panel motor installseasonnhl teamhockeyplayoff puckleague flyersdefensiveplayerisrael israeli lebanese arab lebanon arabs civilian territory palestinian militia</td></tr><tr><td rowspan=1 colspan=1>LDANVLDA</td><td rowspan=1 colspan=1>db file output program line entry write bit int returndrive disk get card scsi use hard ide controller onegame team play win year player get think good makeuse law state health file gun public issue control firearmpeople say one think life make know god man see</td></tr><tr><td rowspan=1 colspan=1>LDADMFVI</td><td rowspan=1 colspan=1>write article dod ride right go get night dealer likegun law use drug crime government court criminal firearm controllunar flyers hitter spacecraft power us existence god go meanstephanopoulos encrypt spacecraft ripem rsa cipher saturn violate lunar cryptofile program available server version include software entry ftp use</td></tr><tr><td rowspan=1 colspan=1>LDACollapsed Gibbs</td><td rowspan=1 colspan=1>get right back light side like see take time onelist mail send post anonymous internet file information user messagethanks please know anyone help look appreciate get need emailjesus church god law say christian one christ day comebike dod ride dog motorcycle write article bmw helmet get</td></tr><tr><td rowspan=1 colspan=1>NVDM</td><td rowspan=1 colspan=1>light die burn body life inside mother tear kill christianinsurance drug different sport friend bank owner vancouver buy prayerinput package interface output tape offer component channel level modelprice quadra hockey slot san playoff jose deal market dealerchristian church gateway catholic christianity homosexual resurrection modem mouse sunday</td></tr></table>
+
+<table><tr><td>3.write article thanks anyone please like get one think look 4.article write one get like know thanks anyone try need</td><td>1. write article get thanks like anyone please know look one 2.article write one please like anyone know make want get</td></tr></table>
+
+Table 7: VAE-LDA fails to learn any meaningful topics when component collapsing occurs. The table shows five randomly sampled topics (, which are essentially slight variants of each other) from when the VAE-LDA model is trained without BN and high momentum training.
+
+black box inference techniques, we presented a new topic model, ProdLDA, which achieves significantly better topics than LDA, while requiring a change of only one line of code from AVITM for LDA. Our results suggest that AVITM inference is ready to take its place alongside mean field and collapsed Gibbs as one of the workhorse inference methods for topic models. Future work could include extending our inference methods to handle dynamic and correlated topic models.
+
+# ACKNOWLEDGMENTS
+
+We thank Andriy Mnih, Chris Dyer, Chris Russell, David Blei, Hannah Wallach, Max Welling, Mirella Lapata and Yishu Miao for helpful comments, discussions and feedback.
+
+# REFERENCES
+
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+Diederik P Kingma and Max Welling. Auto-encoding variational bayes. The International Conference on Learning Representations (ICLR), Banff, 2014.
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+Alp Kucukelbir, Dustin Tran, Rajesh Ranganath, Andrew Gelman, and David M Blei. Automatic differentiation variational inference. arXiv preprint arXiv:1603.00788, 2016.
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+Hugo Larochelle and Stanislas Lauly. A neural autoregressive topic model. In Advances in Neural Information Processing Systems, pp. 2708–2716, 2012.
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+Jey Han Lau, David Newman, and Timothy Baldwin. Machine reading tea leaves: Automatically evaluating topic coherence and topic model quality. In EACL, pp. 530–539, 2014.
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+David JC MacKay. Choice of basis for Laplace approximation. Machine learning, 33(1):77–86, 1998.
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+Andrew McCallum. Mallet: A machine learning for language toolkit. http://mallet.cs. umass.edu, 2002.
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+Yishu Miao, Lei Yu, and Phil Blunsom. Neural variational inference for text processing. pp. 1727– 1736, 2016.
+
+David Mimno. Reconstructing Pompeian households. In Applications of Topic Models Workshop, NIPS, 2009.
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+Andriy Mnih and Karol Gregor. Neural variational inference and learning in belief networks. pp. 1791–1799, 2014.
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+David Newman, Jey Han Lau, Karl Grieser, and Timothy Baldwin. Automatic evaluation of topic coherence. In Human Language Technologies: The 2010 Annual Conference of the North American Chapter of the Association for Computational Linguistics, pp. 100–108. Association for Computational Linguistics, 2010.
+
+Rajesh Ranganath, Sean Gerrish, and David M Blei. Black box variational inference. In AISTATS, pp. 814–822, 2014.
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+Danilo Jimenez Rezende, Shakir Mohamed, and Daan Wierstra. Stochastic backpropagation and approximate inference in deep generative models. pp. 1278–1286, 2014.
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+
+Hanna Wallach, David Mimno, and Andrew McCallum. Rethinking LDA: Why priors matter. In NIPS, 2009.
+
+Max Welling, Michal Rosen-Zvi, and Geoffrey E Hinton. Exponential family harmoniums with an application to information retrieval. In Advances in Neural Information Processing Systems, volume 4, pp. 1481–1488, 2004.
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+Ronald J Williams. Simple statistical gradient-following algorithms for connectionist reinforcement learning. Machine Learning, 8(3-4):229–256, 1992.
+
+A NETWORK ARCHITECTURE
+
+![](images/739c5c2afeba6028c8dc8a3876cc7e62cf223b081b151b4c71c000e9372c9a48.jpg)  
+Figure 2: Architecture of the inference network used in the experiments.

parse/train/BybtVK9lg/BybtVK9lg_content_list.json

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+    {
+        "type": "text",
+        "text": "AUTOENCODING VARIATIONAL INFERENCE FOR TOPIC MODELS ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Akash Srivastava   \nInformatics Forum, University of Edinburgh   \n10, Crichton St   \nEdinburgh, EH89AB, UK   \nakash.srivastava@ed.ac.uk   \nCharles Sutton∗   \nInformatics Forum, University of Edinburgh   \n10, Crichton St   \nEdinburgh, EH89AB, UK   \ncsutton@inf.ed.ac.uk ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            508,
+            170,
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+    },
+    {
+        "type": "text",
+        "text": "ABSTRACT ",
+        "text_level": 1,
+        "bbox": [
+            454,
+            276,
+            544,
+            291
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Topic models are one of the most popular methods for learning representations of text, but a major challenge is that any change to the topic model requires mathematically deriving a new inference algorithm. A promising approach to address this problem is autoencoding variational Bayes (AEVB), but it has proven difficult to apply to topic models in practice. We present what is to our knowledge the first effective AEVB based inference method for latent Dirichlet allocation (LDA), which we call Autoencoded Variational Inference For Topic Model (AVITM). This model tackles the problems caused for AEVB by the Dirichlet prior and by component collapsing. We find that AVITM matches traditional methods in accuracy with much better inference time. Indeed, because of the inference network, we find that it is unnecessary to pay the computational cost of running variational optimization on test data. Because AVITM is black box, it is readily applied to new topic models. As a dramatic illustration of this, we present a new topic model called ProdLDA, that replaces the mixture model in LDA with a product of experts. By changing only one line of code from LDA, we find that ProdLDA yields much more interpretable topics, even if LDA is trained via collapsed Gibbs sampling. ",
+        "bbox": [
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+            309,
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            574,
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+            589
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Topic models (Blei, 2012) are among the most widely used models for learning unsupervised representations of text, with hundreds of different model variants in the literature, and have have found applications ranging from the exploration of the scientific literature (Blei & Lafferty, 2007) to computer vision (Fei-Fei & Perona, 2005), bioinformatics (Rogers et al., 2005), and archaeology (Mimno, 2009). A major challenge in applying topic models and developing new models is the computational cost of computing the posterior distribution. Therefore a large body of work has considered approximate inference methods, the most popular methods being variational methods, especially mean field methods, and Markov chain Monte Carlo, particularly methods based on collapsed Gibbs sampling. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Both mean-field and collapsed Gibbs have the drawback that applying them to new topic models, even if there is only a small change to the modeling assumptions, requires re-deriving the inference methods, which can be mathematically arduous and time consuming, and limits the ability of practitioners to freely explore the space of different modeling assumptions. This has motivated the development of black-box inference methods (Ranganath et al., 2014; Mnih & Gregor, 2014; Kucukelbir et al., 2016; Kingma & Welling, 2014) which require only very limited and easy to compute information from the model, and hence can be applied automatically to new models given a simple declarative specification of the generative process. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Autoencoding variational Bayes (AEVB) (Kingma & Welling, 2014; Rezende et al., 2014) is a particularly natural choice for topic models, because it trains an inference network (Dayan et al., 1995), a neural network that directly maps a document to an approximate posterior distribution, without the need to run further variational updates. This is intuitively appealing because in topic models, we expect the mapping from documents to posterior distributions to be well behaved, that is, that a small change in the document will produce only a small change in topics. This is exactly the type of mapping that a universal function approximator like a neural network should be good at representing. Essentially, the inference network learns to mimic the effect of probabilistic inference, so that on test data, we can enjoy the benefits of probabilistic modeling without paying a further cost for inference. ",
+        "bbox": [
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+    {
+        "type": "text",
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+    {
+        "type": "text",
+        "text": "However, despite some notable successes for latent Gaussian models, black box inference methods are significantly more challenging to apply to topic models. For example, in initial experiments, we tried to apply ADVI (Kucukelbir et al., 2016), a recent black-box variational method, but it was difficult to obtain any meaningful topics. Two main challenges are: first, the Dirichlet prior is not a location scale family, which hinders reparameterisation, and second, the well known problem of component collapsing (Dinh & Dumoulin, 2016), in which the inference network becomes stuck in a bad local optimum in which all topics are identical. ",
+        "bbox": [
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+            208,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In this paper, we present what is, to our knowledge, the first effective AEVB inference method for topic models, which we call Autoencoded Variational Inference for Topic Models or AVITM1. On several data sets, we find that AVITM yields topics of equivalent quality to standard mean-field inference, with a large decrease in training time. We also find that the inference network learns to mimic the process of approximate inference highly accurately, so that it is not necessary to run variational optimization at all on test data. ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "But perhaps more important is that AVITM is a black-box method that is easy to apply to new models. To illustrate this, we present a new topic model, called ProdLDA, in which the distribution over individual words is a product of experts rather than the mixture model used in LDA. We find that ProdLDA consistently produces better topics than standard LDA, whether measured by automatically determined topic coherence or qualitative examination. Furthermore, because we perform probabilistic inference using a neural network, we can fit a topic model on roughly a one million documents in under 80 minutes on a single GPU, and because we are using a black box inference method, implementing ProdLDA requires a change of only one line of code from our implementation of standard LDA. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "To summarize, the main advantages of our methods are: ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "1. Topic coherence: ProdLDA returns consistently better topics than LDA, even when LDA is trained using Gibbs sampling.   \n2. Computational efficiency: Training AVITM is fast and efficient like standard mean-field. On new data, AVITM is much faster than standard mean field, because it requires only one forward pass through a neural network.   \n3. Black box: AVITM does not require rigorous mathematical derivations to handle changes in the model, and can be easily applied to a wide range of topic models. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Overall, our results suggest that AVITM is ready to take its place alongside mean field and collapsed Gibbs as one of the workhorse inference methods for topic models. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "2 BACKGROUND ",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "To fix notation, we begin by describing topic modelling and AVITM. ",
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+        "type": "text",
+        "text": "2.1 LATENT DIRICHLET ALLOCATION ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We describe the most popular topic model, latent Dirichlet allocation (LDA). In LDA, each document of the collection is represented as a mixture of topics, where each topic $\\beta _ { k }$ is a probability distribution over the vocabulary. We also use $\\beta$ to denote the matrix $\\beta = \\left( \\beta _ { 1 } \\ldots \\beta _ { K } \\right)$ . The generative process is then as described in Algorithm 1. Under this generative model, the marginal likelihood of ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "for each document w do Draw topic distribution $\\theta \\sim$ Dirichlet $( \\alpha )$ ; for each word at position $n$ do Sample topic $z _ { n } \\sim$ Multinomial $( 1 , \\theta )$ ; Sample word $w _ { n } \\sim$ Multinomia $( 1 , \\beta _ { z _ { n } } )$ ; end   \nend ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Algorithm 1: LDA as a generative model. ",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "a document w is ",
+        "bbox": [
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+    },
+    {
+        "type": "equation",
+        "img_path": "images/62a74e2e60b6d4d79d2c8f512d79244fc6cc959970f6623a85024f65746023e1.jpg",
+        "text": "$$\np ( \\mathbf { w } | \\alpha , \\beta ) = \\int _ { \\boldsymbol { \\theta } } \\left( \\prod _ { n = 1 } ^ { N } \\sum _ { z _ { n } = 1 } ^ { k } p ( w _ { n } | z _ { n } , \\beta ) p ( z _ { n } | \\boldsymbol { \\theta } ) \\right) p ( \\boldsymbol { \\theta } | \\alpha ) d \\boldsymbol { \\theta } .\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "Posterior inference over the hidden variables $\\theta$ and $z$ is intractable due to the coupling between the $\\theta$ and $\\beta$ under the multinomial assumption (Dickey, 1983). ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "2.2 MEAN FIELD AND AEVB ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "A popular approximation for efficient inference in topic models is mean field variational inference, which breaks the coupling between $\\theta$ and $z$ by introducing free variational parameters $\\gamma$ over $\\theta$ and $\\phi$ over $z$ and dropping the edges between them. This results in an approximate variational posterior $\\begin{array} { r } { q ( \\theta , z | \\gamma , \\phi ) \\stackrel { \\_ } { = } q _ { \\gamma } \\bar { ( \\theta ) } \\prod _ { n } \\bar { q _ { \\phi } } ( z _ { n } ) } \\end{array}$ , which is optimized to best approximate the true posterior $p ( \\boldsymbol { \\theta } , z | \\mathbf { w } , \\alpha , \\beta )$ . The optimization problem is to minimize ",
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+    },
+    {
+        "type": "equation",
+        "img_path": "images/cf22b77c6caa001ab7a3a88872abc28b507750a42cb5d4b17d985ef086d69cb7.jpg",
+        "text": "$$\n\\begin{array} { r } { L ( \\gamma , \\phi \\mid \\alpha , \\beta ) = D _ { K L } \\left[ q ( \\theta , z \\vert \\gamma , \\phi ) \\vert \\vert p ( \\theta , z \\vert \\mathbf { w } , \\alpha , \\beta ) \\right] - \\log p ( \\mathbf { w } \\vert \\alpha , \\beta ) . } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In fact the above equation is a lower bound to the marginal log likelihood, sometimes called an evidence lower bound $( E L B O )$ , a fact which can be easily verified by multiplying and dividing (1) by the variational posterior and then applying Jensen’s inequality on its logarithm. Note that the mean field method optimizes over an independent set of variational parameters for each document. To emphasize this, we will refer to this standard method by the non-standard name of Decoupled Mean-Field Variational Inference (DMFVI). ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "For LDA, this optimization has closed form coordinate descent equations due to the conjugacy between the Dirichlet and multinomial distributions. Although this is a computationally convenient aspect of DMFVI, it also limits its flexibility. Applying DMFVI to new models relies on the practitioner’s ability to derive the closed form updates, which can be impractical and sometimes impossible. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "AEVB (Kingma & Welling, 2014; Rezende et al., 2014) is one of several recent methods that aims at “black box” inference methods to sidestep this issue. First, rewrite the ELBO as ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/27e406dfae7c9013aa7a680260f1aaac40ca4ff80858f7b095d08fc0495f5ec9.jpg",
+        "text": "$$\nL ( \\gamma , \\phi \\mid \\alpha , \\beta ) = - D _ { K L } \\left[ q ( \\theta , z | \\gamma , \\phi ) | | p ( \\theta , z | \\alpha ) \\right] + \\mathbb { E } _ { q ( \\theta , z | \\gamma , \\phi ) } [ \\log p ( \\mathbf { w } | z , \\theta , \\alpha , \\beta ) ]\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "This form is intuitive. The first term attempts to match the variational posterior over latent variables to the prior on the latent variables, while the second term ensures that the variational posterior favors values of the latent variables that are good at explaining the data. By analogy to autoencoders, this second term is referred to as a reconstruction term. ",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "What makes this method “Autoencoding,” and in fact the main difference from DMFVI, is the parameterization of the variational distribution. In AEVB, the variational parameters are computed by using a neural network called an inference network that takes the observed data as input. For example, if the model prior $p ( \\theta )$ were Gaussian, we might define the inference network as a feedforward neural network $( \\mu ( \\mathbf { w } ) , \\mathbf { v } ( \\mathbf { w } ) ) = f ( \\mathbf { w } , \\gamma )$ , where $\\mu ( \\mathbf { w } )$ and $\\mathbf { v } ( \\mathbf { w } )$ are both vectors of length $k$ , and $\\gamma$ are the network’s parameters. Then we might choose a Gaussian variational distribution $q _ { \\gamma } ( \\theta ) = N ( \\theta ; \\mu ( \\mathbf { w } ) , \\mathrm { d i a g } ( \\bar { \\mathbf { v } ( \\mathbf { w } ) } ) )$ , where $\\mathrm { d i a g ( \\cdot \\cdot \\cdot ) }$ produces a diagonal matrix from a column vector. The variational parameters $\\gamma$ can then be chosen by optimizing the ELBO (3). Note that we have now, unlike DMFVI, coupled the variational parameters for different documents because they are all computed from the same neural network. To compute the expectations with respect to $q$ in (3), Kingma & Welling (2014); Rezende et al. (2014) use a Monte Carlo estimator which they call the “reparameterization trick” (RT; appears also in Williams (1992)). In the RT, we define a variate $U$ with a simple distribution that is independent of all variational parameters, like a uniform or standard normal, and a reparameterization function $F$ such that $F ( U , \\gamma )$ has distribution $q _ { \\gamma }$ . This is always possible, as we could choose $F$ to be the inverse cumulative distribution function of $q _ { \\gamma }$ , although we will additionally want $F$ to be easy to compute and differentiable. If we can determine a suitable $F$ , then we can approximate (3) by taking Monte Carlo samples of $U$ , and optimize $\\gamma$ using stochastic gradient descent. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3 AUTOENCODING VARIATIONAL BAYES IN LATENT DIRICHLET ALLOCATION ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Although simple conceptually, applying AEVB to topic models raises several practical challenges. The first is the need to determine a reparameterization function for $q ( \\theta )$ and $q ( z _ { n } )$ to use the RT. The $z _ { n }$ are easily dealt with, but $\\theta$ is more difficult; if we choose $q ( \\theta )$ to be Dirichlet, it is difficult to apply the RT, whereas if we choose $q$ to be Gaussian or logistic normal, then the KL divergence in (3) becomes more problematic. The second issue is the well known problem of component collapsing (Dinh & Dumoulin, 2016), which a type of bad local optimum that is particularly endemic to AEVB and similar methods. We describe our solutions to each of those problems in the next few subsections. ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.1 COLLAPSING z’S ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Dealing with discrete variables like $\\mathbf { z }$ using reparameterization can be problematic, but fortunately in LDA the variable $\\mathbf { z }$ can be conveniently summed out. By collapsing $\\mathbf { z }$ we are left with having to sample from $\\theta$ only, reducing (1) to ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/cdb64b776252e4c0dbe9747c33bbd26d6dd89835bfea59a1060c4438c7e90214.jpg",
+        "text": "$$\np ( \\mathbf { w } | \\alpha , \\beta ) = \\int _ { \\theta } \\left( \\prod _ { n = 1 } ^ { N } p ( w _ { n } | \\beta , \\theta ) \\right) p ( \\theta | \\alpha ) d \\theta .\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where the distribution of $w _ { n } | \\beta , \\theta$ is Multinomial(1, $\\beta \\theta ,$ ), recalling that $\\beta$ denotes the matrix of all topic-word probability vectors. ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.2 WORKING WITH DIRICHLET BELIEFS: LAPLACE APPROXIMATION ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "LDA gets its name from the Dirichlet prior on the topic proportions $\\theta$ , and the choice of Dirichlet prior is important to obtaining interpretable topics (Wallach et al., 2009). But it is difficult to handle the Dirichlet within AEVB because it is difficult to develop an effective reparameterization function for the RT. Fortunately, a RT does exist for the Gaussian distribution and has been shown to perform quite well in the context of variational autoencoder (VAE) (Kingma & Welling, 2014). ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We resolve this issue by constructing a Laplace approximation to the Dirichlet prior. Following MacKay (1998), we do so in the softmax basis instead of the simplex. There are two benefits of this choice. First, Dirichlet distributions are unimodal in the softmax basis with their modes coinciding with the means of the transformed densities. Second, the softmax basis also allows for carrying out unconstrained optimization of the cost function without the simplex constraints. The Dirichlet probability density function in this basis over the softmax variable $\\mathbf { h }$ is given by ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/8a99ac3aa617bd8f498a65960710a13a64ff1bae248d3877f646c5d4e2bb514f.jpg",
+        "text": "$$\nP ( \\theta ( \\mathbf { h } ) | \\alpha ) = \\frac { \\Gamma ( \\sum _ { k } \\alpha _ { k } ) } { \\prod _ { k } \\Gamma ( \\alpha _ { k } ) } \\prod _ { k } \\theta _ { k } ^ { \\alpha _ { k } } g ( \\mathbf { 1 } ^ { T } \\mathbf { h } ) .\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Here $\\theta = \\sigma ( { \\bf h } )$ , where $\\sigma ( . )$ represents the softmax function. Recall that the Jacobian of $\\sigma$ is proportional to $\\textstyle \\prod _ { k } \\theta _ { k }$ and $g ( \\cdot )$ is an arbitrary density that ensures integrability by constraining the redundant degree of freedom. We use the Laplace approximation of Hennig et al. (2012), which ",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "has the property that the covariance matrix becomes diagonal for large $k$ (number of topics). This approximation to the Dirichlet prior $p ( \\theta | \\alpha )$ is results in the distribution over the softmax variables h as a multivariate normal with mean $\\mu _ { 1 }$ and covariance matrix $\\Sigma _ { 1 }$ where ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/884bf7a81b00b2e1e0d1f408b65164ecf64d04d823c3f3964eb8a724b7781bc3.jpg",
+        "text": "$$\n\\begin{array} { c l } { \\displaystyle \\mu _ { 1 k } = \\log \\alpha _ { k } - \\frac 1 K \\sum _ { i } \\log \\alpha _ { i } } \\\\ { \\displaystyle \\sum _ { 1 k k } = \\frac 1 { \\alpha _ { k } } \\left( 1 - \\frac 2 K \\right) + \\frac 1 { K ^ { 2 } } \\sum _ { i } \\frac 1 { \\alpha _ { k } } . } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
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+            152,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Finally, we approximate $p ( \\theta | \\alpha )$ in the simplex basis with $\\hat { p } ( \\theta | \\mu _ { 1 } , \\Sigma _ { 1 } ) = \\mathcal { L N } ( \\theta | \\mu _ { 1 } , \\Sigma _ { 1 } )$ where $\\mathcal { L N }$ is a logistic normal distribution with parameters $\\mu _ { 1 } , \\Sigma _ { 1 }$ . Although we approximate the Dirichlet prior in LDA with a logistic normal, this is not the same idea as a correlated topic model (Blei & Lafferty, 2006), because we use a diagonal covariance matrix. Rather, it is an approximation to standard LDA. ",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.3 VARIATIONAL OBJECTIVE ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Now we can write the modified variational objective function. We use a logistic normal variational distribution over $\\theta$ with diagonal covariance. More precisely, we define two inference networks as feed forward neural networks $f _ { \\mu }$ and $f _ { \\Sigma }$ with parameters $\\delta$ ; the output of each network is a vector in $\\mathbb { R } ^ { K }$ . Then for a document w, we define $q ( \\theta )$ to be logistic normal with mean $\\mu _ { 0 } = f _ { \\mu } ( \\mathbf { w } , \\pmb \\delta )$ and diagonal covariance $\\pmb { \\Sigma } _ { 0 } = \\mathrm { d i a g } ( f _ { \\Sigma } ( \\mathbf { w } , \\pmb { \\delta } ) )$ , where diag converts a column vector to a diagonal matrix. Note that we can generate samples from $q ( \\theta )$ by sampling $\\epsilon \\sim \\mathcal { N } ( 0 , I )$ and computing $\\theta = \\sigma ( \\pmb { \\mu } _ { 0 } + \\pmb { \\Sigma } _ { 0 } ^ { 1 / 2 } \\pmb { \\epsilon } ) .$ . ",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We can now write the ELBO as ",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/911fb0c748f01e2c6655956acdfd19eb8f0d8d96319048eba29a0f859178078d.jpg",
+        "text": "$$\n\\begin{array} { r } { L ( \\boldsymbol { \\Theta } ) = \\displaystyle \\sum _ { d = 1 } ^ { D } \\Bigg [ - \\left( \\frac { 1 } { 2 } \\Big \\{ t r ( \\boldsymbol { \\Sigma } _ { 1 } ^ { - 1 } \\boldsymbol { \\Sigma } _ { 0 } ) + ( \\boldsymbol { \\mu } _ { 1 } - \\boldsymbol { \\mu } _ { 0 } ) ^ { T } \\boldsymbol { \\Sigma } _ { 1 } ^ { - 1 } ( \\boldsymbol { \\mu } _ { 1 } - \\boldsymbol { \\mu } _ { 0 } ) - K + \\log \\frac { | \\boldsymbol { \\Sigma } _ { 1 } | } { | \\boldsymbol { \\Sigma } _ { 0 } | } \\Big \\} \\right) } \\\\ { + \\mathbb { E } _ { \\epsilon \\sim \\mathcal { N } ( 0 , I ) } \\Bigg [ \\mathbf { w } _ { d } ^ { \\top } \\log \\Big ( \\sigma ( \\boldsymbol { \\beta } ) \\sigma ( \\boldsymbol { \\mu } _ { 0 } + \\boldsymbol { \\Sigma } _ { 0 } ^ { 1 / 2 } \\boldsymbol { \\epsilon } ) \\Big ) \\Bigg ] \\Bigg ] , } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            220,
+            484,
+            777,
+            573
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where $\\Theta$ represents the set of all the model and variational parameters and $\\mathbf { w } _ { 1 } \\ldots \\mathbf { w } _ { D }$ are the documents in the corpus. The first line in this equation arises from the KL divergence between the two logistic normal distributions $q$ and $\\hat { p }$ , while the second line is the reconstruction error. ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "In order to impose the simplex constraint on the $\\beta$ matrix during the optimization, we apply the softmax transformation. That is, each topic $\\beta _ { k } \\in \\mathbb { R } ^ { V }$ is unconstrained, and the notation $\\sigma ( \\beta )$ means to apply the softmax function separately to each column of the matrix $\\beta$ . Note that the mixture of multinomials for each word $w _ { n }$ can then be written as $p ( w _ { n } | \\beta , \\theta ) = [ \\sigma ( \\beta ) \\theta ] _ { w _ { n } }$ , which explains the ndot product in (7). To optimize (7), we use stochastic gradient descent using Monte Carlo samples from \u000f, following the Law of the Unconscious Statistician. ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.4 TRAINING AND PRACTICAL CONSIDERATIONS: DEALING WITH COMPONENT COLLAPSING ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "AEVB is prone to component collapsing (Dinh & Dumoulin, 2016), which is a particular type of local optimum very close to the prior belief, early on in the training. As the latent dimensionality of the model is increased, the KL regularization in the variational objective dominates, so that the outgoing decoder weights collapse for the components of the latent variable that reach close to the prior and do not show any posterior divergence. In our case, the collapsing specifically occurs because of the inclusion of the softmax transformation to produce $\\theta$ . The result is that the $k$ inferred topics are identical as shown in table 7. ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We were able to resolve this issue by tweaking the optimization. Specifically, we train the network with the ADAM optimizer (Kingma & Ba, 2015) using high moment weight $( \\beta 1 )$ and learning rate $( \\eta )$ . Through training at higher rates, early peaks in the functional space can be easily avoided. The problem is that momentum based training coupled with higher learning rate causes the optimizer to diverge. While explicit gradient clipping helps to a certain extent, we found that batch normalization (Ioffe & Szegedy, 2015) does even better by smoothing out the functional space and hence curbing sudden divergence. ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Finally, we also found an increase in performance with dropout units when applied to $\\theta$ to force the network to use more of its capacity. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "While more prominent in the AEVB framework, the collapsing can also occurs in DMFVI if the learning offset (referred to as the $\\tau$ parameter (Hofmann, 1999)) is not set properly. Interestingly, a similar learning offset or annealing based approach can also be used to down-weight the KL term in early iterations of the training to avoid local optima. ",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4 PRODLDA: LATENT DIRICHLET ALLOCATION WITH PRODUCTS OF EXPERTS ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "In LDA, the distribution $p ( \\mathbf { w } | \\theta , \\beta )$ is a mixture of multinomials. A problem with this assumption is that it can never make any predictions that are sharper than the components that are being mixed (Hinton & Salakhutdinov, 2009). This can result in some topics appearing that are poor quality and do not correspond well with human judgment. One way to resolve this issue is to replace this word-level mixture with a weighted product of experts which by definition is capable of making sharper predictions than any of the constituent experts (Hinton, 2002). In this section we present a novel topic model PRODLDA that replaces the mixture assumption at the word-level in LDA with a weighted product of experts, resulting in a drastic improvement in topic coherence. This is a good illustration of the benefits of a black box inference method, like AVITM, to allow exploration of new models. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.1 MODEL ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "The PRODLDA model can be simply described as latent Dirichlet allocation where the word-level mixture over topics is carried out in natural parameter space, i.e. the topic matrix is not constrained to exist in a multinomial simplex prior to mixing. In other words, the only changes from LDA are that $\\beta$ is unnormalized, and that the conditional distribution of $w _ { n }$ is defined as $w _ { n } | \\beta , \\theta \\ \\sim$ Multinomia $( 1 , \\sigma ( \\beta \\theta ) )$ . ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "The connection to a product of experts is straightforward, as for the multinomial, a mixture of natural parameters corresponds to a weighted geometric average of the mean parameters. That is, consider two $N$ dimensional multinomials parametrized by mean vectors $\\mathbf { p }$ and $\\mathbf { q }$ . Define the corresponding natural parameters as $\\mathbf { p } = \\sigma ( \\pmb { r } )$ and $\\mathbf { q } = \\sigma ( \\pmb { \\mathscr { s } } )$ , and let $\\delta \\in [ 0 , 1 ]$ . It is then easy to show that ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "img_path": "images/bc79e27465f523217704db7c38625437154c97ebe632d4c497b66cf51b0a0213.jpg",
+        "text": "$$\nP \\Big ( \\mathbf { x } | \\delta r + ( 1 - \\delta ) \\pmb { s } \\Big ) \\propto \\prod _ { i = 1 } ^ { N } \\sigma ( \\delta r _ { i } + ( 1 - \\delta ) s _ { i } ) ^ { x _ { i } } \\propto \\prod _ { i = 1 } ^ { N } [ r _ { i } ^ { \\delta } \\cdot s _ { i } ^ { ( 1 - \\delta ) } ] ^ { x _ { i } } .\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "So the PRODLDA model can be simply described as a product of experts, that is, $p ( w _ { n } | \\theta , \\beta ) \\ \\propto$ $\\begin{array} { r } { \\prod _ { k } p ( w _ { n } | z _ { n } = k , \\beta ) ^ { \\theta _ { k } } } \\end{array}$ . PRODLDA is an instance of the exponential-family PCA (Collins et al., 2001) class, and relates to the exponential-family harmoniums (Welling et al., 2004) but with nonGaussian priors. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5 RELATED WORK ",
+        "text_level": 1,
+        "bbox": [
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+            773,
+            344,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "For an overview of topic modeling, see Blei (2012). There are several examples of topic models based on neural networks and neural variational inference (Hinton & Salakhutdinov, 2009; Larochelle & Lauly, 2012; Mnih & Gregor, 2014; Miao et al., 2016) but we are unaware of methods that apply AEVB generically to a topic model specified by an analyst, or even of a successful application of AEVB to the most widely used topic model, latent Dirichlet allocation. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Recently, Miao et al. (2016) introduced a closely related model called the Neural Variational Document Model (NVDM). This method uses a latent Gaussian distribution over topics, like probabilistic latent semantic indexing, and averages over topic-word distributions in the logit space. However, they do not use either of the two key aspects of our work: explicitly approximating the Dirichlet prior using a Gaussian, or high-momentum training. In the experiments we show that these aspects lead to much improved training and much better topics. ",
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+    {
+        "type": "text",
+        "text": "6 EXPERIMENTS AND RESULTS ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Qualitative evaluation of topic models is a challenging task and consequently a large body of work has developed automatic evaluation metrics that attempt to match human judgment of topic quality. Traditionally, perplexity has been used to measure the goodness-of-fit of the model but it has been repeatedly shown that perplexity is not a good metric for qualitative evaluation of topics (Newman et al., 2010). Several new metrics of topic coherence evaluation have thus been proposed; see Lau et al. (2014) for a comparative review. Lau et al. (2014) showed that among all the competing metrics, normalized pointwise mutual information (NPMI) between all the pairs of words in a set of topics matches human judgment most closely, so we adopt it in this work. We also report perplexity, primarily as a way of evaluating the capability of different optimizers. Following standard practice (Blei et al., 2003), for variational methods we use the ELBO to calculate perplexity. For AEVB methods, we calculate the ELBO using the same Monte Carlo approximation as for training. ",
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+    {
+        "type": "text",
+        "text": "We run experiments on both the 20 Newsgroups (11,000 training instances with 2000 word vocabulary) and RCV1 Volume 2 ( 800K training instances with 10000 word vocabulary) datasets. Our preprocessing involves tokenization, removal of some non UTF-8 characters for 20 Newsgroups and English stop word removal. We first compare our AVITM inference method with the standard online mean-field variational inference (Hoffman et al., 2010) and collapsed Gibbs sampling (Griffiths & Steyvers, 2004) on the LDA model. We use standard implementations of both methods, scikit-learn for DMFVI and mallet (McCallum, 2002) for collapsed Gibbs. Then we compare two autoencoding inference methods on three different topic models: standard LDA, PRODLDA using our inference method and the Neural Variational Document Model (NVDM) (Miao et al., 2016), using the inference described in the paper.2 ",
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+        "table_caption": [
+            "Table 1: Average topic coherence on the 20 Newsgroups dataset. Higher is better. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=1 colspan=1># topics</td><td rowspan=1 colspan=1>ProdLDAVAE</td><td rowspan=1 colspan=1>LDAVAE</td><td rowspan=1 colspan=1>LDADMFVI</td><td rowspan=1 colspan=1>LDACollapsed Gibbs</td><td rowspan=1 colspan=1>NVDM</td></tr><tr><td rowspan=1 colspan=1>50</td><td rowspan=1 colspan=1>0.24</td><td rowspan=1 colspan=1>0.11</td><td rowspan=1 colspan=1>0.11</td><td rowspan=1 colspan=1>0.17</td><td rowspan=1 colspan=1>0.08</td></tr><tr><td rowspan=1 colspan=1>200</td><td rowspan=1 colspan=1>0.19</td><td rowspan=1 colspan=1>0.11</td><td rowspan=1 colspan=1>0.06</td><td rowspan=1 colspan=1>0.14</td><td rowspan=1 colspan=1>0.06</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Tables 1 and 2 show the average topic coherence values for all the models for two different settings of $k$ , the number of topics. Comparing the different inference methods for LDA, we find that, consistent with previous work, collapsed Gibbs sampling yields better topics than mean-field methods. Among the variational methods, we find that VAE-LDA model (AVITM) 3 yields similar topic coherence and perplexity to the standard DMFVI (although in some cases, VAE-LDA yields significantly better topics). However, AVITM is significantly faster to train than DMFVI. It takes 46 seconds on 20 Newsgroup compared to 18 minutes for DMFVI. Whereas for a million document corpus of RCV1 it only under 1.5 hours while scikit-learn’s implementation of DMFVI failed to return any results even after running for 24 hours.4 ",
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+        "type": "text",
+        "text": "Comparing the new topic models than LDA, it is clear that PRODLDA finds significantly better topics than LDA, even when trained by collapsed Gibbs sampling. To verify this qualitatively, we display examples of topics from all the models in Table 6. The topics from ProdLDA appear visually more coherent than NVDM or LDA. Unfortunately, NVDM does not perform comparatively to LDA ",
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+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=1 colspan=1># topics</td><td rowspan=1 colspan=1>ProdLDAVAE</td><td rowspan=1 colspan=1>LDAVAE</td><td rowspan=1 colspan=1>LDADMFVI</td><td rowspan=1 colspan=1>LDACollapsed Gibbs</td><td rowspan=1 colspan=1>NVDM</td></tr><tr><td rowspan=1 colspan=1>50</td><td rowspan=1 colspan=1>0.14</td><td rowspan=1 colspan=1>0.07</td><td rowspan=1 colspan=1>-</td><td rowspan=1 colspan=1>0.04</td><td rowspan=1 colspan=1>0.07</td></tr><tr><td rowspan=1 colspan=1>200</td><td rowspan=1 colspan=1>0.12</td><td rowspan=1 colspan=1>0.05</td><td rowspan=1 colspan=1>1</td><td rowspan=1 colspan=1>0.06</td><td rowspan=1 colspan=1>0.05</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Table 2: Average topic coherence on the RCV1 dataset. Higher is better. Results not reported for LDA DMFVI, as inference failed to converge in 24 hours. ",
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+        "table_caption": [
+            "Table 3: Perplexity scores for 20 Newsgroups. Lower is better. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=1 colspan=1># topics</td><td rowspan=1 colspan=1>ProdLDAVAE</td><td rowspan=1 colspan=1>LDAVAE</td><td rowspan=1 colspan=1>LDADMFVI</td><td rowspan=1 colspan=1>LDACollapsed Gibbs</td><td rowspan=1 colspan=1>NVDM</td></tr><tr><td rowspan=1 colspan=1>50</td><td rowspan=1 colspan=1>1172</td><td rowspan=1 colspan=1>1059</td><td rowspan=1 colspan=1>1046</td><td rowspan=1 colspan=1>728</td><td rowspan=1 colspan=1>837</td></tr><tr><td rowspan=1 colspan=1>200</td><td rowspan=1 colspan=1>1168</td><td rowspan=1 colspan=1>1128</td><td rowspan=1 colspan=1>1195</td><td rowspan=1 colspan=1>688</td><td rowspan=1 colspan=1>884</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "for any value of $k$ . To avoid any training dissimilarities we train all the competing models until we reach the perplexities that were reported in previous work. These are reported in Table $3 ^ { 5 }$ . ",
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+    {
+        "type": "text",
+        "text": "A major benefit of AVITM inference is that it does not require running variational optimization, which can be costly, for new data. Rather, the inference network can be used to obtain topic proportions for new documents for new data points without running any optimization. We evaluate whether this approximation is accurate, i.e. whether the neural network effectively learns to mimic probabilistic inference. We verify this by training the model on the training set, then on the test set, holding the topics $\\beta$ matrix) fixed, and comparing the test perplexity if we obtain topic proportions by running the inference neural network directly, or by the standard method of variational optimization of the inference network on the test set. As shown in Table 4, the perplexity remains practically un-changed. The computational benefits of this are remarkable. On both the datasets, computing perplexity using the neural network takes well under a minute, while running the standard variational approximation takes $\\sim 3$ minutes even on the smaller 20 Newsgroups data. Finally, we investigate the reasons behind the improved topic coherence in PRODLDA. First, Table 5 explores the effects of each of our two main ideas separately. In this table, “Dirichlet” means that the prior is the Laplace approximation to Dirichlet $\\langle \\alpha = 0 . 0 2 \\rangle$ , while “Gaussian” indicates that we use a standard Gaussian as prior. ‘High Learning Rate” training means we use $\\beta 1 > 0 . 8$ and $0 . 1 > \\eta > 0 . 0 0 1 ^ { 6 }$ with batch normalization, whereas “Low Learning Rate” means $\\beta 1 > 0 . 8$ and $0 . 0 0 0 9 > \\eta > 0 . 0 0 0 0 9$ without batch normalization. (For both parameters, the precise value was chosen by Bayesian optimization. We found that these values in the ”with BN” cases were close to the default settings in the Adam optimizer.) We find that the high topic coherence that we achieve in this work is only possible if we use both tricks together. In fact the high learning rates with momentum is required to avoid local minima in the beginning of the training and batch-normalization is required to be able to train the network at these values without diverging. If trained at a lower momentum value or at a lower learning rate PRODLDA shows component collapsing. Interestingly, if we choose a Gaussian prior, rather than the logistic normal approximation used in ProdLDA or NVLDA, the model is easier to train even with low learning rate without any momentum or batch normalization. ",
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+    {
+        "type": "text",
+        "text": "The main advantage of AVITM topic models as opposed to NVDM is that the Laplace approximation allows us to match a specific Dirichlet prior of interest. As pointed out by Wallach et al. (2009), the choice of Dirichlet hyperparameter is important to the topic quality of LDA. Following this reasoning, we hypothesize that AVITM topics are higher quality than those of NVDM because they are much more focused, i.e., apply to a more specific subset of documents of interest. We provide support for this hypothesis in Figure 1, by evaluating the sparsity of the posterior proportions over topics, that is, how many of the model’s topics are typically used to explain each document. In order to estimate the sparsity in topic proportions, we project samples from the Gaussian latent spaces of PRODLDA and NVDM in the simplex and average them across documents. We compare the topic sparsity for the standard Gaussian prior used by NVDM to the Laplace approximation of Dirichlet priors with different hyperparameters. Clearly the Laplace approximation to the Dirichlet prior significantly promotes sparsity, providing support for our hypothesis that preserving the Dirichlet prior explains the the increased topic coherence in our method. ",
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+    {
+        "type": "table",
+        "img_path": "images/97d085c8a657535e8bc3d321cc3af25fe230dc71f14cab75c66472fc35dae9e8.jpg",
+        "table_caption": [
+            "Table 4: Evaluation of inference network of VAE-LDA on 20 Newsgroups test set. “Inference network only” shows the test perplexity when the inference network is trained on the training set, but no variational optimization is performed on the test set. “Inference Network $^ +$ Optimization” shows the standard approach of optimizing the ELBO on the test set. The neural network effectively learns to approximate probabilistic inference effectively. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=1 colspan=1># Topics</td><td rowspan=1 colspan=1>Inference Network Only</td><td rowspan=1 colspan=1>Inference Network + Optimization</td></tr><tr><td rowspan=1 colspan=1>50</td><td rowspan=1 colspan=1>1172</td><td rowspan=1 colspan=1>1162</td></tr><tr><td rowspan=1 colspan=1>200</td><td rowspan=1 colspan=1>1168</td><td rowspan=1 colspan=1>1151</td></tr></table>",
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+        "type": "text",
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+        "page_idx": 8
+    },
+    {
+        "type": "image",
+        "img_path": "images/b2094ca292cd2e8de3ce313104a3413e9ae589d52d53d728144ce0132732c235.jpg",
+        "image_caption": [
+            "Figure 1: Effect of prior assumptions on $\\theta$ on sparsity of $\\theta$ in neural topic models. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
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+        "img_path": "images/588b9bae662bacd8432f36c12f5b2fe78236165827b08830d0cd5411350801fb.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>Dirichlet+High Learning Rate</td><td rowspan=1 colspan=1>Dirichlet+Low Learning Rate</td><td rowspan=1 colspan=1>GaussianPrior+High Learning Rate</td><td rowspan=1 colspan=1>GaussianPrior+Low Learning Rate</td></tr><tr><td rowspan=1 colspan=1>Topic Coherence</td><td rowspan=1 colspan=1>0.24</td><td rowspan=1 colspan=1>0.016</td><td rowspan=1 colspan=1>0.08</td><td rowspan=1 colspan=1>0.08</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Table 5: Average topic coherence for different choices of prior and optimization strategies of PRODLDA on 20 Newsgroup for $k = 5 0$ . ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The inference network architecture can be found in figure 2 in the appendix. ",
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+    {
+        "type": "text",
+        "text": "7 DISCUSSION AND FUTURE WORK ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "We present what is to our knowledge the first effective AEVB inference algorithm for latent Dirichlet allocation. Although this combination may seem simple in principle, in practice this method is difficult to train because of the Dirichlet prior and because of the component collapsing problem. By addressing both of these problems, we presented a black-box inference method for topic models with the notable advantage that the neural network allows computing topic proportions for new documents without the need to run any variational optimization. As an illustration of the advantages of ",
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+        "type": "table",
+        "img_path": "images/0b564eed7a07777407715679da29f016aefb0b4c06830e989bfdd20b645ed04c.jpg",
+        "table_caption": [
+            "Table 6: Five randomly selected topics from all the models. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=1 colspan=1>Model</td><td rowspan=1 colspan=1>Topics</td></tr><tr><td rowspan=1 colspan=1>ProdLDA</td><td rowspan=1 colspan=1>motherboard meg printer quadra hd windows processor vga mhz connectorarmenian genocide turks turkish muslim massacre turkey armenians armenia greekvoltage nec outlet circuit cable wiring wire panel motor installseasonnhl teamhockeyplayoff puckleague flyersdefensiveplayerisrael israeli lebanese arab lebanon arabs civilian territory palestinian militia</td></tr><tr><td rowspan=1 colspan=1>LDANVLDA</td><td rowspan=1 colspan=1>db file output program line entry write bit int returndrive disk get card scsi use hard ide controller onegame team play win year player get think good makeuse law state health file gun public issue control firearmpeople say one think life make know god man see</td></tr><tr><td rowspan=1 colspan=1>LDADMFVI</td><td rowspan=1 colspan=1>write article dod ride right go get night dealer likegun law use drug crime government court criminal firearm controllunar flyers hitter spacecraft power us existence god go meanstephanopoulos encrypt spacecraft ripem rsa cipher saturn violate lunar cryptofile program available server version include software entry ftp use</td></tr><tr><td rowspan=1 colspan=1>LDACollapsed Gibbs</td><td rowspan=1 colspan=1>get right back light side like see take time onelist mail send post anonymous internet file information user messagethanks please know anyone help look appreciate get need emailjesus church god law say christian one christ day comebike dod ride dog motorcycle write article bmw helmet get</td></tr><tr><td rowspan=1 colspan=1>NVDM</td><td rowspan=1 colspan=1>light die burn body life inside mother tear kill christianinsurance drug different sport friend bank owner vancouver buy prayerinput package interface output tape offer component channel level modelprice quadra hockey slot san playoff jose deal market dealerchristian church gateway catholic christianity homosexual resurrection modem mouse sunday</td></tr></table>",
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+    {
+        "type": "table",
+        "img_path": "images/781acdad733b25822288b765e852c08b0b23d7bbc25e1ee51a3d0906e234ade5.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>3.write article thanks anyone please like get one think look 4.article write one get like know thanks anyone try need</td><td>1. write article get thanks like anyone please know look one 2.article write one please like anyone know make want get</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Table 7: VAE-LDA fails to learn any meaningful topics when component collapsing occurs. The table shows five randomly sampled topics (, which are essentially slight variants of each other) from when the VAE-LDA model is trained without BN and high momentum training. ",
+        "bbox": [
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+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "black box inference techniques, we presented a new topic model, ProdLDA, which achieves significantly better topics than LDA, while requiring a change of only one line of code from AVITM for LDA. Our results suggest that AVITM inference is ready to take its place alongside mean field and collapsed Gibbs as one of the workhorse inference methods for topic models. Future work could include extending our inference methods to handle dynamic and correlated topic models. ",
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+    {
+        "type": "text",
+        "text": "ACKNOWLEDGMENTS ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "We thank Andriy Mnih, Chris Dyer, Chris Russell, David Blei, Hannah Wallach, Max Welling, Mirella Lapata and Yishu Miao for helpful comments, discussions and feedback. ",
+        "bbox": [
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+    {
+        "type": "text",
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+# NAS-BENCH-ASR: REPRODUCIBLE NEURAL ARCHITECTURE SEARCH FOR SPEECH RECOGNITION
+
+Abhinav Mehrotra1†, Alberto Gil C. P. Ramos1†, Sourav Bhattacharya1†, Łukasz Dudziak1†, Ravichander Vipperla1, Thomas Chau1, Samin Ishtiaq1, Mohamed S. Abdelfattah1, and Nicholas D. Lane1,2
+
+1Samsung AI Center, Cambridge $\cdot$ 2University of Cambridge ⋅ †Equal contribution {a.mehrotra1,a.gilramos,sourav.b1,l.dudziak}@samsung.com
+
+# ABSTRACT
+
+Powered by innovations in novel architecture design, noise tolerance techniques and increasing model capacity, Automatic Speech Recognition (ASR) has made giant strides in reducing word-error-rate over the past decade. ASR models are often trained with tens of thousand hours of high quality speech data to produce state-of-the-art (SOTA) results. Industry-scale ASR model training thus remains computationally heavy and time-consuming, and consequently has attracted little attention in adopting automatic techniques. On the other hand, Neural Architecture Search (NAS) has gained a lot of interest in the recent years thanks to its successes in discovering efficient architectures, often outperforming handcrafted alternatives. However, by changing the standard training process into a bi-level optimisation problem, NAS approaches often require significantly more time and computational power compared to single-model training, and at the same time increase complexity of the overall process. As a result, NAS has been predominately applied to problems which do not require as extensive training as ASR, and even then reproducibility of NAS algorithms is often problematic. Lately, a number of benchmark datasets has been introduced to address reproducibility issues by providing NAS researchers with information about performance of different models obtained through exhaustive evaluation. However, these datasets focus mainly on computer vision and NLP tasks and thus suffer from limited coverage of application domains. In order to increase diversity in the existing NAS benchmarks, and at the same time provide systematic study of the effects of architectural choices for ASR, we release NAS-Bench-ASR – the first NAS benchmark for ASR models. The dataset consists of 8, 242 unique models trained on the TIMIT audio dataset for three different target epochs, and each starting from three different initializations. The dataset also includes runtime measurements of all the models on a diverse set of hardware platforms. Lastly, we show that identified good cell structures in our search space for TIMIT transfer well to a much larger LibriSpeech dataset.
+
+# 1 INTRODUCTION
+
+Innovations in Deep Neural Network (DNN) architecture design, data augmentation techniques and a continuous increase in the amount of available high quality training datasets, resulted in a massive reduction in ASR word-error-rate over the past decade [Amodei et al., 2016; Kim et al., 2019; Park et al., 2019; Synnaeve et al., 2020]. However, training ASR models to achieve state-of-the-art performance remains challenging as it requires computationally heavy training process, e.g., often thousands of GPU-hours are needed for good convergence [Amodei et al., 2016; Kahn et al., 2020]. Furthermore, the requirement of hyper-parameter optimizations increases the computational loads in ASR training. Despite the system-level complexities in the training procedure, the importance of novel architecture design has proven extremely important in a variety of application domains including ASR [Chiu & Raffel, 2018; Pratap et al., 2020], computer vision [He et al., 2016; Krizhevsky et al., 2012], and natural-language processing (NLP) [Devlin et al., 2019; Vaswani et al., 2017].
+
+However, architecture design is a non-trivial task and often depends on years of experience, domain knowledge of the researchers and is driven by empirical successes.
+
+Over the past few years, the deep learning community is witnessing a trend in adopting automatic techniques to find neural network architectures over more traditional hand-designed alternatives. NAS algorithms are highly successful in discovering state-of-the-art architectures in various computer vision tasks [Cai et al., 2020; Howard et al., 2019; Lee et al., 2020; Real et al., 2018; Tan et al., 2019; Tan & Le, 2019]. However, many of them suffer from high computational demands, requiring a large number of architecture variations to be trained [Zoph & Le, 2017]. Furthermore, NAS algorithms are often difficult to reproduce by different researchers, mainly due to a non-standard use of training settings, e.g., hyperparameters, and subtle variations in the architecture search spaces [Li & Talwalkar, 2019; Sciuto et al., 2020]. Recently, a number of attempts have been made to mitigate these problems by releasing various benchmark datasets for the NAS research community [Dong & Yang, 2020; Klyuchnikov et al., 2020; Siems et al., 2020; Ying et al., 2019]. These datasets usually provide a direct mapping between an architecture variant and its post training performances, which can be used efficiently by a NAS algorithm speeding up the search process and, at the same time, providing common, fully reproducible environment for assessment and comparison of different algorithms. Initial attempts of creating benchmark datasets predominantly focus on image classification tasks (with only one existing work targeting NLP at the time of this writing), and thus suffer from poor application coverage.
+
+We address the lack of coverage problem by introducing a new NAS-benchmak dataset in the domain of ASR, to our best knowledge the very first of its kind. To build the dataset, we have trained 8, 242 unique convolutional neural network architectures on the TIMIT dataset [Garofolo et al., 1993]. We consider convolutional architectures due to their recent successes in the domain of ASR [Pratap et al., 2020; Hannun et al., 2019]. Moreover, convolution based architectures are computationally efficient to run on mobile devices, thus favouring real-time on-device deployment. Our dataset contains multiple runs of the entire training procedure of an architecture, spanning three initializations of the network parameters and three target epochs, amounting a total of $7 4 , 1 7 8 \ = \ 8 , 2 4 2 \times 3 \times 3$ training runs. In addition to the per epoch validation and final test metrics, such as Phoneme Error Rate (PER), and CTC loss, we also provide run-times of the architectures on desktop and embedded GPUs for varying batch size. Furthermore, we compare a number of NAS algorithms [Zoph & Le, 2017; Real et al., 2018; Dudziak et al., 2020; Li et al., 2017; Li & Talwalkar, 2019] on our search space, highlighting potential challenges and differences compared to their performances on existing NAS benchmark dataset. Lastly, we show the transferability of the top architecture cells found on TIMIT to a much larger Librispeech dataset [Panayotov et al., 2015].
+
+In summary, the contributions of this paper are:
+
+• Design of ASR NAS Search Space. ASR NAS-Bench is a first-of-its-kind search space for convolutional speech models. It facilitates the reproducible study of ASR through NAS methods and thus fills an important gap in the literature. The associated dataset consists of 8, 242 unique cells and contains validation and test metrics along with model parameters, FLOPs and on-device run-times1.
+
+• Enabling NAS for Large-scale ASR. Prohibitive training times for non-toy ASR datasets, has prevented NAS from strongly influencing the evolution of ASR architecture design. We show that ASR NAS-Bench is able to support the discovery of cell structures that generalize even to largescale datasets like Librispeech – a key breakthrough. We believe the methodological decisions in this paper will act as a blueprint for future work, where NAS plays a prominent role in ASR design.
+
+• Validating Existing NAS Algorithm Design. Existing understanding of NAS is grossly influenced by image-based tasks. By systematically benchmarking popular NAS algorithms, under a rich ASR search space, our findings provide otherwise lacking scientific support for prior results.
+
+# 2 RELATED WORK
+
+NAS Benchmarks. Ying et al. [2019] inroduced NAS-Bench-101 dataset in an attempt to address the difficulties in reproducing NAS research. It contains over 400K unique image classification models trained on the CIFAR10 dataset. Despite being the biggest NAS dataset yet, not all NAS algorithms can utilize the dataset due to the restrictions it imposes on the maximum number of edges to limit the search space size. To mitigate the limitations, NAS-Bench-201 was introduced, which contains 15K image classification models and includes more diagnostic data [Dong & Yang, 2020]. Concurrently to NAS-Bench-201, NAS-Bench-1shot1 [Zela et al., 2020] and NAS-Bench301 [Siems et al., 2020] were introduced. NAS-Bench-1shot1 focuses on benchmarking NAS with weight sharing, whereas, NAS-Bench-301 points out the need for surrogate functions for scaling and uses the DARTS search space [Liu et al., 2019] with approximately ${ 1 0 } ^ { 1 8 }$ models. Lastly, NASBench-NLP [Klyuchnikov et al., 2020] contains models with custom recurrent cells, which are used to replace traditional layers like LSTMs. The dataset contains around 14K different architectures trained on a language modeling task.
+
+NAS in Audio Modeling. Recently, there has been an increasing interest in applying NAS in speechrelated tasks, such as keyword spotting [Mo et al., 2020; Mazzawi et al., 2019], speaker verification [Ding et al., 2020; Qu et al., 2020], and acoustic scene classification [Li et al., 2020]. NAS has also been applied in ASR [He et al., 2020; Chen et al., 2020; Kim et al., 2020; Baruwa et al., 2019]. For example, Chen et al. [2020] used a search methodology based on the vanilla DARTS to optimize a CNN-based feature extractor, followed by a fixed Bi-LSTM module and multiple output heads. The authors evaluated the NAS-discovered models under mono- and multi-lingual settings, using the Full Language Pack from IARPA BABEL [Gales et al., 2014], showing improvements over a VGG-based extractor. In contrast, Kim et al. [2020] considered evolution-based search to optimize a micro-cell used within a transformer architecture. The evaluation was done using English and Korean dataset of approximately 100 hours of speech each, under monolingual setting. Similarly, He et al. [2020] used differentiable search, using P-DARTS [Chen et al., 2019] as the base, to optimize a convolutional model without the recurrent tail. Unlike the previous approaches, the evaluation is done on Mandarin, while using various training datasets spanning between 170 and 10K hours of speech. Closest to our work is the work by Baruwa et al. [2019], where the authors consider both TIMIT and LibriSpeech datasets, but studied them independently rather than using TIMIT as a proxy for LibriSpeech. Further differences include variations in search space design, e.g., the authors only considered operations arranged in a fixed feed-forward manner, and allowed interleaving convolutions with recurrent blocks. Lastly, current work on NAS for ASR focus mainly on using the search to improve prediction accuracy, however, they often lack solid foundations needed for analysing and reasoning about the overall search process and identifying its limitations. This work presents a large-scale study on the effects of architectural changes on ASR models.
+
+# 3 ASR NAS-BENCH
+
+The main purpose of the ASR NAS-Bench dataset is to provide a direct mapping from an architecture instance in the search-space (§3.1) to its training time and final performance metrics. The mapping is designed for any NAS algorithm to quickly navigate the architecture space without requiring the time-consuming and computationally-heavy training procedure. For architecture search we use the TIMIT dataset [Garofolo et al., 1993] and conduct a pilot experiment to select suitable hyperparameters used to train 8, 242 unique models.
+
+# 3.1 ASR ARCHITECTURE SEARCH SPACE
+
+In-line with existing work [Liu et al., 2019; Pham et al., 2018] and NAS Benchmarks [Ying et al., 2019; Dong & Yang, 2020], we restrict our search to a small feed-forward neural network topologyspace, commonly known as cells. We repeat and arrange a chosen cell to construct a predefined macro-architecture, which is then trained on the TIMIT dataset.
+
+Micro-Architecture. A micro-architecture or a cell, as shown in Figure 1(a), is represented by a directed acyclic graph (DAG). We consider DAGs with four nodes $T _ { 1 } , \ldots , T _ { 4 }$ with corresponding incident tensors $t _ { 1 } , \ldots , t _ { 4 }$ and allow two types of edges: main and skip connection edges. A main edge connects two successive nodes $T _ { i - 1 }$ and $T _ { i }$ in the graph as shown by the solid line-arrows in Figure 1(a). A skip connection edge on the other hand, can connect any two nodes $T _ { j }$ and $T _ { i }$ , with the constraint $j < i$ and are depicted as dotted line-arrows in Figure 1(a). Each edge $e _ { j  i }$ represents an operation on the tensor $t _ { j }$ . The tensor $t _ { i }$ is computed by summing the results of operations done by all incoming edges on $T _ { i }$ (i.e., $e _ { j  i }$ , where $j < i$ ).
+
+We consider a choice of six operations for the main edges: linear operation, four convolution operations distinguished by choices of (kernel size, dilation) ∈ $\{ ( 5 , 1 ) , ( 5 , 2 ) , ( 7 , 1 ) , ( 7 , 2 ) \}$ , and a zero operation, which outputs a tensor of zeros with the same shape and type as its input. Skip connection operations on the other hand, can be either the identity operation or the zero operation. We used L2 kernel regularizer with convolution operations and dropouts with linear operations. Within the convolution operations, the size of the kernels (e.g., 5 or 7) is chosen as a trade-off between the audio context duration and the model size. Similarly two dilation factors are considered (e.g., 1 or 2) to investigate the trade-off between audio context duration and time resolution. As the final step of a cell, the value of $t _ { 4 }$ is further passed through a layer normalization to produce the output of the cell. These design choices are made after we have considered the search space that can be used by the vast majority of the NAS algorithms.
+
+Macro-Architecture. One of our focuses in this benchmark is on-device deployment, so the macroarchitecture is made up of convolution and unidirectional LSTM blocks as they are computationally efficient to run on mobile CPUs. The macro architecture, illustrated in Figure 1(b), is a sequential computation composed of four blocks followed by a unidirectional LSTM and a linear layer. Individual blocks are composed of a convolution layer, an activation layer (ReLU), a layer normalization and a composition of $C _ { i }$ $( i = 1 , 2 , 3 , 4 )$ ) search cells, with the same micro architecture across all the blocks. Each block is parametrized by three parameters $F _ { i }$ , $K _ { i }$ and $S _ { i }$ . These are used to define the number of filters $F _ { i }$ , the kernel size $K _ { i }$ and the stride $S _ { i }$ of the convolution layer. Note that $F _ { i }$ is also the number of filters of the convolution layers inside the search cell. We use the following set of parameters to define the macro-architecture while performing all micro-architecture training on the TIMIT dataset: $C _ { 1 : 4 } = [ 3 , 4 , 5 , 6 ]$ , $F _ { 1 : 4 } = [ 6 0 0 , 8 0 0 , 1 0 0 0 , 1 2 0 0 ]$ , $K _ { 1 : 4 } = [ 8 , 8 , 8 , 8 ]$ and $S _ { 1 : 4 } = [ 1 , 1 , 2 , 2 ]$ .
+
+![](images/8c90c5857af224c30d93df8385c104f07c53878301e83d77c1faa5adac0b2f6f.jpg)  
+Figure 1: (a) Example of micro-architectures (cells) trained on TIMIT. The architecture space has 8, 242 unique cells. (b) An overview of the macro-architecture.
+
+# 3.2 TIMIT DATASET
+
+TIMIT [Garofolo et al., 1993] is one of the earliest datasets designed for evaluating and benchmarking phoneme ASR systems. It is ideally suited for neural architecture search experiments due to its small size and high quality transcriptions. It comprises of 6, 300 utterances from 630 speakers, amounting to 5.4 hours of speech. We use the standard training partition of 3, 696 utterances from 462 speakers. Following Lee & Hon [1989], we split the core test dataset into a test partition, consisting of 24 speakers, and a validation partition. Inline with kaldi Timit-s5 recipe, the original 61 phonemes are mapped into a set of 48 phonemes, which forms the output layer targets for all the models. These 48 phonemes were further folded to a set of 39 during evaluations [Lee & Hon, 1989]. We use 80-dimensional log-mel spectrograms computed over $2 5 \mathrm { { m s } }$ sliding window with a stride of $1 0 ~ \mathrm { m s }$ as input features. During training, we employ a curriculum learning strategy [Amodei et al., 2016], where we begin training by iterating twice over audio utterances shorter than 1s, then twice over audio utterances shorter than 2s as a warmup phase followed by training on the entire dataset. For efficiency, we also use a batch bucketing strategy, where a batch size of 64 is used for audio utterances smaller than 2s, and a batch size of 32 is used otherwise. We used CTC beam-search decoder with beam-size of 12. Note, we did not use any language model in our experiments in order to avoid further HPO (e.g., weighting factors) optimization. This also helped us to keep the architecture search for Acoustic Model (AM) tractable. All training experiments on TIMIT report the PER on validation and test partitions.
+
+![](images/d689f534f876402c93481a57d3d7f0f2779c26e73ff384cf57206a8d4bfda0da.jpg)  
+Figure 2: Correlation of best validation and final test PER for top, middle and bottom 1, 000 models.
+
+# 3.3 PILOT EXPERIMENT
+
+As different training procedures can potentially lead to substantially different results [Ying et al., 2019], in this work we employ a single general training procedure for all models. Moreover, we use the same parameter set, e.g., $F , K , S$ , learning rate, and decay across all 8, 242 models. In order to select good values of the parameters, we conducted a range of training experiments, where we performed a grid-search to find good macro structure parameters and optimizer settings.
+
+Macro Structure Parameter Selection. The macro structure considered in this work has four main blocks (see Figure 1(a)) and we considered the following variations in the pilot study: filters $F \in \{ [ 6 0 0 , 8 0 0 , 1 0 0 0 , 1 2 0 0 ]$ , [900, 1100, 1300, 1500], $\mathrm { 1 2 0 0 , 1 3 0 0 , 1 5 0 0 , 1 7 0 0 } ] \}$ , kernel sizes $K \in \{ [ 6 , 8 , 1 0 , 1 2 ]$ , [8, 8, 8, 8], [10, 10, 10, 10], [12, 12, 12, 12]}, and time reduction via strides $S \in \{ [ 2 , 2 , 2 , 1 ] , [ 1 , 1 , 2 , 2 ] , [ 2 , 2 , 1 , 1 ] \}$ .
+
+Optimizer Setting for Training. We further explored good ranges of the learning rate, decay factor, and start epoch for an exponential decay learning rate scheduler used in conjunction with the Adam optimizer. Specifically, we considered the learning rate $( \mathbf { L R } ) \in [ 1 0 ^ { - 3 } , 1 0 ^ { - 4 } , 5 * 1 0 ^ { - 5 } , 1 0 ^ { - 5 } ]$ , the decay factor $\in [ 0 . 9 , 0 . 9 5 , 0 . 9 9 ]$ , and the LR decay start epoch $\in [ 5 , 1 0 , 1 5 ]$ .
+
+Finally, we randomly chose five micro architectures among all possible 8, 242 cells and for each cell we conducted the grid search over the aforementioned parameters. Specifically, for each cell we created a model from a particular macro architecture, which we then trained by selecting a particular optimizer setting on TIMIT. We identified the parametric setting that resulted in the lowest PER across all five cells in the experiments and used the same parameters in all latter model training experiments. The best macro structure parameters are presented above (see $\ S 3 . 1 \ r ]$ , whereas the best LR was $1 0 ^ { - 4 }$ , and the decay factor and start epoch were: (i) 0.9 and 5 for target epoch 40, (ii) 0.631 and 2 for target epoch 10, and (iii) 0.398 and 1 for target epoch 5 respectively. The decay factor and start epoch are chosen such that the learning rate of the optimizer reaches the same value at the end of the target epoch of training.
+
+# 3.4 TRAINING SETUP
+
+Individual models are trained using a TensorFlow-based training pipeline running on a single GPU. We leveraged NVIDIA V100 and P40 GPUs, and decreased training time by increasing throughput via the bucketing strategy based on the audio length. Metrics such as CTC loss and Phoneme Error Rate (PER) for TIMIT were used to measure model performances. Specifically, train and validation metrics were logged at each epoch, and the test metrics were logged at the end of training for the best model (refered to as final test PER). Our dataset contains logs of each of the 8, 242 models trained with three different seeds and for three target epochs (5, 10 and 40), thus generating a total of 74, 178 model training traces. Additionally, we computed the number of parameters and floating point operations (FLOPs) for each of the architectures and measured their latency on two commonly used hardware platforms: Tesla 1080Ti and Jetson Nano.
+
+# 4 ANALYSIS OF NAS-BENCH-ASR DATASET
+
+As described in $\ S 3 . 1$ , our cell search space is constructed by selecting 3 main operations from a set of 6 candidates, and then selecting either identity or zeroize operation for the 6 skip connection edges (see Figure 1(a)). This amounts to 13, 824 $( 6 ^ { 3 } \times 2 ^ { 6 } )$ possible instances for the search-space. However, the use of zero operations introduces computational graph-isomorphism. To identify unique architectures, following [Ying et al., 2019; Dudziak et al., 2020], we first identify nodes with zero operations and disconnect them from their neighbors. Then we perform a reachability test and remove all nodes that can not be reached from the input or output nodes of the cell. Finally, we end up with a minimized graph representation, which we hash using an iterative graph invariant approach [Ying, 2019]. After accounting for isomorphism and discarding the empty graph from the list of valid models, we found 8, 242 unique architectures, out of which 8, 000 are without any zero operations.
+
+Table 1: Summary of test vs. validation analysis on NAS-Bench-ASR, including three subgroups. Spearman-correlation between the test and validation performances are also presented.   
+Table 2: Comparison of correlations between test and validation accuracies reported in the existing image classification benchmarks NAS-Bench-101, NB-Bench-201, and our NAS-Bench-ASR.   
+
+<table><tr><td rowspan="2">Group</td><td rowspan="2">Positions</td><td colspan="3">Test PER (%)</td><td colspan="3">Val. PER (%)</td><td rowspan="2">Test-Val Corr.</td></tr><tr><td>Min.</td><td>Max.</td><td>Avg.</td><td>Min.</td><td>Max.</td><td>Avg.</td></tr><tr><td>Overall</td><td>All</td><td>20.83</td><td>90.28</td><td>30.37±36.47</td><td>18.71</td><td>90.41</td><td>28.21±38.03</td><td>0.8519</td></tr><tr><td>Top</td><td>1-1000</td><td>20.83</td><td>22.29</td><td>21.87±0.52</td><td>18.71</td><td>20.54</td><td>19.52±0.51</td><td>0.2037</td></tr><tr><td>Middle</td><td>2000-3000</td><td>23.19</td><td>23.48</td><td>23.36±0.17</td><td>19.91</td><td>22.59</td><td>21.11±0.58</td><td>0.1408</td></tr><tr><td>Bottom</td><td>7000-8000</td><td>32.16</td><td>84.53</td><td>65.03±42.68</td><td>29.57</td><td>84.6</td><td>64.52±44.21</td><td>0.9977</td></tr></table>
+
+![](images/c0aa9cae86b38f7e55589b7ef2336de40eafa2e09cefd877788706683dd174ce.jpg)  
+Figure 3: Distribution of selected edges for each node (first row) and distribution of skip-connections for possible edges (second row). Top, middle and bottom are grouped by final test PER.
+
+Distribution of Model Performances. Analyzing the model training results we found that the majority of the models have converged and achieved a final test PER within a small range. Specifically, $8 3 . 3 \%$ (6, 869) of the models fall below a PER of $2 6 \%$ , with the best model reaching test PER of $2 0 . 8 3 \%$ . The remaining $1 6 . 7 \%$ of the models form a rather evenly-distributed tail, achieving PER values between $26 \%$ to $100 \%$ . Because of the high density of points below $26 \%$ PER and overall high range of PER values, we conducted our analysis by considering three subgroups of models: TOP models are the top 1, 000 architectures according to test PER, MIDDLE are models at positions between $2 , 0 0 0$ and 3, 000 in the test PER ranking, and BOTTOM are between 7, 000 and 8000.
+
+Correlation Between Validation and Test PERs. Figure 2 shows the correlation between the test PER and the best validation PER. The results indicate that there is a moderate correlation for top models, weak for middle ones, and strong for worst ones. An overall summary is also presented in Table 1. In general, correlation between validation and test accuracy among the top performing models is significantly lower than for image classification benchmarks, which is highlighted in Table 2, can potentially pose additional challenge to NAS algorithms.
+
+Distribution of Operations. Figure 3 (first row) presents the distribution of selected operations among main edges across top, middle and bottom most models. We found that the top models have the highest number of linear operations on the main edges, while the middle and bottom groups have low linear operations but higher convolution operations. Figure 3 (second row) also highlights that the worst models (bottom group) also have the highest selection of skip-connections. Figure 4 further confirms this observations showing how significantly worse the models in the search space become as they include less linear layers, or more than 2 skip connections.
+
+Interestingly, we found that the micro cells in our search space yielding the best validation PER is similar to the structure found in the state-of-the-art convolution models such as time-depth-separable (TDS) models [Pratap et al., 2020]. Figure 5 shows the TDS-cell and
+
+![](images/fc463be9d566d406967f817c7edad10477d1d7a40f7bac6c5148f38ff17efec1.jpg)  
+Figure 4: Ranking of models according to their test PER, when they are grouped according to the number of Linear layers (left) and skip-connections (right) used in their designs.
+
+![](images/2d0af86ca8edae773833df1fed2d52c7d3e28cdb3474189a864fb45257097cfe.jpg)  
+Figure 5: Cell architectures in our search space (from left to right): TDS-like, with best validation and test PERs, and one of the efficient pareto points. Note that the TDS-like cell could also have different convolution selected as the first operation.
+
+the micro-cells with best validation and test PERs (from left to right). This indicates the potential of conducting NAS on smaller datasets to discover new architectures yielding state-of-the-art results on larger datasets.
+
+Latency, Params, FLOPs and PER. Figure 6 investigates the relationship among test PER, number of parameters and latency of models in the dataset. FLOPS counts are closely correlated to the number of parameters so are not shown for simplicity. Although this figure shows only latency measured on a desktop GPU (NVIDIA GeForce GTX $1 0 8 0 ~ \mathrm { T i }$ ) with batch size of 32, the NASBench-ASR includes latency measured on different devices with varying batch sizes. Also shown in the figure are 13 Pareto-optimal models, indicated by purple (x) markers. Also, the best models on test and validation dataset are highlighted in red markers. TDS-like models ([Pratap et al., 2020]) achieve test PER between $2 2 . 7 \%$ and $2 3 . 4 5 \%$ , and the best validation PER model has test PER of $2 2 . 1 3 \%$ . There are Pareto-optimal models that achieve much lower latency without significant increase in PER, for instance, the model indicated by violet $( \bullet )$ has one-fifth of the latency of the best test PER model and still has a test PER of $2 1 . 9 8 \%$ . The distribution of coloured clusters along the y axis suggests that the number of parameters is not a strong factor to determine the accuracy of models. Analogically, models with similar number of parameters can lead to very different latency.
+
+# 5 TRANSFERABILITY
+
+Training an ASR architecture to achieve state-of-the-art WER is a slow process, as it often requires iterating over tens of thousands hours of speech data, and potentially over various hyper-parameter choices. Even when distributed across multiple GPUs, this process can take days or weeks [Amodei et al., 2016; Kahn et al., 2020]. Since the largest strides in lowering WERs have resulted from new architectures being developed manually by speech experts slowly over decades, it would be beneficial to scale such exploration through NAS. However, performing NAS directly on large scale ASR datasets needed for peak performance is not practical due to significantly more computational costs. An issue which is further exacerbated when one is also interested in architectures yielding lower latency and computational cost.
+
+![](images/0a233ba78d8aee5f9c455f2ba91df694b349684b59f498ebb491da70235c132a.jpg)  
+Figure 7: Transfer between TIMIT and Librispeech on validation and test datasets with high validation and test correlation of 0.85 and 0.86, respectively.
+
+![](images/497bc85272436c739e1a2bbaeb0089c0470480b07bbfc555b59bdd88e62e8650.jpg)  
+Figure 6: Test PER versus latency, colorcoded by the number of parameters. Best models, Pareto-optimal models, and selected TDS-like models are highlighted.
+
+For this reason, we explore how well new architectures found by NAS on TIMIT (5 hours) transfer to Librispeech (100 hours). Specifically, we investigate the correlation between the PER of best/random/worst performing architectures found on TIMIT, and the Label Error Rate (LER) (or WER) obtained when training the same architectures on Librispeech. If a high correlation is present, this would mean that one could lower the computational requirements of NAS by running it on a smaller datasets. In our case this would mean a $2 0 \mathrm { x }$ speedup in NAS, and in general this would open a new avenue for research, namely on how much one could save by running NAS on different smaller datasets, or running NAS on a subset of a larger dataset extracted by current or next generation data summarization techniques.
+
+Librispeech Dataset. Librispeech [Panayotov et al., 2015] is a widely used ASR training and benchmarking database of about 1, 000 hours of speech derived from audiobooks. The training dataset is partitioned into clean-100, clean-360 and other-500 sets with the clean partitions exhibiting much higher SNR. The test and dev sets are also partitioned similarly. In our work, we have used clean100 partition for training and dev-clean and test-clean for validation and testing. The choice of 100 hours partition is to strike a balance between building a decent large scale model, while still keeping the computational cost involved in architecture search experiments plausible. Previous literature indicates that the models trained on 100 hours partition are about $1 { - } 1 . 5 \%$ absolute [Panayotov et al., 2015] behind the models trained on 1, 000 hours when evaluated on test-clean set.
+
+Training. Librispeech models were trained with 4 GPUs with Horovod distributed framework. We use 80-dimensional log-mel features computed over $2 5 \mathrm { m s }$ Hamming windows strided by $1 0 \mathrm { m s }$ . Guided by latency considerations, we used a vocabulary of 780 sub-word tokens as output. Model performances are measured by tracking CTC loss, LER, and WER on the validation dataset during training and on test dataset post-training.
+
+Pilot Experiments. Similarly to $\ S 3 . 3$ , we also conducted a pilot experiment to determine appropriate macro structure parameters and hyper-parameters to train the models for Librispeech. To promote transferability between datasets at a reasonable compute cost, with the micro cell of the best model found on TIMIT dataset (out of 8, 242), we conducted another grid search but instead on Librispeech dataset. Accordingly, we chose the final number of filters, kernel size, dilation, learning rate, decay factor and start epoch based on lowest LER/WER on Librispeech.
+
+Correlation Analysis. For a meaningful analysis we selected 100 architectures from our search space based on their TIMIT PER, namely we took the best 20, 70 random, and the worst 10. We then plugged the micro cell architectures into the macro architecture for Librispeech. Finally, we trained these models on Librispeech with the hyper-parameters reported earlier and computed their LERs/WERs. We observe that models that didn’t converge for TIMIT also didn’t converge for Librispeech. For this reason, when looking at the strength of transferability between TIMIT and Librispeech we considered models that had TIMIT PER lower than $5 0 \%$ . As shown in Figure 7, there is a high correlation between TIMIT PER and Librispeech WER. In particular, we observe 0.85 correlation between validation metrics, and 0.86 for test metrics. Thus, it is possible to do indirect NAS for cell micro architecture on Librispeech by first applying NAS on TIMIT, and then reusing the identified cell structures in a macro architecture suitable for Librispeech.
+
+![](images/d186067c75eeae1e888505f877c7e2769abdcbca921b47fe3e35c848d17cfbda.jpg)  
+Figure 8: Performance of NAS algorithms on our ASR search space, where shaded regions mark interquartile ranges. The dashed line represents the best model in the dataset across all seeds.
+
+# 6 NAS EXPERIMENTS
+
+Following existing NAS benchmarks, we include results from running different NAS algorithms on our search space, using the NAS-Bench-ASR to query for accuracy of models. We consider the following standard NAS algorithms: Regularized Evolution (RE) [Real et al., 2018], Hyperband (HYPB) [Li et al., 2017], REINFORCE with an LSTM-based controller (REINF) [Zoph & Le, 2017], Binary Predictor (BP) [Dudziak et al., 2020], and Random Search (RAND) [Li & Talwalkar, 2019]. We also include an algorithm based on Deep Q-Learning (QLRN), which behaves similarly to RE but tries to chain mutations (actions) and learns what mutations can eventually lead to better results. We report results as functions of “trained models” to unify notion of cost. Because in the full training setting we trained models for 40 epochs, if an algorithm trains a model for fewer epochs than that (e.g. HYPB) we consider the cost of such a training to be $n / 4 0$ of a “trained model”, where $n$ is the number of epochs used $0 < n \leq 4 0$ ). We run each algorithm 100 times and present results in Figure 8 as average test PER of the best model found (all algorithms were using validation accuracy as their optimization target), and average validation PER of the most recently trained model (after smoothing the curve using exponential moving average with weight 0.9). We found that none of the algorithms were able to consistently find the best model – this is somewhat surprising given the moderate size our search space and the fact that algorithms like RE are able to consistently find the best model on NAS-Bench-201, given similar budget. Another interesting observation is related to the weak correlation between validation and test accuracies mentioned in the previous sections. By comparing the figures on the right and left sides (Figure 8), we can see that algorithms which tend to better optimize their rewards (validation accuracy) as search progresses are not necessarily better in the test PER objective – this is especially visible in the case of REINFORCE, which significantly outperforms random search if validation accuracy is considered, but when evaluated using test PER it presents comparable results. Another surprise is weak performance of Hyperband – the only algorithm that has the ability to adjust number of epochs to train models. From our observations it seems that many of our models converge to relatively good PER values fast (after 5-10 epochs) so we expected Hyperband to be able to leverage this property. However, it seems that in the case of our search space this is not so helpful – potentially because models might still change relative ordering as they are trained for more epochs despite the fact that they have already achieved decent performance.
+
+# 7 CONCLUSIONS
+
+We introduced NAS-Bench-ASR, a first comprehensive dataset for allowing computationally inexpensive training/test time evaluation of model performances, while conducting NAS research in the domain of ASR. We trained 8, 242 unique models on the TIMIT dataset for three initializations and three target epochs. In addition to the common training metrics in ASR, e.g., PER, CTC-loss, we also provide information on the number of parameters, FLOPS and latency of running all the models on two hardware platforms for varying batch sizes. Model run-times are especially beneficial for NAS researchers interested in optimizing architectures for efficient on-device deployment. We presented a comprehensive analysis of our dataset and evaluated the performances of a number of NAS algorithms on it. Lastly, we show that good cell structures as identified on the TIMIT dataset transfer well to Librispeech, which paves the way for affordable NAS on ASR domain.
+
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+
+# A APPENDIX
+
+Our dataset comprises of 8,242 unique models that were trained for three target epochs and each starting with three different initializations. In this appendix we present the results for the models with different initializations and target epochs.
+
+# A.1 CORRELATION BETWEEN VALIDATION AND TEST PERS FOR THE RUNS WITHDIFFERENT TARGET EPOCHS
+
+In this section we present the correlation of validation and test PERs between different target epochs. Specifically, we correlate each run of target epoch 40 (i.e., runs starting with unique initialization and trained for 40 epochs) with the runs for target epoch 5 and 10. This analysis informs us if reduced training (i.e., target epoch of 5 or 10) can be used as a good proxy for NAS. As shown in Table 3, there is weak correlation of target epoch 40 and 5. However, there is a moderate correlation between target epoch 40 and 10, suggesting that the reduced training might be useful for performing NAS.
+
+Table 3: Correlation of validation and test PERs between different target epochs.   
+
+<table><tr><td rowspan="2">E-40</td><td colspan="2">E-5</td><td colspan="2">E-10</td></tr><tr><td>Validation</td><td>Test</td><td>Validation</td><td>Test</td></tr><tr><td>Run 1</td><td>0.3349</td><td>0.3097</td><td>0.5493</td><td>0.5029</td></tr><tr><td>Run 2</td><td>0.2986</td><td>0.3022</td><td>0.5138</td><td>0.4793</td></tr><tr><td>Run 3</td><td>0.3234</td><td>0.3362</td><td>0.526</td><td>0.5112</td></tr></table>
+
+# A.2 CORRELATION BETWEEN VALIDATION AND TEST PERS
+
+In this section we present the correlation between the final test PER and the best validation PER for the three runs for target epoch 40 starting with different initializations, which is extension of results presented in Figure 2. As shown in Figure 9, the results for all seeds are similar. Specifically, there is moderate correlation for top models, weak for middle ones, and strong for worst ones.
+
+# A.3 CELL ARCHITECTURES IN OUR SEARCH SPACE
+
+In this section we present the micro-cell architectures in our search space that achieved best validation and test PERs for the three runs starting with different initializations. Figure 10 shows the micro-cell architectures that achieved best validation PERs (in top row) and best test PERs (in bottom row). We observe that the micro-cell architectures of top models often start with two convolution layers followed by a linear layer (which is consistent across all architectures).
+
+# A.4 IMPACT OF DIFFERENT OPERATIONS-COUNT ON MODEL PERFORMANCE
+
+In this section we present the impact of the number of selected operation on the model performance. As shown in Figure 11, models with more convolution layers, or with no linear layer are ranked as worst performing models. At the same time, models with a zero ops in the main edge have poor performance. This indicates that the top performing models are designed such that all nodes comprise of linear and convolution layers. We also observe that an increase in the number of skip connections deteriorates performance significantly, with surprisingly two skip connections yielding similar results to the traditional one skip connection, which aims to learn a perturbation of the identity rather than a generic transformation between input and output nodes.
+
+![](images/2aa7682ff6f6d64290a750a2d26b39eb19920f1daafef8c9f300ce841533edbc.jpg)  
+Figure 9: Correlation of best validation and final test PER. Figures in the columns are for top, middle and bottom 1, 000 models. Each row represents the results for runs with unique initialization.
+
+![](images/c0ccbaca6895863c9d9bf36bcfa08a7e0052cf30b1cbfb715abb577138a20acd.jpg)  
+Figure 10: Cell architectures in our search space with best validation and test PERs for the three runs.
+
+![](images/35a23870e5ce55539da32c082d7b165e304948c4426de4dd851989434dd2fb1b.jpg)  
+Figure 11: Positions of models in the ranking according to their test PER, when they are grouped according to the number of Convolution layer (first column), Linear layer (second column), Zero op (third column) and Skip-connections (last column). Each row correspond to the results for a run with unique inititialization.

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+        "text": "Abhinav Mehrotra1†, Alberto Gil C. P. Ramos1†, Sourav Bhattacharya1†, Łukasz Dudziak1†, Ravichander Vipperla1, Thomas Chau1, Samin Ishtiaq1, Mohamed S. Abdelfattah1, and Nicholas D. Lane1,2 ",
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+        "text": "1Samsung AI Center, Cambridge $\\cdot$ 2University of Cambridge ⋅ †Equal contribution {a.mehrotra1,a.gilramos,sourav.b1,l.dudziak}@samsung.com ",
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+        "text": "Powered by innovations in novel architecture design, noise tolerance techniques and increasing model capacity, Automatic Speech Recognition (ASR) has made giant strides in reducing word-error-rate over the past decade. ASR models are often trained with tens of thousand hours of high quality speech data to produce state-of-the-art (SOTA) results. Industry-scale ASR model training thus remains computationally heavy and time-consuming, and consequently has attracted little attention in adopting automatic techniques. On the other hand, Neural Architecture Search (NAS) has gained a lot of interest in the recent years thanks to its successes in discovering efficient architectures, often outperforming handcrafted alternatives. However, by changing the standard training process into a bi-level optimisation problem, NAS approaches often require significantly more time and computational power compared to single-model training, and at the same time increase complexity of the overall process. As a result, NAS has been predominately applied to problems which do not require as extensive training as ASR, and even then reproducibility of NAS algorithms is often problematic. Lately, a number of benchmark datasets has been introduced to address reproducibility issues by providing NAS researchers with information about performance of different models obtained through exhaustive evaluation. However, these datasets focus mainly on computer vision and NLP tasks and thus suffer from limited coverage of application domains. In order to increase diversity in the existing NAS benchmarks, and at the same time provide systematic study of the effects of architectural choices for ASR, we release NAS-Bench-ASR – the first NAS benchmark for ASR models. The dataset consists of 8, 242 unique models trained on the TIMIT audio dataset for three different target epochs, and each starting from three different initializations. The dataset also includes runtime measurements of all the models on a diverse set of hardware platforms. Lastly, we show that identified good cell structures in our search space for TIMIT transfer well to a much larger LibriSpeech dataset. ",
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+        "type": "text",
+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
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+        "text": "Innovations in Deep Neural Network (DNN) architecture design, data augmentation techniques and a continuous increase in the amount of available high quality training datasets, resulted in a massive reduction in ASR word-error-rate over the past decade [Amodei et al., 2016; Kim et al., 2019; Park et al., 2019; Synnaeve et al., 2020]. However, training ASR models to achieve state-of-the-art performance remains challenging as it requires computationally heavy training process, e.g., often thousands of GPU-hours are needed for good convergence [Amodei et al., 2016; Kahn et al., 2020]. Furthermore, the requirement of hyper-parameter optimizations increases the computational loads in ASR training. Despite the system-level complexities in the training procedure, the importance of novel architecture design has proven extremely important in a variety of application domains including ASR [Chiu & Raffel, 2018; Pratap et al., 2020], computer vision [He et al., 2016; Krizhevsky et al., 2012], and natural-language processing (NLP) [Devlin et al., 2019; Vaswani et al., 2017]. ",
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+        "type": "text",
+        "text": "However, architecture design is a non-trivial task and often depends on years of experience, domain knowledge of the researchers and is driven by empirical successes. ",
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+        "text": "Over the past few years, the deep learning community is witnessing a trend in adopting automatic techniques to find neural network architectures over more traditional hand-designed alternatives. NAS algorithms are highly successful in discovering state-of-the-art architectures in various computer vision tasks [Cai et al., 2020; Howard et al., 2019; Lee et al., 2020; Real et al., 2018; Tan et al., 2019; Tan & Le, 2019]. However, many of them suffer from high computational demands, requiring a large number of architecture variations to be trained [Zoph & Le, 2017]. Furthermore, NAS algorithms are often difficult to reproduce by different researchers, mainly due to a non-standard use of training settings, e.g., hyperparameters, and subtle variations in the architecture search spaces [Li & Talwalkar, 2019; Sciuto et al., 2020]. Recently, a number of attempts have been made to mitigate these problems by releasing various benchmark datasets for the NAS research community [Dong & Yang, 2020; Klyuchnikov et al., 2020; Siems et al., 2020; Ying et al., 2019]. These datasets usually provide a direct mapping between an architecture variant and its post training performances, which can be used efficiently by a NAS algorithm speeding up the search process and, at the same time, providing common, fully reproducible environment for assessment and comparison of different algorithms. Initial attempts of creating benchmark datasets predominantly focus on image classification tasks (with only one existing work targeting NLP at the time of this writing), and thus suffer from poor application coverage. ",
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+        "text": "We address the lack of coverage problem by introducing a new NAS-benchmak dataset in the domain of ASR, to our best knowledge the very first of its kind. To build the dataset, we have trained 8, 242 unique convolutional neural network architectures on the TIMIT dataset [Garofolo et al., 1993]. We consider convolutional architectures due to their recent successes in the domain of ASR [Pratap et al., 2020; Hannun et al., 2019]. Moreover, convolution based architectures are computationally efficient to run on mobile devices, thus favouring real-time on-device deployment. Our dataset contains multiple runs of the entire training procedure of an architecture, spanning three initializations of the network parameters and three target epochs, amounting a total of $7 4 , 1 7 8 \\ = \\ 8 , 2 4 2 \\times 3 \\times 3$ training runs. In addition to the per epoch validation and final test metrics, such as Phoneme Error Rate (PER), and CTC loss, we also provide run-times of the architectures on desktop and embedded GPUs for varying batch size. Furthermore, we compare a number of NAS algorithms [Zoph & Le, 2017; Real et al., 2018; Dudziak et al., 2020; Li et al., 2017; Li & Talwalkar, 2019] on our search space, highlighting potential challenges and differences compared to their performances on existing NAS benchmark dataset. Lastly, we show the transferability of the top architecture cells found on TIMIT to a much larger Librispeech dataset [Panayotov et al., 2015]. ",
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+        "text": "In summary, the contributions of this paper are: ",
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+        "text": "• Design of ASR NAS Search Space. ASR NAS-Bench is a first-of-its-kind search space for convolutional speech models. It facilitates the reproducible study of ASR through NAS methods and thus fills an important gap in the literature. The associated dataset consists of 8, 242 unique cells and contains validation and test metrics along with model parameters, FLOPs and on-device run-times1. ",
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+        "text": "• Enabling NAS for Large-scale ASR. Prohibitive training times for non-toy ASR datasets, has prevented NAS from strongly influencing the evolution of ASR architecture design. We show that ASR NAS-Bench is able to support the discovery of cell structures that generalize even to largescale datasets like Librispeech – a key breakthrough. We believe the methodological decisions in this paper will act as a blueprint for future work, where NAS plays a prominent role in ASR design. ",
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+        "text": "• Validating Existing NAS Algorithm Design. Existing understanding of NAS is grossly influenced by image-based tasks. By systematically benchmarking popular NAS algorithms, under a rich ASR search space, our findings provide otherwise lacking scientific support for prior results. ",
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+        "text": "2 RELATED WORK ",
+        "text_level": 1,
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+        "text": "NAS Benchmarks. Ying et al. [2019] inroduced NAS-Bench-101 dataset in an attempt to address the difficulties in reproducing NAS research. It contains over 400K unique image classification models trained on the CIFAR10 dataset. Despite being the biggest NAS dataset yet, not all NAS algorithms can utilize the dataset due to the restrictions it imposes on the maximum number of edges to limit the search space size. To mitigate the limitations, NAS-Bench-201 was introduced, which contains 15K image classification models and includes more diagnostic data [Dong & Yang, 2020]. Concurrently to NAS-Bench-201, NAS-Bench-1shot1 [Zela et al., 2020] and NAS-Bench301 [Siems et al., 2020] were introduced. NAS-Bench-1shot1 focuses on benchmarking NAS with weight sharing, whereas, NAS-Bench-301 points out the need for surrogate functions for scaling and uses the DARTS search space [Liu et al., 2019] with approximately ${ 1 0 } ^ { 1 8 }$ models. Lastly, NASBench-NLP [Klyuchnikov et al., 2020] contains models with custom recurrent cells, which are used to replace traditional layers like LSTMs. The dataset contains around 14K different architectures trained on a language modeling task. ",
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+        "text": "",
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+    {
+        "type": "text",
+        "text": "NAS in Audio Modeling. Recently, there has been an increasing interest in applying NAS in speechrelated tasks, such as keyword spotting [Mo et al., 2020; Mazzawi et al., 2019], speaker verification [Ding et al., 2020; Qu et al., 2020], and acoustic scene classification [Li et al., 2020]. NAS has also been applied in ASR [He et al., 2020; Chen et al., 2020; Kim et al., 2020; Baruwa et al., 2019]. For example, Chen et al. [2020] used a search methodology based on the vanilla DARTS to optimize a CNN-based feature extractor, followed by a fixed Bi-LSTM module and multiple output heads. The authors evaluated the NAS-discovered models under mono- and multi-lingual settings, using the Full Language Pack from IARPA BABEL [Gales et al., 2014], showing improvements over a VGG-based extractor. In contrast, Kim et al. [2020] considered evolution-based search to optimize a micro-cell used within a transformer architecture. The evaluation was done using English and Korean dataset of approximately 100 hours of speech each, under monolingual setting. Similarly, He et al. [2020] used differentiable search, using P-DARTS [Chen et al., 2019] as the base, to optimize a convolutional model without the recurrent tail. Unlike the previous approaches, the evaluation is done on Mandarin, while using various training datasets spanning between 170 and 10K hours of speech. Closest to our work is the work by Baruwa et al. [2019], where the authors consider both TIMIT and LibriSpeech datasets, but studied them independently rather than using TIMIT as a proxy for LibriSpeech. Further differences include variations in search space design, e.g., the authors only considered operations arranged in a fixed feed-forward manner, and allowed interleaving convolutions with recurrent blocks. Lastly, current work on NAS for ASR focus mainly on using the search to improve prediction accuracy, however, they often lack solid foundations needed for analysing and reasoning about the overall search process and identifying its limitations. This work presents a large-scale study on the effects of architectural changes on ASR models. ",
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+    {
+        "type": "text",
+        "text": "3 ASR NAS-BENCH ",
+        "text_level": 1,
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+        "text": "The main purpose of the ASR NAS-Bench dataset is to provide a direct mapping from an architecture instance in the search-space (§3.1) to its training time and final performance metrics. The mapping is designed for any NAS algorithm to quickly navigate the architecture space without requiring the time-consuming and computationally-heavy training procedure. For architecture search we use the TIMIT dataset [Garofolo et al., 1993] and conduct a pilot experiment to select suitable hyperparameters used to train 8, 242 unique models. ",
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+        "text": "3.1 ASR ARCHITECTURE SEARCH SPACE ",
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+        "text": "In-line with existing work [Liu et al., 2019; Pham et al., 2018] and NAS Benchmarks [Ying et al., 2019; Dong & Yang, 2020], we restrict our search to a small feed-forward neural network topologyspace, commonly known as cells. We repeat and arrange a chosen cell to construct a predefined macro-architecture, which is then trained on the TIMIT dataset. ",
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+        "text": "Micro-Architecture. A micro-architecture or a cell, as shown in Figure 1(a), is represented by a directed acyclic graph (DAG). We consider DAGs with four nodes $T _ { 1 } , \\ldots , T _ { 4 }$ with corresponding incident tensors $t _ { 1 } , \\ldots , t _ { 4 }$ and allow two types of edges: main and skip connection edges. A main edge connects two successive nodes $T _ { i - 1 }$ and $T _ { i }$ in the graph as shown by the solid line-arrows in Figure 1(a). A skip connection edge on the other hand, can connect any two nodes $T _ { j }$ and $T _ { i }$ , with the constraint $j < i$ and are depicted as dotted line-arrows in Figure 1(a). Each edge $e _ { j  i }$ represents an operation on the tensor $t _ { j }$ . The tensor $t _ { i }$ is computed by summing the results of operations done by all incoming edges on $T _ { i }$ (i.e., $e _ { j  i }$ , where $j < i$ ). ",
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+        "text": "We consider a choice of six operations for the main edges: linear operation, four convolution operations distinguished by choices of (kernel size, dilation) ∈ $\\{ ( 5 , 1 ) , ( 5 , 2 ) , ( 7 , 1 ) , ( 7 , 2 ) \\}$ , and a zero operation, which outputs a tensor of zeros with the same shape and type as its input. Skip connection operations on the other hand, can be either the identity operation or the zero operation. We used L2 kernel regularizer with convolution operations and dropouts with linear operations. Within the convolution operations, the size of the kernels (e.g., 5 or 7) is chosen as a trade-off between the audio context duration and the model size. Similarly two dilation factors are considered (e.g., 1 or 2) to investigate the trade-off between audio context duration and time resolution. As the final step of a cell, the value of $t _ { 4 }$ is further passed through a layer normalization to produce the output of the cell. These design choices are made after we have considered the search space that can be used by the vast majority of the NAS algorithms. ",
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+        "type": "text",
+        "text": "Macro-Architecture. One of our focuses in this benchmark is on-device deployment, so the macroarchitecture is made up of convolution and unidirectional LSTM blocks as they are computationally efficient to run on mobile CPUs. The macro architecture, illustrated in Figure 1(b), is a sequential computation composed of four blocks followed by a unidirectional LSTM and a linear layer. Individual blocks are composed of a convolution layer, an activation layer (ReLU), a layer normalization and a composition of $C _ { i }$ $( i = 1 , 2 , 3 , 4 )$ ) search cells, with the same micro architecture across all the blocks. Each block is parametrized by three parameters $F _ { i }$ , $K _ { i }$ and $S _ { i }$ . These are used to define the number of filters $F _ { i }$ , the kernel size $K _ { i }$ and the stride $S _ { i }$ of the convolution layer. Note that $F _ { i }$ is also the number of filters of the convolution layers inside the search cell. We use the following set of parameters to define the macro-architecture while performing all micro-architecture training on the TIMIT dataset: $C _ { 1 : 4 } = [ 3 , 4 , 5 , 6 ]$ , $F _ { 1 : 4 } = [ 6 0 0 , 8 0 0 , 1 0 0 0 , 1 2 0 0 ]$ , $K _ { 1 : 4 } = [ 8 , 8 , 8 , 8 ]$ and $S _ { 1 : 4 } = [ 1 , 1 , 2 , 2 ]$ . ",
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+        "img_path": "images/8c90c5857af224c30d93df8385c104f07c53878301e83d77c1faa5adac0b2f6f.jpg",
+        "image_caption": [
+            "Figure 1: (a) Example of micro-architectures (cells) trained on TIMIT. The architecture space has 8, 242 unique cells. (b) An overview of the macro-architecture. "
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+        "text": "3.2 TIMIT DATASET ",
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+        "text": "TIMIT [Garofolo et al., 1993] is one of the earliest datasets designed for evaluating and benchmarking phoneme ASR systems. It is ideally suited for neural architecture search experiments due to its small size and high quality transcriptions. It comprises of 6, 300 utterances from 630 speakers, amounting to 5.4 hours of speech. We use the standard training partition of 3, 696 utterances from 462 speakers. Following Lee & Hon [1989], we split the core test dataset into a test partition, consisting of 24 speakers, and a validation partition. Inline with kaldi Timit-s5 recipe, the original 61 phonemes are mapped into a set of 48 phonemes, which forms the output layer targets for all the models. These 48 phonemes were further folded to a set of 39 during evaluations [Lee & Hon, 1989]. We use 80-dimensional log-mel spectrograms computed over $2 5 \\mathrm { { m s } }$ sliding window with a stride of $1 0 ~ \\mathrm { m s }$ as input features. During training, we employ a curriculum learning strategy [Amodei et al., 2016], where we begin training by iterating twice over audio utterances shorter than 1s, then twice over audio utterances shorter than 2s as a warmup phase followed by training on the entire dataset. For efficiency, we also use a batch bucketing strategy, where a batch size of 64 is used for audio utterances smaller than 2s, and a batch size of 32 is used otherwise. We used CTC beam-search decoder with beam-size of 12. Note, we did not use any language model in our experiments in order to avoid further HPO (e.g., weighting factors) optimization. This also helped us to keep the architecture search for Acoustic Model (AM) tractable. All training experiments on TIMIT report the PER on validation and test partitions. ",
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+        "image_caption": [
+            "Figure 2: Correlation of best validation and final test PER for top, middle and bottom 1, 000 models. "
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+        "type": "text",
+        "text": "3.3 PILOT EXPERIMENT ",
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+        "type": "text",
+        "text": "As different training procedures can potentially lead to substantially different results [Ying et al., 2019], in this work we employ a single general training procedure for all models. Moreover, we use the same parameter set, e.g., $F , K , S$ , learning rate, and decay across all 8, 242 models. In order to select good values of the parameters, we conducted a range of training experiments, where we performed a grid-search to find good macro structure parameters and optimizer settings. ",
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+        "type": "text",
+        "text": "Macro Structure Parameter Selection. The macro structure considered in this work has four main blocks (see Figure 1(a)) and we considered the following variations in the pilot study: filters $F \\in \\{ [ 6 0 0 , 8 0 0 , 1 0 0 0 , 1 2 0 0 ]$ , [900, 1100, 1300, 1500], $\\mathrm { 1 2 0 0 , 1 3 0 0 , 1 5 0 0 , 1 7 0 0 } ] \\}$ , kernel sizes $K \\in \\{ [ 6 , 8 , 1 0 , 1 2 ]$ , [8, 8, 8, 8], [10, 10, 10, 10], [12, 12, 12, 12]}, and time reduction via strides $S \\in \\{ [ 2 , 2 , 2 , 1 ] , [ 1 , 1 , 2 , 2 ] , [ 2 , 2 , 1 , 1 ] \\}$ . ",
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+        "type": "text",
+        "text": "Optimizer Setting for Training. We further explored good ranges of the learning rate, decay factor, and start epoch for an exponential decay learning rate scheduler used in conjunction with the Adam optimizer. Specifically, we considered the learning rate $( \\mathbf { L R } ) \\in [ 1 0 ^ { - 3 } , 1 0 ^ { - 4 } , 5 * 1 0 ^ { - 5 } , 1 0 ^ { - 5 } ]$ , the decay factor $\\in [ 0 . 9 , 0 . 9 5 , 0 . 9 9 ]$ , and the LR decay start epoch $\\in [ 5 , 1 0 , 1 5 ]$ . ",
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+        "text": "Finally, we randomly chose five micro architectures among all possible 8, 242 cells and for each cell we conducted the grid search over the aforementioned parameters. Specifically, for each cell we created a model from a particular macro architecture, which we then trained by selecting a particular optimizer setting on TIMIT. We identified the parametric setting that resulted in the lowest PER across all five cells in the experiments and used the same parameters in all latter model training experiments. The best macro structure parameters are presented above (see $\\ S 3 . 1 \\ r ]$ , whereas the best LR was $1 0 ^ { - 4 }$ , and the decay factor and start epoch were: (i) 0.9 and 5 for target epoch 40, (ii) 0.631 and 2 for target epoch 10, and (iii) 0.398 and 1 for target epoch 5 respectively. The decay factor and start epoch are chosen such that the learning rate of the optimizer reaches the same value at the end of the target epoch of training. ",
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+    {
+        "type": "text",
+        "text": "3.4 TRAINING SETUP ",
+        "text_level": 1,
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+        "text": "Individual models are trained using a TensorFlow-based training pipeline running on a single GPU. We leveraged NVIDIA V100 and P40 GPUs, and decreased training time by increasing throughput via the bucketing strategy based on the audio length. Metrics such as CTC loss and Phoneme Error Rate (PER) for TIMIT were used to measure model performances. Specifically, train and validation metrics were logged at each epoch, and the test metrics were logged at the end of training for the best model (refered to as final test PER). Our dataset contains logs of each of the 8, 242 models trained with three different seeds and for three target epochs (5, 10 and 40), thus generating a total of 74, 178 model training traces. Additionally, we computed the number of parameters and floating point operations (FLOPs) for each of the architectures and measured their latency on two commonly used hardware platforms: Tesla 1080Ti and Jetson Nano. ",
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+    {
+        "type": "text",
+        "text": "4 ANALYSIS OF NAS-BENCH-ASR DATASET ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "As described in $\\ S 3 . 1$ , our cell search space is constructed by selecting 3 main operations from a set of 6 candidates, and then selecting either identity or zeroize operation for the 6 skip connection edges (see Figure 1(a)). This amounts to 13, 824 $( 6 ^ { 3 } \\times 2 ^ { 6 } )$ possible instances for the search-space. However, the use of zero operations introduces computational graph-isomorphism. To identify unique architectures, following [Ying et al., 2019; Dudziak et al., 2020], we first identify nodes with zero operations and disconnect them from their neighbors. Then we perform a reachability test and remove all nodes that can not be reached from the input or output nodes of the cell. Finally, we end up with a minimized graph representation, which we hash using an iterative graph invariant approach [Ying, 2019]. After accounting for isomorphism and discarding the empty graph from the list of valid models, we found 8, 242 unique architectures, out of which 8, 000 are without any zero operations. ",
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+    {
+        "type": "table",
+        "img_path": "images/77ea062c368189785e7300ffa778f2a24a06c1b7ad9649bb85fb2f173a8c6f6c.jpg",
+        "table_caption": [
+            "Table 1: Summary of test vs. validation analysis on NAS-Bench-ASR, including three subgroups. Spearman-correlation between the test and validation performances are also presented. ",
+            "Table 2: Comparison of correlations between test and validation accuracies reported in the existing image classification benchmarks NAS-Bench-101, NB-Bench-201, and our NAS-Bench-ASR. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Group</td><td rowspan=\"2\">Positions</td><td colspan=\"3\">Test PER (%)</td><td colspan=\"3\">Val. PER (%)</td><td rowspan=\"2\">Test-Val Corr.</td></tr><tr><td>Min.</td><td>Max.</td><td>Avg.</td><td>Min.</td><td>Max.</td><td>Avg.</td></tr><tr><td>Overall</td><td>All</td><td>20.83</td><td>90.28</td><td>30.37±36.47</td><td>18.71</td><td>90.41</td><td>28.21±38.03</td><td>0.8519</td></tr><tr><td>Top</td><td>1-1000</td><td>20.83</td><td>22.29</td><td>21.87±0.52</td><td>18.71</td><td>20.54</td><td>19.52±0.51</td><td>0.2037</td></tr><tr><td>Middle</td><td>2000-3000</td><td>23.19</td><td>23.48</td><td>23.36±0.17</td><td>19.91</td><td>22.59</td><td>21.11±0.58</td><td>0.1408</td></tr><tr><td>Bottom</td><td>7000-8000</td><td>32.16</td><td>84.53</td><td>65.03±42.68</td><td>29.57</td><td>84.6</td><td>64.52±44.21</td><td>0.9977</td></tr></table>",
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+        "image_caption": [
+            "Figure 3: Distribution of selected edges for each node (first row) and distribution of skip-connections for possible edges (second row). Top, middle and bottom are grouped by final test PER. "
+        ],
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+    {
+        "type": "text",
+        "text": "Distribution of Model Performances. Analyzing the model training results we found that the majority of the models have converged and achieved a final test PER within a small range. Specifically, $8 3 . 3 \\%$ (6, 869) of the models fall below a PER of $2 6 \\%$ , with the best model reaching test PER of $2 0 . 8 3 \\%$ . The remaining $1 6 . 7 \\%$ of the models form a rather evenly-distributed tail, achieving PER values between $26 \\%$ to $100 \\%$ . Because of the high density of points below $26 \\%$ PER and overall high range of PER values, we conducted our analysis by considering three subgroups of models: TOP models are the top 1, 000 architectures according to test PER, MIDDLE are models at positions between $2 , 0 0 0$ and 3, 000 in the test PER ranking, and BOTTOM are between 7, 000 and 8000. ",
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+        "type": "text",
+        "text": "Correlation Between Validation and Test PERs. Figure 2 shows the correlation between the test PER and the best validation PER. The results indicate that there is a moderate correlation for top models, weak for middle ones, and strong for worst ones. An overall summary is also presented in Table 1. In general, correlation between validation and test accuracy among the top performing models is significantly lower than for image classification benchmarks, which is highlighted in Table 2, can potentially pose additional challenge to NAS algorithms. ",
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+    {
+        "type": "text",
+        "text": "Distribution of Operations. Figure 3 (first row) presents the distribution of selected operations among main edges across top, middle and bottom most models. We found that the top models have the highest number of linear operations on the main edges, while the middle and bottom groups have low linear operations but higher convolution operations. Figure 3 (second row) also highlights that the worst models (bottom group) also have the highest selection of skip-connections. Figure 4 further confirms this observations showing how significantly worse the models in the search space become as they include less linear layers, or more than 2 skip connections. ",
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+        "type": "text",
+        "text": "Interestingly, we found that the micro cells in our search space yielding the best validation PER is similar to the structure found in the state-of-the-art convolution models such as time-depth-separable (TDS) models [Pratap et al., 2020]. Figure 5 shows the TDS-cell and ",
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+        "image_caption": [
+            "Figure 4: Ranking of models according to their test PER, when they are grouped according to the number of Linear layers (left) and skip-connections (right) used in their designs. "
+        ],
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+            "Figure 5: Cell architectures in our search space (from left to right): TDS-like, with best validation and test PERs, and one of the efficient pareto points. Note that the TDS-like cell could also have different convolution selected as the first operation. "
+        ],
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+    {
+        "type": "text",
+        "text": "the micro-cells with best validation and test PERs (from left to right). This indicates the potential of conducting NAS on smaller datasets to discover new architectures yielding state-of-the-art results on larger datasets. ",
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+    {
+        "type": "text",
+        "text": "Latency, Params, FLOPs and PER. Figure 6 investigates the relationship among test PER, number of parameters and latency of models in the dataset. FLOPS counts are closely correlated to the number of parameters so are not shown for simplicity. Although this figure shows only latency measured on a desktop GPU (NVIDIA GeForce GTX $1 0 8 0 ~ \\mathrm { T i }$ ) with batch size of 32, the NASBench-ASR includes latency measured on different devices with varying batch sizes. Also shown in the figure are 13 Pareto-optimal models, indicated by purple (x) markers. Also, the best models on test and validation dataset are highlighted in red markers. TDS-like models ([Pratap et al., 2020]) achieve test PER between $2 2 . 7 \\%$ and $2 3 . 4 5 \\%$ , and the best validation PER model has test PER of $2 2 . 1 3 \\%$ . There are Pareto-optimal models that achieve much lower latency without significant increase in PER, for instance, the model indicated by violet $( \\bullet )$ has one-fifth of the latency of the best test PER model and still has a test PER of $2 1 . 9 8 \\%$ . The distribution of coloured clusters along the y axis suggests that the number of parameters is not a strong factor to determine the accuracy of models. Analogically, models with similar number of parameters can lead to very different latency. ",
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+        "type": "text",
+        "text": "5 TRANSFERABILITY ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Training an ASR architecture to achieve state-of-the-art WER is a slow process, as it often requires iterating over tens of thousands hours of speech data, and potentially over various hyper-parameter choices. Even when distributed across multiple GPUs, this process can take days or weeks [Amodei et al., 2016; Kahn et al., 2020]. Since the largest strides in lowering WERs have resulted from new architectures being developed manually by speech experts slowly over decades, it would be beneficial to scale such exploration through NAS. However, performing NAS directly on large scale ASR datasets needed for peak performance is not practical due to significantly more computational costs. An issue which is further exacerbated when one is also interested in architectures yielding lower latency and computational cost. ",
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+        "image_caption": [
+            "Figure 7: Transfer between TIMIT and Librispeech on validation and test datasets with high validation and test correlation of 0.85 and 0.86, respectively. "
+        ],
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+        "image_caption": [
+            "Figure 6: Test PER versus latency, colorcoded by the number of parameters. Best models, Pareto-optimal models, and selected TDS-like models are highlighted. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "For this reason, we explore how well new architectures found by NAS on TIMIT (5 hours) transfer to Librispeech (100 hours). Specifically, we investigate the correlation between the PER of best/random/worst performing architectures found on TIMIT, and the Label Error Rate (LER) (or WER) obtained when training the same architectures on Librispeech. If a high correlation is present, this would mean that one could lower the computational requirements of NAS by running it on a smaller datasets. In our case this would mean a $2 0 \\mathrm { x }$ speedup in NAS, and in general this would open a new avenue for research, namely on how much one could save by running NAS on different smaller datasets, or running NAS on a subset of a larger dataset extracted by current or next generation data summarization techniques. ",
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+    {
+        "type": "text",
+        "text": "Librispeech Dataset. Librispeech [Panayotov et al., 2015] is a widely used ASR training and benchmarking database of about 1, 000 hours of speech derived from audiobooks. The training dataset is partitioned into clean-100, clean-360 and other-500 sets with the clean partitions exhibiting much higher SNR. The test and dev sets are also partitioned similarly. In our work, we have used clean100 partition for training and dev-clean and test-clean for validation and testing. The choice of 100 hours partition is to strike a balance between building a decent large scale model, while still keeping the computational cost involved in architecture search experiments plausible. Previous literature indicates that the models trained on 100 hours partition are about $1 { - } 1 . 5 \\%$ absolute [Panayotov et al., 2015] behind the models trained on 1, 000 hours when evaluated on test-clean set. ",
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+    {
+        "type": "text",
+        "text": "Training. Librispeech models were trained with 4 GPUs with Horovod distributed framework. We use 80-dimensional log-mel features computed over $2 5 \\mathrm { m s }$ Hamming windows strided by $1 0 \\mathrm { m s }$ . Guided by latency considerations, we used a vocabulary of 780 sub-word tokens as output. Model performances are measured by tracking CTC loss, LER, and WER on the validation dataset during training and on test dataset post-training. ",
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+    {
+        "type": "text",
+        "text": "Pilot Experiments. Similarly to $\\ S 3 . 3$ , we also conducted a pilot experiment to determine appropriate macro structure parameters and hyper-parameters to train the models for Librispeech. To promote transferability between datasets at a reasonable compute cost, with the micro cell of the best model found on TIMIT dataset (out of 8, 242), we conducted another grid search but instead on Librispeech dataset. Accordingly, we chose the final number of filters, kernel size, dilation, learning rate, decay factor and start epoch based on lowest LER/WER on Librispeech. ",
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+    {
+        "type": "text",
+        "text": "Correlation Analysis. For a meaningful analysis we selected 100 architectures from our search space based on their TIMIT PER, namely we took the best 20, 70 random, and the worst 10. We then plugged the micro cell architectures into the macro architecture for Librispeech. Finally, we trained these models on Librispeech with the hyper-parameters reported earlier and computed their LERs/WERs. We observe that models that didn’t converge for TIMIT also didn’t converge for Librispeech. For this reason, when looking at the strength of transferability between TIMIT and Librispeech we considered models that had TIMIT PER lower than $5 0 \\%$ . As shown in Figure 7, there is a high correlation between TIMIT PER and Librispeech WER. In particular, we observe 0.85 correlation between validation metrics, and 0.86 for test metrics. Thus, it is possible to do indirect NAS for cell micro architecture on Librispeech by first applying NAS on TIMIT, and then reusing the identified cell structures in a macro architecture suitable for Librispeech. ",
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+    {
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+        "image_caption": [
+            "Figure 8: Performance of NAS algorithms on our ASR search space, where shaded regions mark interquartile ranges. The dashed line represents the best model in the dataset across all seeds. "
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "6 NAS EXPERIMENTS ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Following existing NAS benchmarks, we include results from running different NAS algorithms on our search space, using the NAS-Bench-ASR to query for accuracy of models. We consider the following standard NAS algorithms: Regularized Evolution (RE) [Real et al., 2018], Hyperband (HYPB) [Li et al., 2017], REINFORCE with an LSTM-based controller (REINF) [Zoph & Le, 2017], Binary Predictor (BP) [Dudziak et al., 2020], and Random Search (RAND) [Li & Talwalkar, 2019]. We also include an algorithm based on Deep Q-Learning (QLRN), which behaves similarly to RE but tries to chain mutations (actions) and learns what mutations can eventually lead to better results. We report results as functions of “trained models” to unify notion of cost. Because in the full training setting we trained models for 40 epochs, if an algorithm trains a model for fewer epochs than that (e.g. HYPB) we consider the cost of such a training to be $n / 4 0$ of a “trained model”, where $n$ is the number of epochs used $0 < n \\leq 4 0$ ). We run each algorithm 100 times and present results in Figure 8 as average test PER of the best model found (all algorithms were using validation accuracy as their optimization target), and average validation PER of the most recently trained model (after smoothing the curve using exponential moving average with weight 0.9). We found that none of the algorithms were able to consistently find the best model – this is somewhat surprising given the moderate size our search space and the fact that algorithms like RE are able to consistently find the best model on NAS-Bench-201, given similar budget. Another interesting observation is related to the weak correlation between validation and test accuracies mentioned in the previous sections. By comparing the figures on the right and left sides (Figure 8), we can see that algorithms which tend to better optimize their rewards (validation accuracy) as search progresses are not necessarily better in the test PER objective – this is especially visible in the case of REINFORCE, which significantly outperforms random search if validation accuracy is considered, but when evaluated using test PER it presents comparable results. Another surprise is weak performance of Hyperband – the only algorithm that has the ability to adjust number of epochs to train models. From our observations it seems that many of our models converge to relatively good PER values fast (after 5-10 epochs) so we expected Hyperband to be able to leverage this property. However, it seems that in the case of our search space this is not so helpful – potentially because models might still change relative ordering as they are trained for more epochs despite the fact that they have already achieved decent performance. ",
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+    {
+        "type": "text",
+        "text": "7 CONCLUSIONS ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "We introduced NAS-Bench-ASR, a first comprehensive dataset for allowing computationally inexpensive training/test time evaluation of model performances, while conducting NAS research in the domain of ASR. We trained 8, 242 unique models on the TIMIT dataset for three initializations and three target epochs. In addition to the common training metrics in ASR, e.g., PER, CTC-loss, we also provide information on the number of parameters, FLOPS and latency of running all the models on two hardware platforms for varying batch sizes. Model run-times are especially beneficial for NAS researchers interested in optimizing architectures for efficient on-device deployment. We presented a comprehensive analysis of our dataset and evaluated the performances of a number of NAS algorithms on it. Lastly, we show that good cell structures as identified on the TIMIT dataset transfer well to Librispeech, which paves the way for affordable NAS on ASR domain. ",
+        "bbox": [
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+    {
+        "type": "text",
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+        "bbox": [
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+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "A APPENDIX ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            102,
+            297,
+            117
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Our dataset comprises of 8,242 unique models that were trained for three target epochs and each starting with three different initializations. In this appendix we present the results for the models with different initializations and target epochs. ",
+        "bbox": [
+            174,
+            133,
+            825,
+            176
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "A.1 CORRELATION BETWEEN VALIDATION AND TEST PERS FOR THE RUNS WITHDIFFERENT TARGET EPOCHS",
+        "text_level": 1,
+        "bbox": [
+            176,
+            193,
+            748,
+            220
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "In this section we present the correlation of validation and test PERs between different target epochs. Specifically, we correlate each run of target epoch 40 (i.e., runs starting with unique initialization and trained for 40 epochs) with the runs for target epoch 5 and 10. This analysis informs us if reduced training (i.e., target epoch of 5 or 10) can be used as a good proxy for NAS. As shown in Table 3, there is weak correlation of target epoch 40 and 5. However, there is a moderate correlation between target epoch 40 and 10, suggesting that the reduced training might be useful for performing NAS. ",
+        "bbox": [
+            173,
+            232,
+            826,
+            329
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "table",
+        "img_path": "images/5088061f5a759f979d88de131bf572316d35e3563432652d93718bd7dc1a3b95.jpg",
+        "table_caption": [
+            "Table 3: Correlation of validation and test PERs between different target epochs. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">E-40</td><td colspan=\"2\">E-5</td><td colspan=\"2\">E-10</td></tr><tr><td>Validation</td><td>Test</td><td>Validation</td><td>Test</td></tr><tr><td>Run 1</td><td>0.3349</td><td>0.3097</td><td>0.5493</td><td>0.5029</td></tr><tr><td>Run 2</td><td>0.2986</td><td>0.3022</td><td>0.5138</td><td>0.4793</td></tr><tr><td>Run 3</td><td>0.3234</td><td>0.3362</td><td>0.526</td><td>0.5112</td></tr></table>",
+        "bbox": [
+            313,
+            366,
+            679,
+            459
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "A.2 CORRELATION BETWEEN VALIDATION AND TEST PERS",
+        "text_level": 1,
+        "bbox": [
+            174,
+            484,
+            602,
+            500
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "In this section we present the correlation between the final test PER and the best validation PER for the three runs for target epoch 40 starting with different initializations, which is extension of results presented in Figure 2. As shown in Figure 9, the results for all seeds are similar. Specifically, there is moderate correlation for top models, weak for middle ones, and strong for worst ones. ",
+        "bbox": [
+            174,
+            511,
+            825,
+            566
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "A.3 CELL ARCHITECTURES IN OUR SEARCH SPACE ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            585,
+            539,
+            598
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "In this section we present the micro-cell architectures in our search space that achieved best validation and test PERs for the three runs starting with different initializations. Figure 10 shows the micro-cell architectures that achieved best validation PERs (in top row) and best test PERs (in bottom row). We observe that the micro-cell architectures of top models often start with two convolution layers followed by a linear layer (which is consistent across all architectures). ",
+        "bbox": [
+            174,
+            609,
+            825,
+            680
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "A.4 IMPACT OF DIFFERENT OPERATIONS-COUNT ON MODEL PERFORMANCE",
+        "text_level": 1,
+        "bbox": [
+            176,
+            698,
+            709,
+            712
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "In this section we present the impact of the number of selected operation on the model performance. As shown in Figure 11, models with more convolution layers, or with no linear layer are ranked as worst performing models. At the same time, models with a zero ops in the main edge have poor performance. This indicates that the top performing models are designed such that all nodes comprise of linear and convolution layers. We also observe that an increase in the number of skip connections deteriorates performance significantly, with surprisingly two skip connections yielding similar results to the traditional one skip connection, which aims to learn a perturbation of the identity rather than a generic transformation between input and output nodes. ",
+        "bbox": [
+            174,
+            723,
+            825,
+            834
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "image",
+        "img_path": "images/2aa7682ff6f6d64290a750a2d26b39eb19920f1daafef8c9f300ce841533edbc.jpg",
+        "image_caption": [
+            "Figure 9: Correlation of best validation and final test PER. Figures in the columns are for top, middle and bottom 1, 000 models. Each row represents the results for runs with unique initialization. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            204,
+            126,
+            792,
+            463
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "image",
+        "img_path": "images/c0ccbaca6895863c9d9bf36bcfa08a7e0052cf30b1cbfb715abb577138a20acd.jpg",
+        "image_caption": [
+            "Figure 10: Cell architectures in our search space with best validation and test PERs for the three runs. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            281,
+            560,
+            712,
+            856
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "image",
+        "img_path": "images/35a23870e5ce55539da32c082d7b165e304948c4426de4dd851989434dd2fb1b.jpg",
+        "image_caption": [
+            "Figure 11: Positions of models in the ranking according to their test PER, when they are grouped according to the number of Convolution layer (first column), Linear layer (second column), Zero op (third column) and Skip-connections (last column). Each row correspond to the results for a run with unique inititialization. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            174,
+            339,
+            818,
+            614
+        ],
+        "page_idx": 14
+    }
+]

parse/train/CzVPfeqPOBu/CzVPfeqPOBu.md

@@ -0,0 +1,269 @@
+# Transfer Learning of Graph Neural Networks with Ego-graph Information Maximization
+
+Qi Zhu1∗, Carl Yang2∗, Yidan $\mathbf { X } \mathbf { u } ^ { 3 }$ , Haonan Wang1, Chao Zhang4, Jiawei Han1
+
+1University of Illinois Urbana-Champaign, 2Emory University, 3University of Washington, 4Georgia Institute of Technology 1{qiz3,haonan3,hanj}@illinois.edu, 2j.carlyang@emory.edu, 3yx2516@uw.edu, 4chaozhang@gatech.edu
+
+# Abstract
+
+Graph neural networks (GNNs) have achieved superior performance in various applications, but training dedicated GNNs can be costly for large-scale graphs. Some recent work started to study the pre-training of GNNs. However, none of them provide theoretical insights into the design of their frameworks, or clear requirements and guarantees towards their transferability. In this work, we establish a theoretically grounded and practically useful framework for the transfer learning of GNNs. Firstly, we propose a novel view towards the essential graph information and advocate the capturing of it as the goal of transferable GNN training, which motivates the design of EGI (Ego-Graph Information maximization) to analytically achieve this goal. Secondly, when node features are structure-relevant, we conduct an analysis of EGI transferability regarding the difference between the local graph Laplacians of the source and target graphs. We conduct controlled synthetic experiments to directly justify our theoretical conclusions. Comprehensive experiments on two real-world network datasets show consistent results in the analyzed setting of direct-transfering, while those on large-scale knowledge graphs show promising results in the more practical setting of transfering with fine-tuning.1
+
+# 1 Introduction
+
+Graph neural networks (GNNs) have been intensively studied recently [29, 26, 39, 68], due to their established performance towards various real-world tasks [15, 69, 53], as well as close connections to spectral graph theory [12, 9, 16]. While most GNN architectures are not very complicated, the training of GNNs can still be costly regarding both memory and computation resources on real-world large-scale graphs [10, 63]. Moreover, it is intriguing to transfer learned structural information across different graphs and even domains in settings like few-shot learning [56, 44, 25]. Therefore, several very recent studies have been conducted on the transferability of GNNs [21, 23, 22, 59, 31, 3, 47]. However, it is unclear in what situations the models will excel or fail especially when the pre-training and fine-tuning tasks are different. To provide rigorous analysis and guarantee on the transferability of GNNs, we focus on the setting of direct-transfering between the source and target graphs, under an analogous setting of “domain adaptation” [7, 59].
+
+In this work, we establish a theoretically grounded framework for the transfer learning of GNNs, and leverage it to design a practically transferable GNN model. Figure 1 gives an overview of our framework. It is based on a novel view of a graph as samples from the joint distribution of its $\mathbf { k }$ -hop ego-graph structures and node features, which allows us to define graph information and similarity, so as to analyze GNN transferability (§3). This view motivates us to design EGI, a novel GNN training objective based on ego-graph information maximization, which is effective in capturing the graph information as we define (§3.1). Then we further specify the requirement on transferable node features and analyze the transferability of EGI that is dependent on the local graph Laplacians of source and target graphs (§3.2).
+
+![](images/a75bc7d9606ed20d147da05c975e5dc6b5ac8fd6fcd0435db56e2c88a14c0797.jpg)  
+Figure 1: Overview of our GNN transfer learning framework: (1) we represent the toy graph as a combination of its 1-hop ego-graph and node feature distributions; (2) we design a transferable GNN regarding the capturing of such essential graph information; (3) we establish a rigorous guarantee of GNN transferability based on the node feature requirement and graph structure difference.
+
+All of our theoretical conclusions have been directly validated through controlled synthetic experiments (Table 1), where we use structural-equivalent role identification in an direct-transfering setting to analyze the impacts of different model designs, node features and source-target structure similarities on GNN transferability. In $\ S 4$ , we conduct real-world experiments on multiple publicly available network datasets. On the Airport and Gene graphs (§4.1), we closely follow the settings of our synthetic experiments and observe consistent but more detailed results supporting the design of EGI and the utility of our theoretical analysis. On the YAGO graphs (§4.2), we further evaluate EGI on the more generalized and practical setting of transfer learning with task-specific fine-tuning. We find our theoretical insights still indicative in such scenarios, where EGI consistently outperforms state-of-the-art GNN representation and transfer learning frameworks with significant margins.
+
+# 2 Related Work
+
+Representation learning on graphs has been studied for decades, with earlier spectral-based methods [6, 46, 52] theoretically grounded but hardly scaling up to graphs with over a thousand of nodes. With the emergence of neural networks, unsupervised network embedding methods based on the Skip-gram objective [37] have replenished the field [51, 14, 42, 45, 66, 62, 65]. Equipped with efficient structural sampling (random walk, neighborhood, etc.) and negative sampling schemes, these methods are easily parallelizable and scalable to graphs with thousands to millions of nodes. However, these models are essentially transductive as they compute fully parameterized embeddings only for nodes seen during training, which are impossible to be transfered to unseen graphs.
+
+More recently, researchers introduce the family of graph neural networks (GNNs) that are capable of inductive learning and generalizing to unseen nodes given meaningful node features [29, 12, 15, 67]. Yet, most existing GNNs require task-specific labels for training in a semi-supervised fashion to achieve satisfactory performance [29, 15, 53, 64], and their usage is limited to single graphs where the downstream task is fixed. To this end, several unsupervised GNNs are presented, such as the auto-encoder-based ones like VGAE [28] and GNFs [35], as well as the deep-infomax-based ones like DGI [54] and InfoGraph [50]. Their potential in the transfer learning of GNN remains unclear when the node features and link structures vary across different graphs.
+
+Although the architectures of popular GNNs such as GCN [29] may not be very complicated compared with heavy vision and language models, training a dedicated GNN for each graph can still be cumbersome [10, 63]. Moreover, as pre-training neural networks are proven to be successful in other domains [13, 18], the idea is intriguing to transfer well-trained GNNs from relevant source graphs to improve the modeling of target graphs or enable few-shot learning [59, 31, 3] when labeled data are scarce. In light of this, pioneering works have studied both generative [22] and discriminative [21, 23] GNN pre-training schemes. Though Graph Contrastive Coding [43] shares the most similar view towards graph structures as us, it utilizes contrastive learning across all graphs instead of focusing on the transfer learning between any specific pairs. On the other hand, unsupervised domain adaptive GCNs [59] study the domain adaption problem only when the source and target tasks are homogeneous.
+
+Most previous pre-training and self-supervised GNNs lack a rigorous analysis towards their transferability and thus have unpredictable effectiveness. The only existing theoretical work on GNN transferability studies the performance of GNNs across different permutations of a single original graph [33, 34] and the tradeoff between discriminability and transferability of GNNs [47]. We, instead, are the first to rigorously study the more practical setting of transferring GNNs across pairs of different source and target graphs.
+
+# 3 Transferable Graph Neural Networks
+
+In this paper, we design a more transferable training objective for GNN (EGI) based on our novel view of essential graph information (§3.1). We then analyze its transferability as the gap between its abilities to model the source and target graphs, based on their local graph Laplacians (§3.2).
+
+Based on the connection between GNN and spectral graph theory [29], we describe the output of a GNN as a combination of its input node features $X$ , fixed graph Laplacian $L$ and learnable graph filters $\Psi$ . The goal of training a GNN is then to improve its utility by learning the graph filters that are compatible with the other two components towards specific tasks.
+
+In the graph transfer learning setting where downstream tasks are often unknown during pre-training, we argue that the general utility of a GNN should be optimized and quantified w.r.t. its ability of capturing the essential graph information in terms of the joint distribution of its topology structures and node features, which motivates us to design a novel ego-graph information maximization model (EGI) (§3.1). The general transferability of a GNN is then quantified by the gap between its abilities to model the source and target graphs. Under reasonable requirements such as using structurerespecting node features as the GNN input, we analyze this gap for EGI based on the structural difference between two graphs w.r.t. their local graph Laplacians (§3.2).
+
+# 3.1 Transferable GNN via Ego-graph Information Maximization
+
+In this work, we focus on the direct-transfering setting where a GNN is pre-trained on a source graph $G _ { a }$ in an unsupervised fashion and applied on a target graph $G _ { b }$ without fine-tuning.2 Consider a graph $G = \{ V , E \}$ , where the set of nodes $V$ are associated with certain features $X$ and the set of edges $E$ form graph structures. Intuitively, the transfer learning will be successful only if both the features and structures of $G _ { a }$ and $G _ { b }$ are similar in some ways, so that the graph filters of a GNN learned on $G _ { a }$ are compatible with the features and structures of $G _ { b }$ .
+
+Graph kernels [57, 8, 30, 38] are well-known for their capability of measuring similarity between pair of graphs. Motivated by $\mathrm { k }$ -hop subgraph kernels [4], we introduce a novel view of a graph as samples from the joint distribution of its $k$ -hop ego-graph structures and node features. Since GNN essentially encodes such $\mathbf { k }$ -hop ego graph samples, this view allows us to give concrete definitions towards structural information of graphs in the transfer learning setting, which facilitates the measuring of similarity (difference) among graphs. Yet, none of the existing GNN training objectives are capable of recovering such distributional signals of ego graphs. To this end, we design $E g o$ -Graph Information maximization (EGI), which alternatively reconstructs the $\mathbf { k }$ -hop ego-graph of each center node via mutual information maximization [20].
+
+Definition 3.1 (K-hop ego-graph). We call a graph $g _ { i } = \{ V ( g _ { i } ) , E ( g _ { i } ) \}$ a $k$ -hop ego-graph centered at node $v _ { i }$ if it has a $k$ -layer centroid expansion [4] such that the greatest distance between $v _ { i }$ and any other nodes in the ego-graph is $k ,$ i.e. $\forall v _ { j } \in V ( g _ { i } ) , | d ( v _ { i } , v _ { j } ) | \leq k$ , where $d ( v _ { i } , v _ { j } )$ is the graph distance between $v _ { i }$ and $v _ { j }$ .
+
+In this paper, we use directed $\mathrm { k }$ -hop ego-graph and its direction is decided by whether it is composed of incoming or outgoing edges to the center node, i.e., $g _ { i }$ and $\tilde { g _ { i } }$ . The results apply trivially to undirected graphs with $g _ { i } = { \tilde { g } } _ { i }$ .
+
+Definition 3.2 (Structural information). Let $\mathcal { G }$ be a topological space of sub-graphs, we view a graph $G$ as samples of $k$ -hop ego-graphs $\{ g _ { i } \} _ { i = 1 } ^ { n }$ drawn i.i.d. from $\mathcal { G }$ with probability $\mu _ { ; }$ , i.e., $g _ { i } \stackrel { \scriptscriptstyle 1 . 1 . 0 . } { \sim } \mu \forall i = 1 , \cdot \cdot \cdot , n$ . The structural information of $G$ is then defined to be the set of $k$ -hop ego-graphs of $\{ g _ { i } \} _ { i = 1 } ^ { n }$ and their empirical distribution.
+
+As shown in Figure 1, three graphs $G _ { 0 }$ , $G _ { 1 }$ and $G _ { 2 }$ are characterized by a set of 1-hop ego-graphs and their empirical distributions, which allows us to quantify the structural similarity among graphs as shown in $\ S 3 . 2$ (i.e., $G _ { 0 }$ is more similar to $G _ { 1 }$ than $G _ { 2 }$ under such characterization). In practice, the nodes in a graph $G$ are characterized not only by their $\mathbf { k }$ -hop ego-graph structures but also their associated node features. Therefore, $G$ should be regarded as samples $\{ ( g _ { i } , x _ { i } ) \}$ drawn from the joint distribution $\mathbb { P }$ on the product space of $\mathcal { G }$ and a node feature space $\mathcal { X }$ .
+
+![](images/944c7f1b43a9719fbce6b9550bca8c7dabe51127e2788d932f346c930653c8d4.jpg)  
+Figure 2: The overall EGI training framework.
+
+Ego-Graph Information Maximization. Given a set of ego-graphs $\{ ( g _ { i } , x _ { i } ) \} _ { i }$ drawn from an empirical joint distribution $( g _ { i } , x _ { i } ) \sim \mathbb { P }$ . We aim to train an GNN encoder $\Psi$ to maximize the mutual informaion (MI $( g _ { i } , \Psi ( g _ { i } , x _ { i } ) )$ ) between the defined structural information $g _ { i } { } ^ { 3 }$ (i.e. k-hop ego-graph) and node embedding $z _ { i } ~ = ~ \Psi ( g _ { i } , x _ { i } )$ . To maximize the MI, another discriminator $\mathcal { D } ( g _ { i } , z _ { i } ) : E ( g _ { i } ) \times z _ { i }  \mathbb { R } ^ { + }$ is introduced to compute the probability of an edge $e$ belongs to the given ego-graph $g _ { i }$ . We use the Jensen-Shannon MI estimator [20] in the EGI objective,
+
+$$
+\mathcal { L } _ { \mathrm { E G I } } = - \mathbf { M } \mathbf { I } ^ { \mathrm { ( J S D ) } } \left( \boldsymbol { \mathcal { G } } , \boldsymbol { \Psi } \right) = \frac { 1 } { N } \sum _ { i = 1 } ^ { N } \left[ \mathsf { s p } \left( \mathcal { D } ( g _ { i } , z _ { i } ^ { \prime } ) \right) + \mathsf { s p } \left( - \mathcal { D } ( g _ { i } , z _ { i } ) \right) \right] ,
+$$
+
+where $\operatorname { s p } ( x ) = \log ( 1 + e ^ { x } )$ is the softplus function and $( g _ { i } , z _ { i } ^ { \prime } )$ is randomly drawn from the product of marginal distributions, i.e. $z _ { i } ^ { \prime } = \Psi ( g _ { i ^ { \prime } } , x _ { i ^ { \prime } } ) , ( g _ { i ^ { \prime } } , x _ { i ^ { \prime } } ) \sim \mathbb { P } , i ^ { \prime } \neq i$ . In general, we can also randomly draw negative $g _ { i } ^ { \prime }$ in the topological space, while enumerating all possible graphs $g _ { i ^ { \prime } }$ leads to high computation cost.
+
+In Eq. 1, the computation of $\mathcal { D }$ on $E ( g _ { i } )$ depends on the node orders. Following the common practice in graph generation [70], we characterize the decision process of $\mathcal { D }$ with a fixed graph ordering, i.e., the BFS-ordering $\pi$ over edges $E ( g _ { i } )$ . $\mathcal { D } = f \circ \Phi$ is composed by another GNN encoder $\Phi$ and scoring function $f$ over an edge sequence $E ^ { \pi } : \{ e _ { 1 } , e _ { 2 } , . . . , e _ { n } \}$ , which makes predictions on the BFS-ordered edges.
+
+Recall our previous definition on the direction of $\mathrm { k }$ -hop ego-graph, the center node encoder $\Psi$ receives pairs of $( g _ { i } , x _ { i } )$ while the neighbor node encoder $\Phi$ in discriminator $\mathcal { D }$ receives $( \tilde { g } _ { i } , x _ { i } )$ . Both encoders are parameterized as GNNs,
+
+$$
+\Psi ( g _ { i } , x _ { i } ) = { \bf G } { \bf N } \mathrm { N } _ { \Psi } ( A _ { i } , X _ { i } ) , \Phi ( \tilde { g _ { i } } , x _ { i } ) = { \bf G } { \bf N } \mathrm { N } _ { \Phi } ( A _ { i } ^ { \prime } , X _ { i } ) ,
+$$
+
+where $A _ { i } , A _ { i } ^ { \prime }$ is the adjacency matrix with self-loops of $g _ { i }$ and $\tilde { g _ { i } }$ , respectively. The self-loops are added following the common design of GNNs, which allows the convolutional node embeddings to always incorporate the influence of the center node. $A _ { i } = A _ { i } ^ { \prime \intercal }$ . The output of $\Psi$ , i.e., $z _ { i } \in \mathbb { R } ^ { n }$ , is the center node embedding, while $\Phi$ outputs representation $H \in \mathbb { R } ^ { | g _ { i } | \times n }$ for neighbor nodes in the ego-graph.
+
+Once node representation $H$ is computed, we now describe the scoring function $f$ . For each of the node pair $\bar { ( } p , q ) \in E ^ { \pi }$ , $h _ { p }$ is the source node representation from $\Phi$ , $x _ { q }$ is the destination node features. The scoring function is,
+
+$$
+\begin{array} { r } { f ( h _ { p } , x _ { q } , z _ { i } ) = \sigma \left( U ^ { T } \cdot \tau \left( W ^ { T } [ h _ { p } | | x _ { q } | | z _ { i } ] \right) \right) , } \end{array}
+$$
+
+where $\sigma$ and $\tau$ are Sigmoid and ReLU activation functions. Thus, the discriminator $\mathcal { D }$ is asked to distinguish a positive $\left( ( p , q ) , z _ { i } \right)$ and negative pair $( ( p , q ) , z _ { i } ^ { \prime } ) )$ for each edge in $g _ { i }$ .
+
+$$
+\mathcal { D } ( g _ { i } , z _ { i } ) = \sum _ { ( p , q ) \in E ^ { \pi } } \log f ( h _ { p } , x _ { q } , z _ { i } ) , \mathcal { D } ( g _ { i } , z _ { i } ^ { \prime } ) = \sum _ { ( p , q ) } ^ { E ^ { \pi } } \log f ( h _ { p } , x _ { q } , z _ { i } ^ { \prime } ) .
+$$
+
+There are two types of edges $( p , q )$ in our consideration of node orders, type-a - the edges across different hops (from the center node), and type- $^ { b }$ - the edges within the same hop (from the center node). The aforementioned BFS-based node ordering guarantees that Eq. 3 is sensitive to the ordering of type-a edges, and invariant to the ordering of type- $\mathbf { \delta } .$ edges, which is consistent with the requirement of our theoretical analysis on $\Delta _ { \mathcal { D } }$ . Due to the fact that the output of a $\mathbf { k }$ -layer GNN only depends on a $\mathbf { k }$ -hop ego-graph for both encoders $\Psi$ and $\Phi$ , EGI can be trained in parallel by sampling batches of $g _ { i }$ ’s. Besides, the training objective of EGI is transferable as long as $( g _ { i } , x _ { i } )$ across source graph $G _ { a }$ and $G _ { b }$ satisfies the conditions given in $\ S 3 . 2$ . More model details in Appendix $\ S _ { \mathbf { B } }$ and source code in the Supplementary Materials.
+
+Connection with existing work. To provide more insights into the EGI objective, we also present it as a dual problem of ego-graph reconstruction. Recall our definition of ego-graph mutual information $\mathbf { M I } ( g _ { i } , \Psi ( g _ { i } , x _ { i } ) )$ . It can be related to an ego-graph reconstruction loss $R { \big ( } g _ { i } | \Psi { \big ( } g _ { i } , x _ { i } ) { \big ) }$ as
+
+$$
+\operatorname* { m a x } \mathbf { M } [ ( g _ { i } , \Psi ( g _ { i } , x _ { i } ) ) = H ( g _ { i } ) - H ( g _ { i } | \Psi ( g _ { i } , x _ { i } ) ) \leq H ( g _ { i } ) - R ( g _ { i } | \Psi ( g _ { i } , x _ { i } ) ) .
+$$
+
+When EGI is maximizing the mutual information, it simultaneously minimizes the upper error bound of reconstructing an ego-graph $g _ { i }$ . In this view, the key difference between EGI and VGAE [28] is they assume each edge in a graph to be observed independently during the reconstruction. While in EGI, edges in an ego-graph are observed jointly during the GNN decoding. Moreover, existing mutual information based GNNs such as DGI [54] and GMI [41] explicitly measure the mutual information between node features $x$ and GNN output $\Psi$ . In this way, they tend to capture node features instead of graph structures, which we deem more essential in graph transfer learning as discussed in $\ S 3 . 2$ .
+
+Use cases of EGI framework. In this paper, we focus on the classical domain adaption (directtransferring) setting [7], where no target domain labels are available and transferability is measured by the performance discrepancy without fine-tuning. In this setting, the transferability of EGI is theoretically guaranteed by Theorem 3.1. In $\ S 4 . 1$ , we validated this with the airport datasets. Beyond direct-transferring, EGI is also useful in the more generalized and practical setting of transfer learning with fine-tuning, which we introduced in $\ S 4 . 2$ and validated with the YAGO datasets. In this setting, the transferability of EGI is not rigorously studied yet, but is empirically shown promising.
+
+Supportive observations. In the first three columns of our synthetic experimental results (Table 1), in both cases of transfering GNNs between similar graphs (F-F) and dissimilar graphs (B-F), EGI significantly outperforms all competitors when using node degree one-hot encoding as transferable node features. In particular, the performance gains over the untrained GIN show the effectiveness of training and transfering, and our gains are always larger than the two state-of-the-art unsupervised GNNs. Such results clearly indicate advantageous structure preserving capability and transferability of EGI.
+
+# 3.2 Transferability analysis based on local graph Laplacians
+
+We now study the transferability of a GNN (in particular, with the training objective of ${ \mathcal { L } } _ { \mathrm { E G I } } ,$ ) between the source graph $G _ { a }$ and target graph $G _ { b }$ based on their graph similarity. We firstly establish the requirement towards node features, under which we then focus on analyzing the transferability of EGI w.r.t. the structural information of $G _ { a }$ and $G _ { b }$ .
+
+Recall our view of the GNN output as a combination of its input node features, fixed graph Laplacian and learnable graph filters. The utility of a GNN is determined by the compatibility among the three. In order to fulfill such compatibility, we require the node features to be structure-respecting:
+
+Definnode Then ion 3.3 (Structure-respectwith a set of node featuree say the node features on es). , where respect $g _ { i }$ -th hop of or any no $v _ { i }$ $\bar { \{ x _ { p , q } ^ { i } \} } _ { p = 0 , q = 1 } ^ { k , | V _ { p } ( g _ { i } ) | }$ $V _ { p } ( g _ { i } )$ $p$ $g _ { i }$ $g _ { i }$ $\cdot x _ { p , q } ^ { i } = [ f ( g _ { i } ) ] _ { p , q } \in \mathbb { R } ^ { d }$ $v _ { q } \in V _ { p } ( g _ { i } )$ , where $f : \mathcal { G }  \mathbb { R } ^ { d \times \lvert V ( g _ { i } ) \rvert }$ is a function. In the strict case, $f$ should be injective.
+
+In its essence, Def 3.3 requires the node features to be a function of the graph structures, which is sensitive to changes in the graph structures, and in an ideal case, injective to the graph structures (i.e., mapping different graphs to different features). In this way, when the learned graph filters of a transfered GNN is compatible to the structure of $G$ , they are also compatible to the node features of $G$ . As we will explain in Remark 2 of Theorem 3.1, this requirement is also essential for the analysis of EGI transferability which eventually only depends on the structural difference between two graphs.
+
+In practice, commonly used node features like node degrees, PageRank scores [40], spectral embeddings [11], and many pre-computed unsupervised network embeddings [42, 51, 14] are all structure-respecting in nature. However, other commonly used node features like random vectors [68] or uniform vectors [60] are not and thus non-transferable. When raw node attributes are available, they are transferable as long as the concept of homophily [36] applies, which also implies Def 3.3, but we do not have a rigorous analysis on it yet.
+
+Supportive observations. In the fifth and sixth columns in Table 1, where we use same fixed vectors as non-transferable node features to contrast with the first three columns, there is almost no transferability (see $\delta ( a c c . ) )$ for all compared methods when non-transferable features are used, as the performance of trained GNNs are similar to or worse than their untrained baselines. More detailed experiments on different transferable and non-transferable features can be found in Appendix $\ S { \bf C } . 1$ .
+
+With our view of graphs and requirement on node features both established, now we derive the following theorem by characterizing the performance difference of EGI on two graphs based on Eq. 1.
+
+Theorem 3.1 (GNN transferability). Let ${ \cal G } _ { a } = \{ ( g _ { i } , x _ { i } ) \} _ { i = 1 } ^ { n }$ and $G _ { b } = \{ ( g _ { i ^ { \prime } } , x _ { i ^ { \prime } } ) \} _ { i ^ { \prime } = 1 } ^ { m }$ be two graphs, and assume node features are structure-relevant. Consider GCN $\Psi _ { \theta }$ with $k$ layers and $a$ $I$ -hop polynomial filter $\phi$ . With reasonable assumptions on the local spectrum of $G _ { a }$ and $G _ { b }$ , the empirical performance difference of $\Psi _ { \theta }$ evaluated on $\mathcal { L } _ { \mathrm { E G I } }$ satisfies
+
+$$
+| \mathcal { L } _ { \mathrm { E G I } } ( G _ { a } ) - \mathcal { L } _ { \mathrm { E G I } } ( G _ { b } ) | \leq \mathcal { O } \left( \Delta _ { \mathcal { D } } ( G _ { a } , G _ { b } ) + C \right) .
+$$
+
+On the RHS, $C$ is only dependent on the graph encoders and node features, while $\Delta _ { \mathcal { D } } ( G _ { a } , G _ { b } )$ measures the structural difference between the source and target graphs as follows,
+
+$$
+\Delta _ { \mathcal { D } } ( G _ { a } , G _ { b } ) = \tilde { C } \frac { 1 } { n m } \sum _ { i = 1 } ^ { n } \sum _ { i ^ { \prime } = 1 } ^ { m } \lambda _ { \mathrm { m a x } } ( \tilde { L } _ { g _ { i } } - \tilde { L } _ { g _ { i ^ { \prime } } } )
+$$
+
+where $\lambda _ { \operatorname* { m a x } } ( A ) : = \lambda _ { \operatorname* { m a x } } ( A ^ { T } A ) ^ { 1 / 2 }$ , and ${ \tilde { L } } _ { g _ { i } }$ denotes the normalised graph Laplacian of $\tilde { g } _ { i }$ by its in-degree. $\tilde { C }$ is a constant dependant on $\lambda _ { \operatorname* { m a x } } ( \tilde { L } _ { g _ { i } } )$ and $\mathcal { D }$ .
+
+Proof. The full proof is detailed in Appendix $\ S \mathrm { A }$ .
+
+The analysis in Theorem 3.1 naturally instantiates our insight about the correspondence between structural similarity and GNN transferability. It allows us to tell how well an EGI trained on $G _ { a }$ can work on $G _ { b }$ by only checking the local graph Laplacians of $G _ { a }$ and $G _ { b }$ without actually training any model. In particular, we define the EGI gap as $\Delta _ { \mathcal { D } }$ in Eq. 6, as other term $C$ is the same for different methods using same GNN encoder. It can be computed to bound the transferability of EGI regarding its loss difference on the source and target graphs.
+
+Remark 1. Our view of a graph $G$ as samples of $k$ -hop ego-graphs is important, as it allows us to obtain node-wise characterization of GNN similarly as in [55]. It also allows us to set the depth of ego-graphs in the analysis to be the same as the number of GNN layers (k), since the GNN embedding of each node mostly depends on its $k$ -hop ego-graph instead of the whole graph.
+
+Remark 2. For Eq. 1, Def 3.3 ensures the sampling of GNN embedding at a node always corresponds to sampling an ego-graph from $\mathcal { G }$ , which reduces to uniformly sampling from $G = \{ g _ { i } \} _ { i = 1 } ^ { n }$ under the setting of Theorem 3.1. Therefore, the requirement of Def 3.3 in the context of Theorem 3.1 guarantees the analysis to be only depending on the structural information of the graph.
+
+Supportive observations. In Table 1, in the $\bar { d }$ columns, we compute the average structural difference between two Forest-fire graphs $( \Delta _ { \mathcal { D } } ( \mathrm { F } , \mathrm { F } ) )$ and between Barabasi and Forest-fire graphs $\scriptstyle ( \Delta _ { \mathcal { D } } ( \mathbf { B } , \mathrm { F } ) )$ , based on the RHS of Eq. 5. The results validate the topological difference between graphs generated by different random-graph models, while also verifying our view of graph as $\mathbf { k }$ -hop ego-graph samples and the way we propose based on it to characterize structural information of graphs. We further highlight in the $\delta ( \mathrm { a c c } )$ columns the accuracy difference between the GNNs transfered from Forest-fire graphs and Barabasi graphs to Forest-fire graphs. Since Forest-fire graphs are more similar to Forest-fire graphs than Barabasi graphs (as verified in the $\Delta _ { \mathcal { D } }$ columns), we expect $\delta ( \mathrm { a c c . } )$ to be positive and large, indicating more positive transfer between the more similar graphs. Indeed, the behaviors of EGI align well with the expectation, which indicates its well-understood transferability and the utility of our theoretical analysis.
+
+Use cases of Theorem 3.1. Our Theorem 3.1 naturally allows for two practical use cases among many others: point-wise pre-judge and pair-wise pre-selection for EGI pre-training. Suppose we have a target graph $G _ { b }$ which does not have sufficient training labels. In the first setting, we have a single source graph $G _ { a }$ which might be useful for pre-training a GNN to be used on $G _ { b }$ . The EGI gap $\Delta _ { \mathcal { D } } ( G _ { a } , G _ { b } )$ in Eq. 6 can then be computed between $G _ { a }$ and $G _ { b }$ to pre-judge whether such transfer learning would be successful before any actual GNN training (i.e., yes if $\Delta _ { \mathcal { D } } ( G _ { a } , G _ { b } )$ is empirically much smaller than 1.0; no otherwise). In the second setting, we have two or more source graphs $\{ G _ { a } ^ { 1 } , G _ { a } ^ { 2 } , . . . \}$ which might be useful for pre-training the GNN. The EGI gap can then be computed between every pair of $G _ { a } ^ { i }$ and $G _ { b }$ to pre-select the best source graph (i.e., select the one with the least EGI gap).
+
+In practice, the computation of eigenvalues on the small ego-graphs can be rather efficient [2], and we do not need to enumerate all pairs of ego-graphs on two compared graphs especially if the graphs are really large (e.g., with more than a thousand nodes). Instead, we can randomly sample pairs of ego-graphs from the two graphs, update the average difference on-the-fly, and stop when it converges. Suppose we need to sample $M$ pairs of $\mathbf { k }$ -hop ego-graphs to compare two large graphs, and the average size of ego-graphs are $L$ , then the overall complexity of computing Eq. 5 is $\bar { \mathcal { O } } ( \bar { M } L ^ { 2 } )$ , where $M$ is often less than 1K and $L$ less than 50. In Appendix $\ S { \bf C . 4 }$ , we report the approximated $\Delta _ { \mathcal { D } }$ ’s w.r.t. different sampling frequencies, and they are indeed pretty close to the actual value even with smaller sample frequencies, showing the feasible efficiency of computing $\Delta _ { \mathcal { D } }$ through sampling.
+
+Limitations. EGI is designed to account for the structural difference captured by GNNs (i.e., khop ego-graphs). The effectiveness of EGI could be limited if the tasks on target graphs depend on different structural signals. For example, as Eq. 6 is computing the average pairwise distances between the graph Laplacians of local ego-graphs, $\Delta _ { \mathcal { D } }$ is possibly less effective in explicitly capturing global graph properties such as numbers of connected components (CCs). In some specific tasks (such as counting CCs or community detection) where such properties become the key factors, $\Delta _ { \mathcal { D } }$ may fail to predict the transferability of GNNs.
+
+# 4 Real Data Experiments
+
+Baselines. We compare the proposed model against existing self-supervised GNNs and pre-training GNN algorithms. To exclude the impact of different GNN encoders $\Psi$ on transferability, we always use the same encoder architecture for all compared methods (i.e., GIN [60] for direct-transfering experiments, GCN [29] for transfering with fine-tuning).
+
+The self-supervised GNN baselines are GVAE [28], DGI [54] and two latest mutual information estimation methods GMI [41] and MVC [17]. As for pre-training GNN algorithms, MaskGNN and ContextPredGNN are two node-level pre-training models proposed in [21] Besides, Structural Pre-train [23] also conducts unsupervised node-level pre-training with structural features like node degrees and clustering coefficients.
+
+Table 1: Synthetic experiments of identifying structural equivalent nodes. We randomly generate 40 graphs with the Forest-fire model (F) [32] and 40 graphs with the Barabasi model (B) [1], The GNN model is GIN [60] with random parameters (baseline with only the neighborhood aggregation function), VGAE[28], DGI [54], and EGI with GIN encoder. We train VGAE, DGI and EGI on one graph from either set (F and B), and test them on the rest of Forest-fire graphs (F). Transferable feature is node degree one-hot encoding and non-transferable feature is uniform vectors. More details about the results and dataset can be found in Appendix $\ S { \bf C } . 1$   
+
+<table><tr><td rowspan="2">Method</td><td colspan="3">transferable features</td><td colspan="3">non-transferable feature</td><td rowspan="2">structural difference △D(F,F)</td><td rowspan="2">△D(B,F)</td></tr><tr><td>F-F</td><td>B-F</td><td>8(acc.)</td><td>F-F</td><td>B-F</td><td>8(acc.)</td></tr><tr><td>GIN (untrained)</td><td>0.572</td><td>0.572</td><td>/</td><td>0.358</td><td>0.358</td><td>/</td><td></td><td></td></tr><tr><td>VGAE (GIN)</td><td>0.498</td><td>0.432</td><td>+0.066</td><td>0.240</td><td>0.239</td><td>0.001</td><td></td><td></td></tr><tr><td>DGI (GIN)</td><td>0.578</td><td>0.591</td><td>-0.013</td><td>0.394</td><td>0.213</td><td>+0.181</td><td>0.752</td><td>0.883</td></tr><tr><td>EGI (GIN)</td><td>0.710</td><td>0.616</td><td>+0.094</td><td>0.376</td><td>0.346</td><td>+0.03</td><td></td><td></td></tr></table>
+
+Experimental Settings. The main hyperparameter $k$ is set 2 in EGI as a common practice. We use Adam [27] as optimizer and learning rate is 0.01. We provide the experimental result with varying $k$ in the Appendix $\ S { \bf C . 4 }$ . All baselines are set with the default parameters. Our experiments were run on an AWS g4dn.2xlarge machine with 1 Nvidia T4 GPU. By default, we use node degree one-hot encoding as the transferable feature across all different graphs. As stated before, other transferable features like spectral and other pre-computed node embeddings are also applicable. We focus on the setting where the downstream tasks on target graphs are unspecified but assumed to be structure-relevant, and thus pre-train the GNNs on source graphs in an unsupervised fashion.4 In terms of evaluation, we design two realistic experimental settings: (1) Direct-transfering on the more structure-relevant task of role identification without given node features to directly evaluate the utility and transferability of EGI. (2) Few-shot learning on relation prediction with task-specific node features to evaluate the generalization ability of EGI.
+
+# 4.1 Direct-transfering on role identification
+
+First, we use the role identification without node features in a direct-transfering setting as a reliable proxy to evaluate transfer learning performance regarding different pre-training objectives. Role in a network is defined as nodes with similar structural behaviors, such as clique members, hub and bridge [19]. Across graphs in the same domain, we assume the definition of role to be consistent, and the task of role identification is highly structure-relevant, which can directly reflect the transferability of different methods and allows us to conduct the analysis according to Theorem 3.1. Upon convergence of pre-training each model on the source graphs, we directly apply them to the target graphs and further train a multi-layer perceptron (MLP) upon their outputs. The GNN parameters are frozen during the MLP training. We refer to this strategy as direct-transfering since there is no fine-tuning of the models after transfering to the target graphs.
+
+We use two real-world network datasets with role-based node labels: (1) Airport [45] contains three networks from different regions– Brazil, USA and Europe. Each node is an airport and each link is the flight between airports. The airports are assigned with external labels based on their level of popularity. (2) Gene [68] contains the gene interactions regarding 50 different cancers. Each gene has a binary label indicating whether it is a transcription factor. More details about the results and dataset can be found in Appendix C.2.
+
+The experimental setup on the Airport dataset closely resembles that of our synthetic experiments in Table 1, but with real data and more detailed comparisons. We train all models (except for the untrained ones) on the Europe network, and test them on all three networks. The results are presented in Table 2. We notice that the node degree features themselves (with MLP) show reasonable performance in all three networks, which is not surprising since the popularity-based airport role labels are highly relevant to node degrees. The untrained GIN encoder yields a significant margin over just node features, as GNN encoder incorporates structural information to node representations.
+
+While training of the DGI can further improve the performance on the source graph, EGI shows the best performance there with the structure-relevant node degree features, corroborating the claimed effectiveness of EGI in capturing the essential graph information (i.e. recover the $\mathbf { k }$ -hop ego-graph distributions) as we stress in $\ S 3$ .
+
+When transfering the models to USA and Brazil networks, EGI further achieves the best performance compared with all baselines when structure relevant features are used (64.55 and 73.15), which reflects the most significant positive transfer. Interestingly, direct application of GVAE, DGI and MVC that do not capture the input k-hop graph jointly, leads to rather limited and even negative transferrability (through comparison against the untrained GIN encoders). The recently proposed transfer learning frameworks for GNN like MaskGNN and Structural Pre-train are able to mitigate negative transfer to some extent, but their performances are still inferior to EGI. We believe this is because their models are prone to learn the graph-specific information that is less transferable across different graphs. GMI is also known to capture the graph structure and node features, so it achieves second best result comparing with EGI.
+
+Similarly as in Table 1, we also compute the structural differences among three networks w.r.t. the EGI gap in Eq. 6. The structural difference is 0.869 between the Europe and USA networks, and 0.851 between the Europe and Brazil datasets, which are pretty close. Consequently, the transferability of EGI regarding its performance gain over the untrained GIN baseline is $4 . 8 \%$ on the USA network and $4 . 4 \%$ on the Brazil network, which are also close. Such observations again align well with our conclusion in Theorem 3.1 that the transferability of EGI is closely related to the structural differences between source and target graphs.
+
+Table 2: Results of role identification with direct-transfering on the Airport dataset. We report mean and standard deviation over 100 runs. The scores marked with ∗∗ passed t-test with $p < 0 . 0 1$ over the second runners.   
+
+<table><tr><td>Method</td><td colspan="3">Airport [45]</td></tr><tr><td></td><td>Europe</td><td>USA</td><td>Brazil</td></tr><tr><td>features</td><td>0.528±0.052</td><td>0.557±0.028</td><td>0.671±0.089</td></tr><tr><td>GIN (random-init)</td><td>0.558±0.050</td><td>0.616±0.030</td><td>0.700±0.082</td></tr><tr><td>GVAE(GIN) [28]</td><td>0.539±0.053</td><td>0.555±0.029</td><td>0.663±0.089</td></tr><tr><td>DGI(GIN） [54]</td><td>0.578±0.050</td><td>0.549±0.028</td><td>0.673±0.084</td></tr><tr><td>Mask-GIN [21]</td><td>0.564±0.053</td><td>0.608±0.027</td><td>0.667±0.073</td></tr><tr><td>ContextPred-GIN [21]</td><td>0.527±0.048</td><td>0.504±0.030</td><td>0.621±0.078</td></tr><tr><td>Structural Pre-train [23]</td><td>0.560±0.050</td><td>0.622±0.030</td><td>0.688±0.082</td></tr><tr><td>MVC[17]</td><td>0.532±0.050</td><td>0.597±0.030</td><td>0.661±0.093</td></tr><tr><td>GMI [41]</td><td>0.581±0.054</td><td>0.593±0.031</td><td>0.731±0.107</td></tr><tr><td>EGI (GIN)</td><td>0.592±0.046**</td><td>0.646±0.029 **</td><td>0.732±0.078</td></tr></table>
+
+On the Gene dataset, with more graphs available, we focus on EGI to further validate the utility of Eq. 5 in Theorem 3.1, regarding the connection between the EGI gap (Eq. 6) and the performance gap (micro-F1) of EGI on them. Due to severe label imbalance that removes the performance gaps, we only use the seven brain cancer networks that have a more consistent balance of labels. As shown in Figure 3, we train EGI on one graph and test it on the other graphs. The $x$ -axis shows the EGI gap, and $y$ -axis shows the improvement on micro-F1 compared with an untrained GIN. The negative correlation between two quantities is obvious. Specifically, when the structural difference is smaller than 1, positive transfer is observed (upper left area) as the performance of transferred EGI is better than untrained GIN, and when the structural difference becomes large $( > 1 )$ , negative transfer is observed. We also notice a similar graph pattern, i.e. single dense cluster, between source graph and positive transferred target graph $G _ { 2 }$ .
+
+# 4.2 Few-shot learning on relation prediction
+
+Here we evaluate EGI in the more generalized and practical setting of few-shot learning on the less structure-relevant task of relation prediction, with task-specific node features and fine-tuning. The source graph contains a cleaned full dump of 579K entities from YAGO [49], and we investigate 20- shot relation prediction on a target graph with 24 relation types, which is a sub-graph of 115K entities sampled from the same dump. In post-fine-tuning, the models are pre-trained with an unsupervised loss on the source graph and fine-tuned with the task-specific loss on the target graph. In joint-finetuning, the same pre-trained models are jointly optimized w.r.t. the unsupervised pre-training loss and task-specific fine-tuning loss on the target graph. In Table 3, we observe most of the existing models fail to transfer across pre-training and fine-tuning tasks, especially in the joint-fine-tuning setting. In particular, both Mask-GIN and ContextPred-GIN rely a lot on task-specific fine-tuning, while EGI focuses on the capturing of similar ego-graph structures that are transferable across graphs. The mutual information based method GMI also demonstrates considerable transferability and we believe the ability to capture the graph structure is the key to the transferability. As a consequence, EGI significantly outperforms all compared methods in both settings. More detailed statistics and running time are in Appendix $\ S { \bf C } . 3$ .
+
+![](images/179fd55c88fad38b5d7c38fd504139f6a34d959c09babb9dae016dffbc51c9a9.jpg)  
+Figure 3: Transfer learning performance of role identification on the Gene dataset. We visualize the source graph $G _ { 0 }$ and two example target graphs that are relatively more different $\left( G _ { 4 } \right)$ or similar $\left( G _ { 2 } \right)$ with $G _ { 0 }$ .
+
+Table 3: Performance of few-shot relation prediction on YAGO. The scores marked with ∗∗ passed t-test with $p < 0 . 0 1$ over the second best results.   
+
+<table><tr><td rowspan="2">Method</td><td colspan="2">post-fine-tuning</td><td colspan="2"> joint-fine-tuning</td></tr><tr><td>AUROC</td><td>MRR</td><td>AUROC</td><td>MRR</td></tr><tr><td>No pre-train</td><td>0.687±0.002</td><td>0.596±0.003</td><td>N.A.</td><td>N.A.</td></tr><tr><td>GVAE</td><td>0.701±0.003</td><td>0.601±0.007</td><td>0.679±0.004</td><td>0.568±0.008</td></tr><tr><td>DGI</td><td>0.689±0.011</td><td>0.586±0.025</td><td>0.688±0.012</td><td>0.537±0.023</td></tr><tr><td>MaskGNN</td><td>0.713±0.009</td><td>0.631±0.015</td><td>0.712±0.005</td><td>0.560±0.010</td></tr><tr><td>ContextPredGNN</td><td>0.692±0.030</td><td>0.662±0.030</td><td>0.705±0.011</td><td>0.575±0.021</td></tr><tr><td>GMI</td><td>0.728±0.005</td><td>0.625±0.009</td><td>0.721±0.007</td><td>0.643±0.011</td></tr><tr><td>Structural Pre-train</td><td>OOM</td><td>OOM</td><td>OOM</td><td>OOM</td></tr><tr><td>MVC</td><td>OOM</td><td>OOM</td><td>OOM</td><td>OOM</td></tr><tr><td>EGI</td><td>0.739± 0.009**</td><td>0.670±0.014</td><td>0.787 ± 0.011**</td><td>0.729 ± 0.016**</td></tr></table>
+
+# 5 Conclusion
+
+To the best of our knowledge, this is the first research effort towards establishing a theoretically grounded framework to analyze GNN transferability, which we also demonstrate to be practically useful for guiding the design and conduct of transfer learning with GNNs. For future work, it is intriguing to further strengthen the bound with relaxed assumptions, rigorously extend it to the more complicated and less restricted settings regarding node features and downstream tasks, as well as analyze and improve the proposed framework over more transfer learning scenarios and datasets. It is also important to protect the privacy of pre-training data to avoid potential negative societal impacts.
+
+# Acknowledgments and Disclosure of Funding
+
+Research was supported in part by US DARPA KAIROS Program No. FA8750-19-2-1004, SocialSim Program No. W911NF-17-C-0099, and INCAS Program No. HR001121C0165, National Science Foundation IIS-19-56151, IIS-17-41317, and IIS 17-04532, and the Molecule Maker Lab Institute: An AI Research Institutes program supported by NSF under Award No. 2019897. Chao Zhang is supported NSF IIS-2008334, IIS-2106961, and ONR MURI N00014-17-1-2656. We would like to thank AWS Machine Learning Research Awards program for providing computational resources for the experiments in this paper. This work is also partially supported by the internal funding and GPU servers provided by the Computer Science Department of Emory University. Any opinions, findings, and conclusions or recommendations expressed herein are those of the authors and do not necessarily represent the views, either expressed or implied, of DARPA or the U.S. Government.
+
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parse/train/CzVPfeqPOBu/CzVPfeqPOBu_content_list.json

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+    {
+        "type": "text",
+        "text": "Transfer Learning of Graph Neural Networks with Ego-graph Information Maximization ",
+        "text_level": 1,
+        "bbox": [
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+            122,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Qi Zhu1∗, Carl Yang2∗, Yidan $\\mathbf { X } \\mathbf { u } ^ { 3 }$ , Haonan Wang1, Chao Zhang4, Jiawei Han1 ",
+        "bbox": [
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+            224,
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1University of Illinois Urbana-Champaign, 2Emory University, 3University of Washington, 4Georgia Institute of Technology 1{qiz3,haonan3,hanj}@illinois.edu, 2j.carlyang@emory.edu, 3yx2516@uw.edu, 4chaozhang@gatech.edu ",
+        "bbox": [
+            258,
+            241,
+            741,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Abstract ",
+        "text_level": 1,
+        "bbox": [
+            462,
+            333,
+            535,
+            349
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Graph neural networks (GNNs) have achieved superior performance in various applications, but training dedicated GNNs can be costly for large-scale graphs. Some recent work started to study the pre-training of GNNs. However, none of them provide theoretical insights into the design of their frameworks, or clear requirements and guarantees towards their transferability. In this work, we establish a theoretically grounded and practically useful framework for the transfer learning of GNNs. Firstly, we propose a novel view towards the essential graph information and advocate the capturing of it as the goal of transferable GNN training, which motivates the design of EGI (Ego-Graph Information maximization) to analytically achieve this goal. Secondly, when node features are structure-relevant, we conduct an analysis of EGI transferability regarding the difference between the local graph Laplacians of the source and target graphs. We conduct controlled synthetic experiments to directly justify our theoretical conclusions. Comprehensive experiments on two real-world network datasets show consistent results in the analyzed setting of direct-transfering, while those on large-scale knowledge graphs show promising results in the more practical setting of transfering with fine-tuning.1 ",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1 Introduction ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            614,
+            310,
+            631
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Graph neural networks (GNNs) have been intensively studied recently [29, 26, 39, 68], due to their established performance towards various real-world tasks [15, 69, 53], as well as close connections to spectral graph theory [12, 9, 16]. While most GNN architectures are not very complicated, the training of GNNs can still be costly regarding both memory and computation resources on real-world large-scale graphs [10, 63]. Moreover, it is intriguing to transfer learned structural information across different graphs and even domains in settings like few-shot learning [56, 44, 25]. Therefore, several very recent studies have been conducted on the transferability of GNNs [21, 23, 22, 59, 31, 3, 47]. However, it is unclear in what situations the models will excel or fail especially when the pre-training and fine-tuning tasks are different. To provide rigorous analysis and guarantee on the transferability of GNNs, we focus on the setting of direct-transfering between the source and target graphs, under an analogous setting of “domain adaptation” [7, 59]. ",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "In this work, we establish a theoretically grounded framework for the transfer learning of GNNs, and leverage it to design a practically transferable GNN model. Figure 1 gives an overview of our framework. It is based on a novel view of a graph as samples from the joint distribution of its $\\mathbf { k }$ -hop ego-graph structures and node features, which allows us to define graph information and similarity, so as to analyze GNN transferability (§3). This view motivates us to design EGI, a novel GNN training objective based on ego-graph information maximization, which is effective in capturing the graph information as we define (§3.1). Then we further specify the requirement on transferable node features and analyze the transferability of EGI that is dependent on the local graph Laplacians of source and target graphs (§3.2). ",
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+    },
+    {
+        "type": "image",
+        "img_path": "images/a75bc7d9606ed20d147da05c975e5dc6b5ac8fd6fcd0435db56e2c88a14c0797.jpg",
+        "image_caption": [
+            "Figure 1: Overview of our GNN transfer learning framework: (1) we represent the toy graph as a combination of its 1-hop ego-graph and node feature distributions; (2) we design a transferable GNN regarding the capturing of such essential graph information; (3) we establish a rigorous guarantee of GNN transferability based on the node feature requirement and graph structure difference. "
+        ],
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+    {
+        "type": "text",
+        "text": "All of our theoretical conclusions have been directly validated through controlled synthetic experiments (Table 1), where we use structural-equivalent role identification in an direct-transfering setting to analyze the impacts of different model designs, node features and source-target structure similarities on GNN transferability. In $\\ S 4$ , we conduct real-world experiments on multiple publicly available network datasets. On the Airport and Gene graphs (§4.1), we closely follow the settings of our synthetic experiments and observe consistent but more detailed results supporting the design of EGI and the utility of our theoretical analysis. On the YAGO graphs (§4.2), we further evaluate EGI on the more generalized and practical setting of transfer learning with task-specific fine-tuning. We find our theoretical insights still indicative in such scenarios, where EGI consistently outperforms state-of-the-art GNN representation and transfer learning frameworks with significant margins. ",
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+    {
+        "type": "text",
+        "text": "2 Related Work ",
+        "text_level": 1,
+        "bbox": [
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+            617,
+            321,
+            633
+        ],
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+    },
+    {
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+        "text": "Representation learning on graphs has been studied for decades, with earlier spectral-based methods [6, 46, 52] theoretically grounded but hardly scaling up to graphs with over a thousand of nodes. With the emergence of neural networks, unsupervised network embedding methods based on the Skip-gram objective [37] have replenished the field [51, 14, 42, 45, 66, 62, 65]. Equipped with efficient structural sampling (random walk, neighborhood, etc.) and negative sampling schemes, these methods are easily parallelizable and scalable to graphs with thousands to millions of nodes. However, these models are essentially transductive as they compute fully parameterized embeddings only for nodes seen during training, which are impossible to be transfered to unseen graphs. ",
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+    {
+        "type": "text",
+        "text": "More recently, researchers introduce the family of graph neural networks (GNNs) that are capable of inductive learning and generalizing to unseen nodes given meaningful node features [29, 12, 15, 67]. Yet, most existing GNNs require task-specific labels for training in a semi-supervised fashion to achieve satisfactory performance [29, 15, 53, 64], and their usage is limited to single graphs where the downstream task is fixed. To this end, several unsupervised GNNs are presented, such as the auto-encoder-based ones like VGAE [28] and GNFs [35], as well as the deep-infomax-based ones like DGI [54] and InfoGraph [50]. Their potential in the transfer learning of GNN remains unclear when the node features and link structures vary across different graphs. ",
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+        "type": "text",
+        "text": "Although the architectures of popular GNNs such as GCN [29] may not be very complicated compared with heavy vision and language models, training a dedicated GNN for each graph can still be cumbersome [10, 63]. Moreover, as pre-training neural networks are proven to be successful in other domains [13, 18], the idea is intriguing to transfer well-trained GNNs from relevant source graphs to improve the modeling of target graphs or enable few-shot learning [59, 31, 3] when labeled data are scarce. In light of this, pioneering works have studied both generative [22] and discriminative [21, 23] GNN pre-training schemes. Though Graph Contrastive Coding [43] shares the most similar view towards graph structures as us, it utilizes contrastive learning across all graphs instead of focusing on the transfer learning between any specific pairs. On the other hand, unsupervised domain adaptive GCNs [59] study the domain adaption problem only when the source and target tasks are homogeneous. ",
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+        "type": "text",
+        "text": "",
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+        "type": "text",
+        "text": "Most previous pre-training and self-supervised GNNs lack a rigorous analysis towards their transferability and thus have unpredictable effectiveness. The only existing theoretical work on GNN transferability studies the performance of GNNs across different permutations of a single original graph [33, 34] and the tradeoff between discriminability and transferability of GNNs [47]. We, instead, are the first to rigorously study the more practical setting of transferring GNNs across pairs of different source and target graphs. ",
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+        "type": "text",
+        "text": "3 Transferable Graph Neural Networks ",
+        "text_level": 1,
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+        "text": "In this paper, we design a more transferable training objective for GNN (EGI) based on our novel view of essential graph information (§3.1). We then analyze its transferability as the gap between its abilities to model the source and target graphs, based on their local graph Laplacians (§3.2). ",
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+        "type": "text",
+        "text": "Based on the connection between GNN and spectral graph theory [29], we describe the output of a GNN as a combination of its input node features $X$ , fixed graph Laplacian $L$ and learnable graph filters $\\Psi$ . The goal of training a GNN is then to improve its utility by learning the graph filters that are compatible with the other two components towards specific tasks. ",
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+        "type": "text",
+        "text": "In the graph transfer learning setting where downstream tasks are often unknown during pre-training, we argue that the general utility of a GNN should be optimized and quantified w.r.t. its ability of capturing the essential graph information in terms of the joint distribution of its topology structures and node features, which motivates us to design a novel ego-graph information maximization model (EGI) (§3.1). The general transferability of a GNN is then quantified by the gap between its abilities to model the source and target graphs. Under reasonable requirements such as using structurerespecting node features as the GNN input, we analyze this gap for EGI based on the structural difference between two graphs w.r.t. their local graph Laplacians (§3.2). ",
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+        "type": "text",
+        "text": "3.1 Transferable GNN via Ego-graph Information Maximization ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "In this work, we focus on the direct-transfering setting where a GNN is pre-trained on a source graph $G _ { a }$ in an unsupervised fashion and applied on a target graph $G _ { b }$ without fine-tuning.2 Consider a graph $G = \\{ V , E \\}$ , where the set of nodes $V$ are associated with certain features $X$ and the set of edges $E$ form graph structures. Intuitively, the transfer learning will be successful only if both the features and structures of $G _ { a }$ and $G _ { b }$ are similar in some ways, so that the graph filters of a GNN learned on $G _ { a }$ are compatible with the features and structures of $G _ { b }$ . ",
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+        "type": "text",
+        "text": "Graph kernels [57, 8, 30, 38] are well-known for their capability of measuring similarity between pair of graphs. Motivated by $\\mathrm { k }$ -hop subgraph kernels [4], we introduce a novel view of a graph as samples from the joint distribution of its $k$ -hop ego-graph structures and node features. Since GNN essentially encodes such $\\mathbf { k }$ -hop ego graph samples, this view allows us to give concrete definitions towards structural information of graphs in the transfer learning setting, which facilitates the measuring of similarity (difference) among graphs. Yet, none of the existing GNN training objectives are capable of recovering such distributional signals of ego graphs. To this end, we design $E g o$ -Graph Information maximization (EGI), which alternatively reconstructs the $\\mathbf { k }$ -hop ego-graph of each center node via mutual information maximization [20]. ",
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+        "type": "text",
+        "text": "Definition 3.1 (K-hop ego-graph). We call a graph $g _ { i } = \\{ V ( g _ { i } ) , E ( g _ { i } ) \\}$ a $k$ -hop ego-graph centered at node $v _ { i }$ if it has a $k$ -layer centroid expansion [4] such that the greatest distance between $v _ { i }$ and any other nodes in the ego-graph is $k ,$ i.e. $\\forall v _ { j } \\in V ( g _ { i } ) , | d ( v _ { i } , v _ { j } ) | \\leq k$ , where $d ( v _ { i } , v _ { j } )$ is the graph distance between $v _ { i }$ and $v _ { j }$ . ",
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+        "type": "text",
+        "text": "",
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+        "type": "text",
+        "text": "In this paper, we use directed $\\mathrm { k }$ -hop ego-graph and its direction is decided by whether it is composed of incoming or outgoing edges to the center node, i.e., $g _ { i }$ and $\\tilde { g _ { i } }$ . The results apply trivially to undirected graphs with $g _ { i } = { \\tilde { g } } _ { i }$ . ",
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+    {
+        "type": "text",
+        "text": "Definition 3.2 (Structural information). Let $\\mathcal { G }$ be a topological space of sub-graphs, we view a graph $G$ as samples of $k$ -hop ego-graphs $\\{ g _ { i } \\} _ { i = 1 } ^ { n }$ drawn i.i.d. from $\\mathcal { G }$ with probability $\\mu _ { ; }$ , i.e., $g _ { i } \\stackrel { \\scriptscriptstyle 1 . 1 . 0 . } { \\sim } \\mu \\forall i = 1 , \\cdot \\cdot \\cdot , n$ . The structural information of $G$ is then defined to be the set of $k$ -hop ego-graphs of $\\{ g _ { i } \\} _ { i = 1 } ^ { n }$ and their empirical distribution. ",
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+        "type": "text",
+        "text": "As shown in Figure 1, three graphs $G _ { 0 }$ , $G _ { 1 }$ and $G _ { 2 }$ are characterized by a set of 1-hop ego-graphs and their empirical distributions, which allows us to quantify the structural similarity among graphs as shown in $\\ S 3 . 2$ (i.e., $G _ { 0 }$ is more similar to $G _ { 1 }$ than $G _ { 2 }$ under such characterization). In practice, the nodes in a graph $G$ are characterized not only by their $\\mathbf { k }$ -hop ego-graph structures but also their associated node features. Therefore, $G$ should be regarded as samples $\\{ ( g _ { i } , x _ { i } ) \\}$ drawn from the joint distribution $\\mathbb { P }$ on the product space of $\\mathcal { G }$ and a node feature space $\\mathcal { X }$ . ",
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+    {
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+        "img_path": "images/944c7f1b43a9719fbce6b9550bca8c7dabe51127e2788d932f346c930653c8d4.jpg",
+        "image_caption": [
+            "Figure 2: The overall EGI training framework. "
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+        "image_footnote": [],
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+        "text": "Ego-Graph Information Maximization. Given a set of ego-graphs $\\{ ( g _ { i } , x _ { i } ) \\} _ { i }$ drawn from an empirical joint distribution $( g _ { i } , x _ { i } ) \\sim \\mathbb { P }$ . We aim to train an GNN encoder $\\Psi$ to maximize the mutual informaion (MI $( g _ { i } , \\Psi ( g _ { i } , x _ { i } ) )$ ) between the defined structural information $g _ { i } { } ^ { 3 }$ (i.e. k-hop ego-graph) and node embedding $z _ { i } ~ = ~ \\Psi ( g _ { i } , x _ { i } )$ . To maximize the MI, another discriminator $\\mathcal { D } ( g _ { i } , z _ { i } ) : E ( g _ { i } ) \\times z _ { i }  \\mathbb { R } ^ { + }$ is introduced to compute the probability of an edge $e$ belongs to the given ego-graph $g _ { i }$ . We use the Jensen-Shannon MI estimator [20] in the EGI objective, ",
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+        "type": "equation",
+        "img_path": "images/9b85a2539e90bb6fa854d183774a935f01848c5777f1aafc853a6afa7499816b.jpg",
+        "text": "$$\n\\mathcal { L } _ { \\mathrm { E G I } } = - \\mathbf { M } \\mathbf { I } ^ { \\mathrm { ( J S D ) } } \\left( \\boldsymbol { \\mathcal { G } } , \\boldsymbol { \\Psi } \\right) = \\frac { 1 } { N } \\sum _ { i = 1 } ^ { N } \\left[ \\mathsf { s p } \\left( \\mathcal { D } ( g _ { i } , z _ { i } ^ { \\prime } ) \\right) + \\mathsf { s p } \\left( - \\mathcal { D } ( g _ { i } , z _ { i } ) \\right) \\right] ,\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where $\\operatorname { s p } ( x ) = \\log ( 1 + e ^ { x } )$ is the softplus function and $( g _ { i } , z _ { i } ^ { \\prime } )$ is randomly drawn from the product of marginal distributions, i.e. $z _ { i } ^ { \\prime } = \\Psi ( g _ { i ^ { \\prime } } , x _ { i ^ { \\prime } } ) , ( g _ { i ^ { \\prime } } , x _ { i ^ { \\prime } } ) \\sim \\mathbb { P } , i ^ { \\prime } \\neq i$ . In general, we can also randomly draw negative $g _ { i } ^ { \\prime }$ in the topological space, while enumerating all possible graphs $g _ { i ^ { \\prime } }$ leads to high computation cost. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In Eq. 1, the computation of $\\mathcal { D }$ on $E ( g _ { i } )$ depends on the node orders. Following the common practice in graph generation [70], we characterize the decision process of $\\mathcal { D }$ with a fixed graph ordering, i.e., the BFS-ordering $\\pi$ over edges $E ( g _ { i } )$ . $\\mathcal { D } = f \\circ \\Phi$ is composed by another GNN encoder $\\Phi$ and scoring function $f$ over an edge sequence $E ^ { \\pi } : \\{ e _ { 1 } , e _ { 2 } , . . . , e _ { n } \\}$ , which makes predictions on the BFS-ordered edges. ",
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+        "type": "text",
+        "text": "Recall our previous definition on the direction of $\\mathrm { k }$ -hop ego-graph, the center node encoder $\\Psi$ receives pairs of $( g _ { i } , x _ { i } )$ while the neighbor node encoder $\\Phi$ in discriminator $\\mathcal { D }$ receives $( \\tilde { g } _ { i } , x _ { i } )$ . Both encoders are parameterized as GNNs, ",
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+        "img_path": "images/8dc87e421fca6094578e2af76e3b4189402d9e4b534ab1acf2d3077008176c89.jpg",
+        "text": "$$\n\\Psi ( g _ { i } , x _ { i } ) = { \\bf G } { \\bf N } \\mathrm { N } _ { \\Psi } ( A _ { i } , X _ { i } ) , \\Phi ( \\tilde { g _ { i } } , x _ { i } ) = { \\bf G } { \\bf N } \\mathrm { N } _ { \\Phi } ( A _ { i } ^ { \\prime } , X _ { i } ) ,\n$$",
+        "text_format": "latex",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "where $A _ { i } , A _ { i } ^ { \\prime }$ is the adjacency matrix with self-loops of $g _ { i }$ and $\\tilde { g _ { i } }$ , respectively. The self-loops are added following the common design of GNNs, which allows the convolutional node embeddings to always incorporate the influence of the center node. $A _ { i } = A _ { i } ^ { \\prime \\intercal }$ . The output of $\\Psi$ , i.e., $z _ { i } \\in \\mathbb { R } ^ { n }$ , is the center node embedding, while $\\Phi$ outputs representation $H \\in \\mathbb { R } ^ { | g _ { i } | \\times n }$ for neighbor nodes in the ego-graph. ",
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+    {
+        "type": "text",
+        "text": "Once node representation $H$ is computed, we now describe the scoring function $f$ . For each of the node pair $\\bar { ( } p , q ) \\in E ^ { \\pi }$ , $h _ { p }$ is the source node representation from $\\Phi$ , $x _ { q }$ is the destination node features. The scoring function is, ",
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+    {
+        "type": "equation",
+        "img_path": "images/73423d19b1a147a869c46d25f1b12b652725dd1dc00c2f60da4eb5e8c83082c7.jpg",
+        "text": "$$\n\\begin{array} { r } { f ( h _ { p } , x _ { q } , z _ { i } ) = \\sigma \\left( U ^ { T } \\cdot \\tau \\left( W ^ { T } [ h _ { p } | | x _ { q } | | z _ { i } ] \\right) \\right) , } \\end{array}\n$$",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "where $\\sigma$ and $\\tau$ are Sigmoid and ReLU activation functions. Thus, the discriminator $\\mathcal { D }$ is asked to distinguish a positive $\\left( ( p , q ) , z _ { i } \\right)$ and negative pair $( ( p , q ) , z _ { i } ^ { \\prime } ) )$ for each edge in $g _ { i }$ . ",
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+    {
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+        "img_path": "images/cbe2168eda7a3313b0f1af526b528bae1125010523581f7902097aab7b326df8.jpg",
+        "text": "$$\n\\mathcal { D } ( g _ { i } , z _ { i } ) = \\sum _ { ( p , q ) \\in E ^ { \\pi } } \\log f ( h _ { p } , x _ { q } , z _ { i } ) , \\mathcal { D } ( g _ { i } , z _ { i } ^ { \\prime } ) = \\sum _ { ( p , q ) } ^ { E ^ { \\pi } } \\log f ( h _ { p } , x _ { q } , z _ { i } ^ { \\prime } ) .\n$$",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "There are two types of edges $( p , q )$ in our consideration of node orders, type-a - the edges across different hops (from the center node), and type- $^ { b }$ - the edges within the same hop (from the center node). The aforementioned BFS-based node ordering guarantees that Eq. 3 is sensitive to the ordering of type-a edges, and invariant to the ordering of type- $\\mathbf { \\delta } .$ edges, which is consistent with the requirement of our theoretical analysis on $\\Delta _ { \\mathcal { D } }$ . Due to the fact that the output of a $\\mathbf { k }$ -layer GNN only depends on a $\\mathbf { k }$ -hop ego-graph for both encoders $\\Psi$ and $\\Phi$ , EGI can be trained in parallel by sampling batches of $g _ { i }$ ’s. Besides, the training objective of EGI is transferable as long as $( g _ { i } , x _ { i } )$ across source graph $G _ { a }$ and $G _ { b }$ satisfies the conditions given in $\\ S 3 . 2$ . More model details in Appendix $\\ S _ { \\mathbf { B } }$ and source code in the Supplementary Materials. ",
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+    {
+        "type": "text",
+        "text": "Connection with existing work. To provide more insights into the EGI objective, we also present it as a dual problem of ego-graph reconstruction. Recall our definition of ego-graph mutual information $\\mathbf { M I } ( g _ { i } , \\Psi ( g _ { i } , x _ { i } ) )$ . It can be related to an ego-graph reconstruction loss $R { \\big ( } g _ { i } | \\Psi { \\big ( } g _ { i } , x _ { i } ) { \\big ) }$ as ",
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+        "text": "$$\n\\operatorname* { m a x } \\mathbf { M } [ ( g _ { i } , \\Psi ( g _ { i } , x _ { i } ) ) = H ( g _ { i } ) - H ( g _ { i } | \\Psi ( g _ { i } , x _ { i } ) ) \\leq H ( g _ { i } ) - R ( g _ { i } | \\Psi ( g _ { i } , x _ { i } ) ) .\n$$",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "When EGI is maximizing the mutual information, it simultaneously minimizes the upper error bound of reconstructing an ego-graph $g _ { i }$ . In this view, the key difference between EGI and VGAE [28] is they assume each edge in a graph to be observed independently during the reconstruction. While in EGI, edges in an ego-graph are observed jointly during the GNN decoding. Moreover, existing mutual information based GNNs such as DGI [54] and GMI [41] explicitly measure the mutual information between node features $x$ and GNN output $\\Psi$ . In this way, they tend to capture node features instead of graph structures, which we deem more essential in graph transfer learning as discussed in $\\ S 3 . 2$ . ",
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+        "type": "text",
+        "text": "Use cases of EGI framework. In this paper, we focus on the classical domain adaption (directtransferring) setting [7], where no target domain labels are available and transferability is measured by the performance discrepancy without fine-tuning. In this setting, the transferability of EGI is theoretically guaranteed by Theorem 3.1. In $\\ S 4 . 1$ , we validated this with the airport datasets. Beyond direct-transferring, EGI is also useful in the more generalized and practical setting of transfer learning with fine-tuning, which we introduced in $\\ S 4 . 2$ and validated with the YAGO datasets. In this setting, the transferability of EGI is not rigorously studied yet, but is empirically shown promising. ",
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+    {
+        "type": "text",
+        "text": "Supportive observations. In the first three columns of our synthetic experimental results (Table 1), in both cases of transfering GNNs between similar graphs (F-F) and dissimilar graphs (B-F), EGI significantly outperforms all competitors when using node degree one-hot encoding as transferable node features. In particular, the performance gains over the untrained GIN show the effectiveness of training and transfering, and our gains are always larger than the two state-of-the-art unsupervised GNNs. Such results clearly indicate advantageous structure preserving capability and transferability of EGI. ",
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+    {
+        "type": "text",
+        "text": "3.2 Transferability analysis based on local graph Laplacians ",
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+        "type": "text",
+        "text": "We now study the transferability of a GNN (in particular, with the training objective of ${ \\mathcal { L } } _ { \\mathrm { E G I } } ,$ ) between the source graph $G _ { a }$ and target graph $G _ { b }$ based on their graph similarity. We firstly establish the requirement towards node features, under which we then focus on analyzing the transferability of EGI w.r.t. the structural information of $G _ { a }$ and $G _ { b }$ . ",
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+    {
+        "type": "text",
+        "text": "Recall our view of the GNN output as a combination of its input node features, fixed graph Laplacian and learnable graph filters. The utility of a GNN is determined by the compatibility among the three. In order to fulfill such compatibility, we require the node features to be structure-respecting: ",
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+    {
+        "type": "text",
+        "text": "Definnode Then ion 3.3 (Structure-respectwith a set of node featuree say the node features on es). , where respect $g _ { i }$ -th hop of or any no $v _ { i }$ $\\bar { \\{ x _ { p , q } ^ { i } \\} } _ { p = 0 , q = 1 } ^ { k , | V _ { p } ( g _ { i } ) | }$ $V _ { p } ( g _ { i } )$ $p$ $g _ { i }$ $g _ { i }$ $\\cdot x _ { p , q } ^ { i } = [ f ( g _ { i } ) ] _ { p , q } \\in \\mathbb { R } ^ { d }$ $v _ { q } \\in V _ { p } ( g _ { i } )$ , where $f : \\mathcal { G }  \\mathbb { R } ^ { d \\times \\lvert V ( g _ { i } ) \\rvert }$ is a function. In the strict case, $f$ should be injective. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "In its essence, Def 3.3 requires the node features to be a function of the graph structures, which is sensitive to changes in the graph structures, and in an ideal case, injective to the graph structures (i.e., mapping different graphs to different features). In this way, when the learned graph filters of a transfered GNN is compatible to the structure of $G$ , they are also compatible to the node features of $G$ . As we will explain in Remark 2 of Theorem 3.1, this requirement is also essential for the analysis of EGI transferability which eventually only depends on the structural difference between two graphs. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "In practice, commonly used node features like node degrees, PageRank scores [40], spectral embeddings [11], and many pre-computed unsupervised network embeddings [42, 51, 14] are all structure-respecting in nature. However, other commonly used node features like random vectors [68] or uniform vectors [60] are not and thus non-transferable. When raw node attributes are available, they are transferable as long as the concept of homophily [36] applies, which also implies Def 3.3, but we do not have a rigorous analysis on it yet. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Supportive observations. In the fifth and sixth columns in Table 1, where we use same fixed vectors as non-transferable node features to contrast with the first three columns, there is almost no transferability (see $\\delta ( a c c . ) )$ for all compared methods when non-transferable features are used, as the performance of trained GNNs are similar to or worse than their untrained baselines. More detailed experiments on different transferable and non-transferable features can be found in Appendix $\\ S { \\bf C } . 1$ . ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "With our view of graphs and requirement on node features both established, now we derive the following theorem by characterizing the performance difference of EGI on two graphs based on Eq. 1. ",
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+    {
+        "type": "text",
+        "text": "Theorem 3.1 (GNN transferability). Let ${ \\cal G } _ { a } = \\{ ( g _ { i } , x _ { i } ) \\} _ { i = 1 } ^ { n }$ and $G _ { b } = \\{ ( g _ { i ^ { \\prime } } , x _ { i ^ { \\prime } } ) \\} _ { i ^ { \\prime } = 1 } ^ { m }$ be two graphs, and assume node features are structure-relevant. Consider GCN $\\Psi _ { \\theta }$ with $k$ layers and $a$ $I$ -hop polynomial filter $\\phi$ . With reasonable assumptions on the local spectrum of $G _ { a }$ and $G _ { b }$ , the empirical performance difference of $\\Psi _ { \\theta }$ evaluated on $\\mathcal { L } _ { \\mathrm { E G I } }$ satisfies ",
+        "bbox": [
+            173,
+            592,
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+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "img_path": "images/199808c0b80475946a3236d5d4c865c32b3b7d4f09f2adb9ec23f6def6465f2c.jpg",
+        "text": "$$\n| \\mathcal { L } _ { \\mathrm { E G I } } ( G _ { a } ) - \\mathcal { L } _ { \\mathrm { E G I } } ( G _ { b } ) | \\leq \\mathcal { O } \\left( \\Delta _ { \\mathcal { D } } ( G _ { a } , G _ { b } ) + C \\right) .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            331,
+            651,
+            666,
+            670
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "On the RHS, $C$ is only dependent on the graph encoders and node features, while $\\Delta _ { \\mathcal { D } } ( G _ { a } , G _ { b } )$ measures the structural difference between the source and target graphs as follows, ",
+        "bbox": [
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+            674,
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+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "img_path": "images/abc24ee1cf36e601c3fe5d69c88b59c20553c5b1e1dd4fa4831c8094e37330b2.jpg",
+        "text": "$$\n\\Delta _ { \\mathcal { D } } ( G _ { a } , G _ { b } ) = \\tilde { C } \\frac { 1 } { n m } \\sum _ { i = 1 } ^ { n } \\sum _ { i ^ { \\prime } = 1 } ^ { m } \\lambda _ { \\mathrm { m a x } } ( \\tilde { L } _ { g _ { i } } - \\tilde { L } _ { g _ { i ^ { \\prime } } } )\n$$",
+        "text_format": "latex",
+        "bbox": [
+            334,
+            705,
+            663,
+            747
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where $\\lambda _ { \\operatorname* { m a x } } ( A ) : = \\lambda _ { \\operatorname* { m a x } } ( A ^ { T } A ) ^ { 1 / 2 }$ , and ${ \\tilde { L } } _ { g _ { i } }$ denotes the normalised graph Laplacian of $\\tilde { g } _ { i }$ by its in-degree. $\\tilde { C }$ is a constant dependant on $\\lambda _ { \\operatorname* { m a x } } ( \\tilde { L } _ { g _ { i } } )$ and $\\mathcal { D }$ . ",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Proof. The full proof is detailed in Appendix $\\ S \\mathrm { A }$ . ",
+        "bbox": [
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+            797,
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+            814
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "The analysis in Theorem 3.1 naturally instantiates our insight about the correspondence between structural similarity and GNN transferability. It allows us to tell how well an EGI trained on $G _ { a }$ can work on $G _ { b }$ by only checking the local graph Laplacians of $G _ { a }$ and $G _ { b }$ without actually training any model. In particular, we define the EGI gap as $\\Delta _ { \\mathcal { D } }$ in Eq. 6, as other term $C$ is the same for different methods using same GNN encoder. It can be computed to bound the transferability of EGI regarding its loss difference on the source and target graphs. ",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Remark 1. Our view of a graph $G$ as samples of $k$ -hop ego-graphs is important, as it allows us to obtain node-wise characterization of GNN similarly as in [55]. It also allows us to set the depth of ego-graphs in the analysis to be the same as the number of GNN layers (k), since the GNN embedding of each node mostly depends on its $k$ -hop ego-graph instead of the whole graph. ",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Remark 2. For Eq. 1, Def 3.3 ensures the sampling of GNN embedding at a node always corresponds to sampling an ego-graph from $\\mathcal { G }$ , which reduces to uniformly sampling from $G = \\{ g _ { i } \\} _ { i = 1 } ^ { n }$ under the setting of Theorem 3.1. Therefore, the requirement of Def 3.3 in the context of Theorem 3.1 guarantees the analysis to be only depending on the structural information of the graph. ",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Supportive observations. In Table 1, in the $\\bar { d }$ columns, we compute the average structural difference between two Forest-fire graphs $( \\Delta _ { \\mathcal { D } } ( \\mathrm { F } , \\mathrm { F } ) )$ and between Barabasi and Forest-fire graphs $\\scriptstyle ( \\Delta _ { \\mathcal { D } } ( \\mathbf { B } , \\mathrm { F } ) )$ , based on the RHS of Eq. 5. The results validate the topological difference between graphs generated by different random-graph models, while also verifying our view of graph as $\\mathbf { k }$ -hop ego-graph samples and the way we propose based on it to characterize structural information of graphs. We further highlight in the $\\delta ( \\mathrm { a c c } )$ columns the accuracy difference between the GNNs transfered from Forest-fire graphs and Barabasi graphs to Forest-fire graphs. Since Forest-fire graphs are more similar to Forest-fire graphs than Barabasi graphs (as verified in the $\\Delta _ { \\mathcal { D } }$ columns), we expect $\\delta ( \\mathrm { a c c . } )$ to be positive and large, indicating more positive transfer between the more similar graphs. Indeed, the behaviors of EGI align well with the expectation, which indicates its well-understood transferability and the utility of our theoretical analysis. ",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Use cases of Theorem 3.1. Our Theorem 3.1 naturally allows for two practical use cases among many others: point-wise pre-judge and pair-wise pre-selection for EGI pre-training. Suppose we have a target graph $G _ { b }$ which does not have sufficient training labels. In the first setting, we have a single source graph $G _ { a }$ which might be useful for pre-training a GNN to be used on $G _ { b }$ . The EGI gap $\\Delta _ { \\mathcal { D } } ( G _ { a } , G _ { b } )$ in Eq. 6 can then be computed between $G _ { a }$ and $G _ { b }$ to pre-judge whether such transfer learning would be successful before any actual GNN training (i.e., yes if $\\Delta _ { \\mathcal { D } } ( G _ { a } , G _ { b } )$ is empirically much smaller than 1.0; no otherwise). In the second setting, we have two or more source graphs $\\{ G _ { a } ^ { 1 } , G _ { a } ^ { 2 } , . . . \\}$ which might be useful for pre-training the GNN. The EGI gap can then be computed between every pair of $G _ { a } ^ { i }$ and $G _ { b }$ to pre-select the best source graph (i.e., select the one with the least EGI gap). ",
+        "bbox": [
+            173,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "In practice, the computation of eigenvalues on the small ego-graphs can be rather efficient [2], and we do not need to enumerate all pairs of ego-graphs on two compared graphs especially if the graphs are really large (e.g., with more than a thousand nodes). Instead, we can randomly sample pairs of ego-graphs from the two graphs, update the average difference on-the-fly, and stop when it converges. Suppose we need to sample $M$ pairs of $\\mathbf { k }$ -hop ego-graphs to compare two large graphs, and the average size of ego-graphs are $L$ , then the overall complexity of computing Eq. 5 is $\\bar { \\mathcal { O } } ( \\bar { M } L ^ { 2 } )$ , where $M$ is often less than 1K and $L$ less than 50. In Appendix $\\ S { \\bf C . 4 }$ , we report the approximated $\\Delta _ { \\mathcal { D } }$ ’s w.r.t. different sampling frequencies, and they are indeed pretty close to the actual value even with smaller sample frequencies, showing the feasible efficiency of computing $\\Delta _ { \\mathcal { D } }$ through sampling. ",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Limitations. EGI is designed to account for the structural difference captured by GNNs (i.e., khop ego-graphs). The effectiveness of EGI could be limited if the tasks on target graphs depend on different structural signals. For example, as Eq. 6 is computing the average pairwise distances between the graph Laplacians of local ego-graphs, $\\Delta _ { \\mathcal { D } }$ is possibly less effective in explicitly capturing global graph properties such as numbers of connected components (CCs). In some specific tasks (such as counting CCs or community detection) where such properties become the key factors, $\\Delta _ { \\mathcal { D } }$ may fail to predict the transferability of GNNs. ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4 Real Data Experiments ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            784,
+            400,
+            801
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Baselines. We compare the proposed model against existing self-supervised GNNs and pre-training GNN algorithms. To exclude the impact of different GNN encoders $\\Psi$ on transferability, we always use the same encoder architecture for all compared methods (i.e., GIN [60] for direct-transfering experiments, GCN [29] for transfering with fine-tuning). ",
+        "bbox": [
+            174,
+            820,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "The self-supervised GNN baselines are GVAE [28], DGI [54] and two latest mutual information estimation methods GMI [41] and MVC [17]. As for pre-training GNN algorithms, MaskGNN and ContextPredGNN are two node-level pre-training models proposed in [21] Besides, Structural Pre-train [23] also conducts unsupervised node-level pre-training with structural features like node degrees and clustering coefficients. ",
+        "bbox": [
+            174,
+            882,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/31484d528b69298a5af431729fcb5507a630f03d593645952b5e96cc467c4669.jpg",
+        "table_caption": [
+            "Table 1: Synthetic experiments of identifying structural equivalent nodes. We randomly generate 40 graphs with the Forest-fire model (F) [32] and 40 graphs with the Barabasi model (B) [1], The GNN model is GIN [60] with random parameters (baseline with only the neighborhood aggregation function), VGAE[28], DGI [54], and EGI with GIN encoder. We train VGAE, DGI and EGI on one graph from either set (F and B), and test them on the rest of Forest-fire graphs (F). Transferable feature is node degree one-hot encoding and non-transferable feature is uniform vectors. More details about the results and dataset can be found in Appendix $\\ S { \\bf C } . 1$ "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"3\">transferable features</td><td colspan=\"3\">non-transferable feature</td><td rowspan=\"2\">structural difference △D(F,F)</td><td rowspan=\"2\">△D(B,F)</td></tr><tr><td>F-F</td><td>B-F</td><td>8(acc.)</td><td>F-F</td><td>B-F</td><td>8(acc.)</td></tr><tr><td>GIN (untrained)</td><td>0.572</td><td>0.572</td><td>/</td><td>0.358</td><td>0.358</td><td>/</td><td></td><td></td></tr><tr><td>VGAE (GIN)</td><td>0.498</td><td>0.432</td><td>+0.066</td><td>0.240</td><td>0.239</td><td>0.001</td><td></td><td></td></tr><tr><td>DGI (GIN)</td><td>0.578</td><td>0.591</td><td>-0.013</td><td>0.394</td><td>0.213</td><td>+0.181</td><td>0.752</td><td>0.883</td></tr><tr><td>EGI (GIN)</td><td>0.710</td><td>0.616</td><td>+0.094</td><td>0.376</td><td>0.346</td><td>+0.03</td><td></td><td></td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+            280,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Experimental Settings. The main hyperparameter $k$ is set 2 in EGI as a common practice. We use Adam [27] as optimizer and learning rate is 0.01. We provide the experimental result with varying $k$ in the Appendix $\\ S { \\bf C . 4 }$ . All baselines are set with the default parameters. Our experiments were run on an AWS g4dn.2xlarge machine with 1 Nvidia T4 GPU. By default, we use node degree one-hot encoding as the transferable feature across all different graphs. As stated before, other transferable features like spectral and other pre-computed node embeddings are also applicable. We focus on the setting where the downstream tasks on target graphs are unspecified but assumed to be structure-relevant, and thus pre-train the GNNs on source graphs in an unsupervised fashion.4 In terms of evaluation, we design two realistic experimental settings: (1) Direct-transfering on the more structure-relevant task of role identification without given node features to directly evaluate the utility and transferability of EGI. (2) Few-shot learning on relation prediction with task-specific node features to evaluate the generalization ability of EGI. ",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "4.1 Direct-transfering on role identification ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            517,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "First, we use the role identification without node features in a direct-transfering setting as a reliable proxy to evaluate transfer learning performance regarding different pre-training objectives. Role in a network is defined as nodes with similar structural behaviors, such as clique members, hub and bridge [19]. Across graphs in the same domain, we assume the definition of role to be consistent, and the task of role identification is highly structure-relevant, which can directly reflect the transferability of different methods and allows us to conduct the analysis according to Theorem 3.1. Upon convergence of pre-training each model on the source graphs, we directly apply them to the target graphs and further train a multi-layer perceptron (MLP) upon their outputs. The GNN parameters are frozen during the MLP training. We refer to this strategy as direct-transfering since there is no fine-tuning of the models after transfering to the target graphs. ",
+        "bbox": [
+            173,
+            541,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "We use two real-world network datasets with role-based node labels: (1) Airport [45] contains three networks from different regions– Brazil, USA and Europe. Each node is an airport and each link is the flight between airports. The airports are assigned with external labels based on their level of popularity. (2) Gene [68] contains the gene interactions regarding 50 different cancers. Each gene has a binary label indicating whether it is a transcription factor. More details about the results and dataset can be found in Appendix C.2. ",
+        "bbox": [
+            174,
+            688,
+            825,
+            770
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "The experimental setup on the Airport dataset closely resembles that of our synthetic experiments in Table 1, but with real data and more detailed comparisons. We train all models (except for the untrained ones) on the Europe network, and test them on all three networks. The results are presented in Table 2. We notice that the node degree features themselves (with MLP) show reasonable performance in all three networks, which is not surprising since the popularity-based airport role labels are highly relevant to node degrees. The untrained GIN encoder yields a significant margin over just node features, as GNN encoder incorporates structural information to node representations. ",
+        "bbox": [
+            173,
+            776,
+            825,
+            875
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "While training of the DGI can further improve the performance on the source graph, EGI shows the best performance there with the structure-relevant node degree features, corroborating the claimed effectiveness of EGI in capturing the essential graph information (i.e. recover the $\\mathbf { k }$ -hop ego-graph distributions) as we stress in $\\ S 3$ . ",
+        "bbox": [
+            174,
+            90,
+            825,
+            147
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "When transfering the models to USA and Brazil networks, EGI further achieves the best performance compared with all baselines when structure relevant features are used (64.55 and 73.15), which reflects the most significant positive transfer. Interestingly, direct application of GVAE, DGI and MVC that do not capture the input k-hop graph jointly, leads to rather limited and even negative transferrability (through comparison against the untrained GIN encoders). The recently proposed transfer learning frameworks for GNN like MaskGNN and Structural Pre-train are able to mitigate negative transfer to some extent, but their performances are still inferior to EGI. We believe this is because their models are prone to learn the graph-specific information that is less transferable across different graphs. GMI is also known to capture the graph structure and node features, so it achieves second best result comparing with EGI. ",
+        "bbox": [
+            174,
+            154,
+            825,
+            291
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Similarly as in Table 1, we also compute the structural differences among three networks w.r.t. the EGI gap in Eq. 6. The structural difference is 0.869 between the Europe and USA networks, and 0.851 between the Europe and Brazil datasets, which are pretty close. Consequently, the transferability of EGI regarding its performance gain over the untrained GIN baseline is $4 . 8 \\%$ on the USA network and $4 . 4 \\%$ on the Brazil network, which are also close. Such observations again align well with our conclusion in Theorem 3.1 that the transferability of EGI is closely related to the structural differences between source and target graphs. ",
+        "bbox": [
+            174,
+            297,
+            825,
+            395
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "table",
+        "img_path": "images/340f714bdbf6f3956e9fe9ca6005935375ce982404f523556ffcfe4e9fb80339.jpg",
+        "table_caption": [
+            "Table 2: Results of role identification with direct-transfering on the Airport dataset. We report mean and standard deviation over 100 runs. The scores marked with ∗∗ passed t-test with $p < 0 . 0 1$ over the second runners. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td colspan=\"3\">Airport [45]</td></tr><tr><td></td><td>Europe</td><td>USA</td><td>Brazil</td></tr><tr><td>features</td><td>0.528±0.052</td><td>0.557±0.028</td><td>0.671±0.089</td></tr><tr><td>GIN (random-init)</td><td>0.558±0.050</td><td>0.616±0.030</td><td>0.700±0.082</td></tr><tr><td>GVAE(GIN) [28]</td><td>0.539±0.053</td><td>0.555±0.029</td><td>0.663±0.089</td></tr><tr><td>DGI(GIN） [54]</td><td>0.578±0.050</td><td>0.549±0.028</td><td>0.673±0.084</td></tr><tr><td>Mask-GIN [21]</td><td>0.564±0.053</td><td>0.608±0.027</td><td>0.667±0.073</td></tr><tr><td>ContextPred-GIN [21]</td><td>0.527±0.048</td><td>0.504±0.030</td><td>0.621±0.078</td></tr><tr><td>Structural Pre-train [23]</td><td>0.560±0.050</td><td>0.622±0.030</td><td>0.688±0.082</td></tr><tr><td>MVC[17]</td><td>0.532±0.050</td><td>0.597±0.030</td><td>0.661±0.093</td></tr><tr><td>GMI [41]</td><td>0.581±0.054</td><td>0.593±0.031</td><td>0.731±0.107</td></tr><tr><td>EGI (GIN)</td><td>0.592±0.046**</td><td>0.646±0.029 **</td><td>0.732±0.078</td></tr></table>",
+        "bbox": [
+            258,
+            441,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "On the Gene dataset, with more graphs available, we focus on EGI to further validate the utility of Eq. 5 in Theorem 3.1, regarding the connection between the EGI gap (Eq. 6) and the performance gap (micro-F1) of EGI on them. Due to severe label imbalance that removes the performance gaps, we only use the seven brain cancer networks that have a more consistent balance of labels. As shown in Figure 3, we train EGI on one graph and test it on the other graphs. The $x$ -axis shows the EGI gap, and $y$ -axis shows the improvement on micro-F1 compared with an untrained GIN. The negative correlation between two quantities is obvious. Specifically, when the structural difference is smaller than 1, positive transfer is observed (upper left area) as the performance of transferred EGI is better than untrained GIN, and when the structural difference becomes large $( > 1 )$ , negative transfer is observed. We also notice a similar graph pattern, i.e. single dense cluster, between source graph and positive transferred target graph $G _ { 2 }$ . ",
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "4.2 Few-shot learning on relation prediction ",
+        "text_level": 1,
+        "bbox": [
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+        "type": "text",
+        "text": "Here we evaluate EGI in the more generalized and practical setting of few-shot learning on the less structure-relevant task of relation prediction, with task-specific node features and fine-tuning. The source graph contains a cleaned full dump of 579K entities from YAGO [49], and we investigate 20- shot relation prediction on a target graph with 24 relation types, which is a sub-graph of 115K entities sampled from the same dump. In post-fine-tuning, the models are pre-trained with an unsupervised loss on the source graph and fine-tuned with the task-specific loss on the target graph. In joint-finetuning, the same pre-trained models are jointly optimized w.r.t. the unsupervised pre-training loss and task-specific fine-tuning loss on the target graph. In Table 3, we observe most of the existing models fail to transfer across pre-training and fine-tuning tasks, especially in the joint-fine-tuning setting. In particular, both Mask-GIN and ContextPred-GIN rely a lot on task-specific fine-tuning, while EGI focuses on the capturing of similar ego-graph structures that are transferable across graphs. The mutual information based method GMI also demonstrates considerable transferability and we believe the ability to capture the graph structure is the key to the transferability. As a consequence, EGI significantly outperforms all compared methods in both settings. More detailed statistics and running time are in Appendix $\\ S { \\bf C } . 3$ . ",
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+        "img_path": "images/179fd55c88fad38b5d7c38fd504139f6a34d959c09babb9dae016dffbc51c9a9.jpg",
+        "image_caption": [
+            "Figure 3: Transfer learning performance of role identification on the Gene dataset. We visualize the source graph $G _ { 0 }$ and two example target graphs that are relatively more different $\\left( G _ { 4 } \\right)$ or similar $\\left( G _ { 2 } \\right)$ with $G _ { 0 }$ . "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "text": "",
+        "bbox": [
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+    {
+        "type": "table",
+        "img_path": "images/44efd225773c53f074205f3058ce5df0abeaaecedea508c3a403e199552537dd.jpg",
+        "table_caption": [
+            "Table 3: Performance of few-shot relation prediction on YAGO. The scores marked with ∗∗ passed t-test with $p < 0 . 0 1$ over the second best results. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"2\">post-fine-tuning</td><td colspan=\"2\"> joint-fine-tuning</td></tr><tr><td>AUROC</td><td>MRR</td><td>AUROC</td><td>MRR</td></tr><tr><td>No pre-train</td><td>0.687±0.002</td><td>0.596±0.003</td><td>N.A.</td><td>N.A.</td></tr><tr><td>GVAE</td><td>0.701±0.003</td><td>0.601±0.007</td><td>0.679±0.004</td><td>0.568±0.008</td></tr><tr><td>DGI</td><td>0.689±0.011</td><td>0.586±0.025</td><td>0.688±0.012</td><td>0.537±0.023</td></tr><tr><td>MaskGNN</td><td>0.713±0.009</td><td>0.631±0.015</td><td>0.712±0.005</td><td>0.560±0.010</td></tr><tr><td>ContextPredGNN</td><td>0.692±0.030</td><td>0.662±0.030</td><td>0.705±0.011</td><td>0.575±0.021</td></tr><tr><td>GMI</td><td>0.728±0.005</td><td>0.625±0.009</td><td>0.721±0.007</td><td>0.643±0.011</td></tr><tr><td>Structural Pre-train</td><td>OOM</td><td>OOM</td><td>OOM</td><td>OOM</td></tr><tr><td>MVC</td><td>OOM</td><td>OOM</td><td>OOM</td><td>OOM</td></tr><tr><td>EGI</td><td>0.739± 0.009**</td><td>0.670±0.014</td><td>0.787 ± 0.011**</td><td>0.729 ± 0.016**</td></tr></table>",
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+    },
+    {
+        "type": "text",
+        "text": "5 Conclusion ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "To the best of our knowledge, this is the first research effort towards establishing a theoretically grounded framework to analyze GNN transferability, which we also demonstrate to be practically useful for guiding the design and conduct of transfer learning with GNNs. For future work, it is intriguing to further strengthen the bound with relaxed assumptions, rigorously extend it to the more complicated and less restricted settings regarding node features and downstream tasks, as well as analyze and improve the proposed framework over more transfer learning scenarios and datasets. It is also important to protect the privacy of pre-training data to avoid potential negative societal impacts. ",
+        "bbox": [
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+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Acknowledgments and Disclosure of Funding ",
+        "text_level": 1,
+        "bbox": [
+            174,
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+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Research was supported in part by US DARPA KAIROS Program No. FA8750-19-2-1004, SocialSim Program No. W911NF-17-C-0099, and INCAS Program No. HR001121C0165, National Science Foundation IIS-19-56151, IIS-17-41317, and IIS 17-04532, and the Molecule Maker Lab Institute: An AI Research Institutes program supported by NSF under Award No. 2019897. Chao Zhang is supported NSF IIS-2008334, IIS-2106961, and ONR MURI N00014-17-1-2656. We would like to thank AWS Machine Learning Research Awards program for providing computational resources for the experiments in this paper. This work is also partially supported by the internal funding and GPU servers provided by the Computer Science Department of Emory University. Any opinions, findings, and conclusions or recommendations expressed herein are those of the authors and do not necessarily represent the views, either expressed or implied, of DARPA or the U.S. Government. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "References ",
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+        "bbox": [
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+            106
+        ],
+        "page_idx": 10
+    },
+    {
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parse/train/H1lmyRNFvr/H1lmyRNFvr.md

@@ -0,0 +1,257 @@
+# AUGMENTING GENETIC ALGORITHMS WITH DEEP NEURAL NETWORKS FOR EXPLORING THE CHEMICAL SPACE
+
+AkshatKumar Nigam1,†, Pascal Friederich1,2,† Mario Krenn, 1,3,4, Alan Aspuru-Guzik ´ 1,3,4,5, $^ *$
+
+1Department of Computer Science, University of Toronto, Canada.   
+2Institute of Nanotechnology, Karlsruhe Institute of Technology, Germany.   
+3Department of Chemistry, University of Toronto, Canada.   
+4Vector Institute for Artificial Intelligence, Toronto, Canada.   
+5Canadian Institute for Advanced Research (CIFAR) Senior Fellow, Toronto, Canada
+
+# ABSTRACT
+
+Challenges in natural sciences can often be phrased as optimization problems. Machine learning techniques have recently been applied to solve such problems. One example in chemistry is the design of tailor-made organic materials and molecules, which requires efficient methods to explore the chemical space. We present a genetic algorithm (GA) that is enhanced with a neural network (DNN) based discriminator model to improve the diversity of generated molecules and at the same time steer the GA. We show that our algorithm outperforms other generative models in optimization tasks. We furthermore present a way to increase interpretability of genetic algorithms, which helped us to derive design principles.
+
+Our open source implementation: https://github.com/aspuru-guzik-group/GA
+
+# 1 INTRODUCTION
+
+The design of optimal structures under constraints is an important problem spanning multiple domains in the physical sciences. Specifically, in chemistry, the design of tailor-made organic materials and molecules requires efficient methods to explore the chemical space. Purely experimental approaches are often time consuming and expensive. Reliable computational tools can accelerate and guide experimental efforts to find new materials faster.
+
+We present a genetic algorithm (GA) (Davis, 1991; Devillers, 1996; Sheridan & Kearsley, 1995; Parrill, 1996) for molecular design that is enhanced with two features:
+
+1. A neural network based adaptive penalty. This promotes exploratory behaviour of the GA and thus improve the diversity of generated molecules.   
+2. Exploiting the robustness of SELFIES (Krenn et al., 2019), we do not need to incorporate any expert based mutation or cross-over rules.
+
+Starting from only simple methane molecules, our algorithm outperforms other generative models in optimization tasks for molecular design. By introducing machine learning (ML) techniques, the long term behaviour is not subject to stagnation, thus solving a significant problem in genetic algorithms (Paszkowicz, 2009).
+
+No domain knowledge is required; thus, our approach is not limited to chemistry-specific questions but can be applied to a wide range of optimization problems.
+
+# 2 RELATED WORKS
+
+Inverse design is the systematic development of structures with desired properties. In chemistry (Sanchez-Lengeling & Aspuru-Guzik, 2018), the challenge of inverse design has been tackled as an optimization problem, among others in the form of variational autoencoders (VAEs), generative adversarial networks (GANs) and genetic algorithms.
+
+Variational autoencoders and generative adversarial networks VAEs (Kingma & Welling, 2013) are a widely used method for direct generation of molecular string or graph representations (Gomez- ´ Bombarelli et al., 2018). They encode discrete representations into a continuous (latent) space. Molecules resembling a known structure can be found by searching around the region of the encoded point. Making using of the continuous latent representation, it is possible to search via gradients or Bayesian Optimization (BO). However, the generation of semantically and syntactically valid molecules is a challenging task. Thus, several follow up works to the VAE have been proposed for inverse design in chemistry. Among them, CVAE (Gomez-Bombarelli et al., 2018), GVAE (Kusner ´ et al., 2017) and SD-VAE (Dai et al., 2018) work directly on string molecular representations. Alternatively, JT-VAE (Jin et al., 2018a) as well as CGVAE Liu et al. (2018) work on molecular graphs. Unlike latent space property optimization, the policy network (PN) based GCPN model (You et al., 2018) proposes a reinforcement learning (RL)-based method for direct optimization on molecular graphs. ORGAN (Guimaraes et al., 2017) demonstrate training string-based generative adversarial networks (GANs) (Goodfellow et al., 2014) via RL. Another method based on adversarial training is VJTNN (Jin et al., 2018b). Segler et al. (2017) first introduced molecule generating models based on language models and reinforcement learning, where actions in an environment are taken to construct a molecule, receiving reward from an external scoring function. This model has also shown strong performance in the GuacaMol benchmark (Brown et al. (2019)).
+
+In all the approaches mentioned above, generative models are trained to mimic the reference data set distributions, thus limiting the exploration ability of VAEs and GANs.
+
+Genetic algorithms & related methods There exist several examples of GA based molecule optimization algorithms in literature (O’Boyle et al., 2011; Virshup et al., 2013; Rupakheti et al., 2015; Jensen, 2019; Sheridan & Kearsley, 1995; Parrill, 1996)). While some of these examples pre-define mutations on a SMILES level to ensure validity of the molecules, other approaches use fragmentbased assembly of molecules. GAs are likely to get trapped in regions of local optima (Paszkowicz, 2009). Thus, for selection of the best molecules, (Rupakheti et al., 2015; Jensen, 2019) report multiple restarts upon stagnation.
+
+We include the aforementioned models as baselines for numerical comparison.
+
+# 3 GA-D ARCHITECTURE
+
+# 3.1 OVERVIEW
+
+Our approach is illustrated in Figure 1. Our generator is a genetic algorithm with a population of molecules $m$ . In each generation, the fitness of all molecules is evaluated as a linear combination of molecular properties $J ( m )$ and the discriminator score $D ( m )$ :
+
+$$
+F ( m ) = J ( m ) + \beta \cdot D ( m ) .
+$$
+
+Random mutations of high fitness (best performing) molecules replace inferior members, while bestperforming molecules continue to a subsequent generation. The probability of replacing a molecule is evaluated using a smooth logistic function based on a ranking of fitness among the molecules of a generation. At the end of each generation, a neural network based discriminator is trained jointly on molecules generated by the GA and a reference data set. The fitness evaluation accounts for the discriminator predictions for each molecule. Therefore, the discriminator plays a role in the selection of the subsequent population.
+
+# 3.2 MUTATION & CROSS-OVER RULES
+
+Mutation of molecules to populate subsequent generations is an important element of the GA. A low degree of mutation can lead to a slow exploration of the chemical space, causing stagnation of the fitness function. Robustness of SELFIES allows us to do random mutations to molecular strings while preserving their validity. Thus, our mutations only include $50 \%$ insertions or $50 \%$ replacements of single SELFIES characters. To accelerate the exploration of the GA, we add one domain-specific mutation rule – the direct addition of phenyl groups in approximately $4 \%$ of cases. Character deletion is implicitly taken into account in SELFIES mutations, and we do not use crossover rules.
+
+![](images/cd8ba097b50038f6cdae830c10832404738ad3b8627fc5dca4f7f4fe13e99c02.jpg)  
+Figure 1: Overview of our hybrid structure, which augments genetic algorithms with ML based neural networks.
+
+![](images/1a7ea4f895854a7ad8f1e31c30dd5d557167d6d4a420117faffe1ea9a85edf30.jpg)  
+Figure 2: Reducing Fitness of $o$ -terphenyl, initially possessing the largest fitness in generation 5 $( R a n k = O )$ ). Due to decreasing discriminator predictions $D ( m )$ , fitness decreases with an increased probability of getting killed (Kill Prob.). The molecule is completely replaced in generation 16. Rank denotes the position of the molecule in an increasing fitness list of generation molecules.
+
+# 3.3 ROLE OF THE DISCRIMINATOR
+
+The fundamental role of the discriminator is to increase molecular diversity by removing longsurviving molecules. Consider the realistic scenario in which a GA has found a molecule close to a local optimum, where all mutations are lowering the fitness. As a result, this molecule survives for multiple generations while occupying a large fraction of the population. During such periods, the GA has limited view of the chemical space as it repeatedly explores mutations of the same high-fitness molecule.
+
+A straightforward solution would be the addition of a linear penalty (Nanakorn & Meesomklin, 2001) in the fitness function that accounts for the number of successive generations a molecule survives. However, this method assigns independent scores to similar-looking molecules, which again results in less variety.
+
+Our solution is the addition of an adaptive penalty (in our case a neural network based discriminator), thus resolving the problem of stagnation. Molecules with similar representation receive similar classification scores. Furthermore, long-surviving molecules are trained longer and receive weaker scores, resulting in decreasing fitness - reducing the chance of long periods of stagnation (illustrated in Figure 2). The task of the discriminator thus is to memorize families of high performing molecules and penalize their fitness to force the GA to explore different regions in chemical space.
+
+# 4 EXPERIMENTS
+
+Comparing to the literature standard, we aim at maximizing the penalized logP objective $J ( m )$ proposed by (Gomez-Bombarelli et al., 2018). For molecule ´ $m$ , the penalized logP function is defined as
+
+$$
+J ( m ) = \log \mathrm { P } ( m ) - \mathrm { S A } ( m ) - \mathrm { R i n g } \mathrm { P e n a l t y } ( m ) ,
+$$
+
+where logP indicates the water-octanol partition coefficient, SA (Ertl & Schuffenhauer, 2009) represents the synthetic accessibility and prevents the formation of chemically unfeasible molecules, and RingPenalty linearly penalizes the presence of rings of size larger than 6. Our reference data set consists of 250,000 commercially available molecules extracted from the ZINC database (Irwin et al., 2012). All three quantities in the above equation are normalized based on this data set.
+
+Table 1: Comparison of our model with maximum penalized logP scores reported in literature. Models in the upper part are forced to optimize within the distributions of given reference data sets while the GA based approaches in the lower part can freely explore chemical space. Direct comparisons need to take into account these different objectives and scopes. The parameter $\beta$ in our GA can be used to balance exploration and exploitation (see Section 4.6).   
+
+<table><tr><td>Model</td><td>Max. Penalized logP</td><td>Model</td></tr><tr><td>GVAE + BO (Kusner et al.,2017) 1</td><td>2.87 ± 0.06</td><td>VAE</td></tr><tr><td>SD-VAE (Dai et al., 2018) 1</td><td>3.50 ± 0.44</td><td>VAE</td></tr><tr><td>CVAE + BO (G6mez-Bombarelli et al., 2018) 2</td><td>4.85 ± 0.17</td><td>VAE</td></tr><tr><td>ORGAN (Guimaraes et al., 2017) 1</td><td>3.52 ± 0.08</td><td>GAN</td></tr><tr><td>JT-VAE (Jin et al., 2018a) 1</td><td>4.90 ± 0.33</td><td>VAE</td></tr><tr><td>ChemTS (Yang et al., 2017)</td><td>5.6 ± 0.5</td><td>RNN</td></tr><tr><td>GCPN(You et al., 2018) 1</td><td>7.87 ± 0.07</td><td>PN + GAN</td></tr><tr><td>Random SELFIES</td><td>6.19 ± 0.63</td><td>Random Search</td></tr><tr><td>GB-GA (Jensen, 2019) 3</td><td>7.4±0.9</td><td>GA</td></tr><tr><td>GB-GA (Jensen, 2019) 4</td><td>15.76 ± 5.71</td><td>GA</td></tr><tr><td>GA (here)</td><td>12.61 ± 0.81</td><td>GA</td></tr><tr><td>GA + D (here)</td><td>13.31 ± 0.63</td><td>GA+DNN</td></tr><tr><td>(GA + D(t) (here) 5</td><td>20.72 ± 3.14)</td><td>GA +DNN</td></tr></table>
+
+1 average of three best molecules after performing Bayesian optimization on the latent representation of a trained VAE 2 two best molecules of a single run 3 averaged over 10 runs with 20 molecules per generation with a molecular weight (excl. hydrogen) smaller than $3 9 . 1 5 \pm 3 . 5 0 \mathrm { g / m o l }$ run for 50 generations 4 averaged over 10 runs with 500 molecules up to 81 characters per generation and 100 generations averaged over 5 runs with 1000 generations each
+
+# 4.1 UNCONSTRAINED OPTIMIZATION AND COMPARISON WITH OTHER GENERATIVE MODELS
+
+We define our fitness function according to Eq. 1 and 2 with $\beta = 0$ and 10. The algorithm is run for 100 generations with a population size of 500. All generated molecules are constrained to a canonical smile length of 81 characters (as in (Yang et al., 2017; Jensen, 2019)). We train the discriminator (fully connected neural network with ReLU activation and sigmoid output layer, the input is a vector of chemical and geometrical properties characterizing the molecules) at the end of each generation for 10 epochs on 500 molecules proposed by the GA and 500 randomly drawn molecules from the ZINC data set. We report maximum $J ( m )$ scores, averaged over 10 independent runs. The highest $J ( m )$ achieved by our approach are $1 3 . 3 1 \pm 0 . 6 3$ $\beta = 1 0 $ ) and
+
+$1 2 . 6 1 \pm 0 . 8 1$ $\beta = 0 ,$ ), respectively, which is almost twice as high es the highest literature value of $7 . 8 7 { \pm } 0 . 0 7$ (See Table 1). Furthermore, we compare to 50,000 random valid SELFIES strings, which surprisingly outperforms some existing generative models. The GA-D(t) results are explained in the next section.
+
+![](images/05992edc307d774b967ad9610de9401894ae39f99f02815e3d93a335121cd6fb.jpg)  
+4.2 LONG TERM EXPERIMENT WITH A TIME-DEPENDENT ADAPTIVE PENALTY  
+Figure 3: Maximum $J ( m )$ values found for 10 independent runs with no discriminator $\mathcal { B } = 0 ,$ ) and 5 independent runs with the introduction of a time-dependent adaptive penalty. The full line is the average of all runs, the shaded areas are the boundaries of all runs and the dashed lines denote the average of all maximal $J ( m )$ values found at any generation.
+
+In Figure 3, we show the results of runs where we use a time-dependent adaptive penalty. During periods of saturation, the weight of the discriminator predictions is switched from 0 to 1000 until stagnation is overcome. The genetic algorithm is hence forced to propose new families of molecules to increase $J ( m )$ . As it can be observed in Figure 3, even after steep decreases in max $J ( m )$ , the scores recover and potentially reach values higher than in previous plateaus. We observe that this approach significantly outperforms all previous methods in maximizing the objective $J ( m )$ .
+
+Visual inspection of the highest performing molecules shows that the GA is exploiting deficiencies of the (penalized) logP metric by generating chemically irrelevant motifs such as sulfur chains. While being of limited relevance for application, this nonetheless shows the that the GA is very efficient in exploring the chemical space and finding solutions for a given task. Analysis of these solutions will help us to better understand and eventually improve objective functions. At the same time, surprising solutions found by an unbiased algorithm can lead to unexpected discovery or boost human creativity (Lehman et al. (2018)). While exploitative tasks that follow some reference database are significant for questions involving drug design, more explorative behaviour could be beneficial in domains such as solar cell design (Yan et al. (2018)), flow battery design (Yang et al. (2018)), and in particular for questions where datas sets are not available, such as design of targets in molecular beam interferometry (Fein et al. (2019)).
+
+# 4.3 ANALYSIS OF MOLECULE CLASSES EXPLORED BY THE GA
+
+Figure 4 shows classes of molecules explored by the GA in a trajectory with 1000 generations and a generation size of 500 (see trajectories in Figure 3). A K-means clustering analysis based in the RDKit fingerprint bit-vectors with 20 clusters was used to automatically generate labels for the 50 best performing molecules (in terms of their properties $J ( m ) )$ in each generation. We find that the algorithm starts with a class of relatively small molecules $\approx 4 0$ generations, see class 10), after which the algorithm explores several different classes of large molecules with e.g. aromatic rings and conjugates carbon chains (see class 15) and long linear sulfur chains (see class 1). Class 1 includes the molecules with the highest $J ( m )$ scores found in this work, exceeding values of 20.
+
+The clustering analysis furthermore helps to analyze the large number of generated molecules. This allows us to learn from the data and derive design rules to achieve high target properties. In case of the penalized logP score, we find that representative examples (short distance to the cluster center) of high performing classes contain aromatic rings, conjugated carbon chains and linear sulfur chains, which can act as design rules for molecules with high penalized logP scores. Using these design rules to construct molecules of the maximally allowed length consisting of only sulfur chains, conjugated carbon chains and chains of benzene rings with sulfur bridges yields $J ( m )$ scores of 31.79, 8.58 and 10.02, respectively. The $J ( m )$ score reached by the linear sulfur chain outperforms the best scores found by the GA and other generative models.
+
+![](images/04234c4f6b79ca40a8d1e626bb482800990dabdb63eb59bb12853abcf43c18cf.jpg)  
+Figure 4: Classes of molecules explored by the GA.
+
+To visualize the explorative behaviour of the GA, we did a two-dimensional principal component analysis (PCA) of the molecular fingerprint vectors of all molecules generated by the GA-D(t) in the trajectory shown in Figure 4. Five snapshots of the trajectory are shown in Figure 5, colored according to their chemical family. The property score $J ( m )$ of the trajectory is visualized in the images. We find that the GA sequentially explores different parts of the 2D projection of the chemical space, finding different families of high performing molecules, while the discriminator prevents the algorithm from searching in the same space repeatedly.
+
+# 4.4 CONSTRAINED OPTIMIZATION
+
+In the previous sections, we aimed to maximize the penalized logP objective. Here, we consider two different tasks: firstly, generating molecules of specific chemical interest and secondly, modifying existing molecules to increase penalized logP scores. We used $\beta = 0$ throughout Section 4.4.
+
+# 4.4.1 GENERATING MOLECULES WITH SPECIFIC PROPERTIES
+
+We run 250 instances of randomly selected sets of target properties (logP in the interval from -5 to 10, SA scores in the range from 1 to 5 and ring penalty for 0 to 3). The fitness function is modified to minimize the summed squared difference between the actual and desired properties. We compute the number of experiments that successfully proposed molecules with a squared difference less than 1.0. Each run is constrained to run for 100 generations with a maximum canonical SMILES length of 81 characters. In $9 0 . 0 \%$ of the cases, our approach proposes the desired molecules.
+
+![](images/6c84c0650154d15dd7d2a99e7ff938cd2a71d8e1ddedddfaa2617c1d53371d24.jpg)  
+Figure 5: Two-dimensional PCA of five time snapshots of the molecular space explored by the GA-D(t).
+
+Table 2: Comparison on constrained improvement of penalized logP of specific molecules.   
+
+<table><tr><td rowspan="2"></td><td colspan="2">δ=0.4</td><td colspan="2">δ=0.6</td></tr><tr><td>Improvement</td><td>Success</td><td>Improvement</td><td> Success</td></tr><tr><td>JT-VAE (Jin et al., 2018a)</td><td>0.84± 1.45</td><td>83.6%</td><td>0.21 ± 0.71</td><td>46.4%</td></tr><tr><td>GCPN (You et al., 2018)</td><td>2.49 ± 1.30</td><td>100.0%</td><td>0.79 ± 0.63</td><td>100.0%</td></tr><tr><td>MMPA (Jin et al., 2018b)</td><td>3.29 ± 1.12</td><td>=</td><td>1.65 ± 1.44</td><td>=</td></tr><tr><td>DEFactor (Assouel et al., 2018)</td><td>3.41 ± 1.67</td><td>85.9%</td><td>1.55 ± 1.19</td><td>72.6%</td></tr><tr><td>VJTNN (Jin et al., 2018b)</td><td>3.55 ± 1.67</td><td></td><td>2.33 ± 1.17</td><td>=</td></tr><tr><td>GA (here)</td><td>5.93 ±1.41</td><td>100.0%</td><td>3.44 ±1.09</td><td>99.8%</td></tr></table>
+
+![](images/0c48f77a68a32c1f7df2c1b10e66a8aca5432b6c736808cfafc20c175d1d3669.jpg)  
+Figure 6: Distributions of logP and QED for a) ZINC and b) GuacaMol data set compared to molecules generated using the GA. c) Examples of molecules generated by the GA with high logP and QED scores.
+
+# 4.4.2 IMPROVING PENALIZED LOGP SCORES OF SPECIFIC MOLECULES
+
+In this experiment, we follow the experimental setup proposed by You et al. (2018). We optimize the penalized logP score of 800 low-scoring molecules from the ZINC data set. Our genetic algorithm is initiated with a molecule from the data set, and we run each experiment for 20 generations and a population size of 500 without the discriminator. For each run, we report the molecule $m$ that increases the penalized logP the greatest, while possessing a similarity $s i m ( m , m ^ { \prime } ) > \delta$ with the respective reference molecules $m ^ { \prime }$ . We calculate molecular similarity based on Morgan Fingerprints of radius 2. To ensure generation of molecules possessing a certain similarity, for molecule $m$ we modify the fitness to:
+
+$$
+F ( m ) = J ( m ) + \mathrm { S i m i l a r i t y P e n a l t y } ( m ) .
+$$
+
+Here, SimilarityPenalty $( m )$ is 0 if $s i m ( m , m ^ { \prime } ) > \delta$ and $- 1 0 ^ { 6 }$ otherwise. In Table 2, we report the average improvement for each molecule. Success is determined when the GA successfully improve upon the penalized logP score, while not violating the similarity constraint. Figure S1 shows examples of improved molecular structures.
+
+# 4.5 SIMULTANEOUS LOGP AND QED OPTIMIZATION
+
+To show the performance of the GA on a drug-discovery task (Brown et al., 2019; Polykovskiy et al., 2018), we modified the objective function to include the drug-likeness score QED (Bickerton et al., 2012). Solubility metric logP and drug-likeness cannot be maximized at the same time, which is shown in Figure 6 at the example of the ZINC and the GuacaMol data set (Brown et al., 2019). The experiment shows that the GA is able to efficiently and densely sample the edge of the property distributions of both data sets. Example molecules that simultaneously maximize logP and QED are shown in Figure 6c.
+
+# 4.6 MODIFICATION OF THE HYPERPARAMETER $\beta$
+
+The definition of the fitness function used in this work (see Equation 1) has a free parameter $( \beta )$ , that balances the relative importance of molecular target properties $J ( m )$ and discriminator score
+
+![](images/703febb1dd3aa996eac8e84ce805c1d68d5a2b27f94cbbda621b493c47357f89.jpg)  
+Figure 7: Variation of the model parameter $\beta$ that weights the discriminator score in the overall fitness function. a) Average $J ( m )$ as a function of the generation. b) Average discriminator score as a function of the generation. c) Distributions of $J ( m )$ and discriminator score $D$ for multiple values of $\beta$ . d) Examples of molecules generated with $\beta = 0$ and $\beta = 5 0$ .
+
+$D ( m )$ . Large values of $\beta$ promote the generation of molecules that resemble the molecules from the reference data set, while small values of $\beta$ let the GA explore molecules outside of the distribution of the reference data set. To systematically explore this behaviour, we varied the $\beta$ parameter and analyzed the resulting values of $J ( m )$ , $D ( m )$ as well as their distributions. Figure 7 illustrates the results of this test, where each curve is obtained from averaging five independent runs with equal settings.
+
+In Figure 7a, we show the average property score $J ( m )$ for 11 different values $\beta$ and observe, as expected, that low values of $\beta$ on average lead to higher $J ( m )$ score while very high values of $\beta$ limit the algorithm to stay inside the reference data set distribution, which, per definition, has a mean $J ( m )$ score of 0. Figure 7b illustrates the low average discriminator scores encountered after a few generations in case of low values of $\beta$ . The curves shown in Figure 7a and b suggest that $\beta$ allows us to interpolate between high and low $J ( m )$ and high and low resemblance with the reference data set. However, as shown in Figure $\mathrm { 7 c }$ , this is not the case. At values of $\beta \approx 2 0$ , there is a rather fast transition from molecules with high values of $J ( m )$ of approximately 12-13 to a $J ( m )$ distribution centered around 0 which is similar to the $J ( m )$ distribution of the reference data set. The same abrupt change is visible in the distributions of the discriminator scores. Only at $\beta \approx 1 8$ , we find a slightly wider distribution of intermediate $J ( m )$ values, which we assume is partially related to the fact that the $\beta = 1 8$ curve shown in Figure 7a is not converged yet.
+
+Figure 7d shows examples of molecules generated with $\beta = 0$ (upper panel) and $\beta = 5 0$ (lower panel). While in the first case, the GA finds large molecules with many aromatic rings and long linear chains, that do not resemble the molecules in the reference data set, the latter case shows molecules with structures and properties resembling the reference data set. In this case, the distribution of $J ( m )$ is comparable to that of the data set (with 0 mean and unit standard deviation), while the discriminator encounters difficulty in correctly classification of the GA molecules, indicated by a mean discriminator score varying around 0.5 across many generations.
+
+# 5 CONCLUSIONS AND FUTURE WORK
+
+We presented a hybrid GA and ML-based generative model and demonstrated its application in molecular design. The model outperforms literature approaches in generating molecules with desired properties. A detailed analysis of the data generated by the genetic algorithm allowed us to
+
+interpret the model and learn rules for the design of high performing molecules. This human expert design inspired from GA molecules outperformed all molecules created by generative models.
+
+For computationally more expensive property evaluations, we will extend our approach by the introduction of an on-the-fly trained ML property evaluation method, which will open new ways of solving the inverse design challenge in chemistry and materials sciences.
+
+Our approach is independent of domain knowledge, thus applicable to design questions in other scientific disciplines beyond chemistry. We therefore plan to generalize the GA-D approach to make it a more general concept of generative modelling.
+
+# ACKNOWLEDGMENTS
+
+The authors thank Gabriel dos Passos Gomes & Andres Aguilar Granda for useful discussions. ´ A. A.-G. acknowledges generous support from the Canada 150 Research Chair Program, Tata Steel, Anders G. Froseth, and the Office of Naval Research. M.K. acknowledges support from the Austrian Science Fund (FWF) through the Erwin Schrodinger fellowship No. J4309. P.F. has received funding ¨ from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 795206.
+
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+
+# 6 SUPPLEMENTARY INFORMATION
+
+![](images/3549f3b7f48130e0d518e5f9934ce9d76c66fecc32988bf1c0754d09c73462b5.jpg)  
+Figure S1 shows examples of the molecules optimized in Section 4.4.   
+Figure S1: Molecular modifications resulting in increased penalized logP scores under similarity constraint $s i m ( m , m ^ { \prime } ) > 0 . 4 , 0 . 6$ . We show the molecules that resulted in largest score improvement.
+
+Figures S2-S4 show comparisons between the property distributions observed in molecule data sets such as the ZINC and the GuacaMol data set and property distributions of molecules generated using random SELFIES (Figure S2), GA generated molecules with the penalized logP objective (Figure S3) and GA generated molecules with an objective function which includes logP and QED (Figure S4). While the average logP scores of average SELFIES are low, the tail of the distribution reaches to high values, explaining the surprisingly high penalized logP scores shown in Table 1. The QED and weight distributions of molecules optimized using the penalized logP objective significantly differ from the distributions of the ZINC and the GuacaMol data set (see Figure S3). As soon as the QED score is simultaneously optimized, the distributions of GA generated molecules and molecules from the reference data sets become more similar (see Figure S4). Figure 6 shows that the GA can simultaneously optimize logP and QED.
+
+![](images/98c1c4d7b4631aecc961db4861ae804b912dc18f02663ebd94fee1dd43123ff1.jpg)  
+Figure S2: Distributions of a) logP, b) SA, c) QED and d) molecular weight for randomly generated SELFIES, molecules from the ZINC data set and molecules from the GuacaMol data set.
+
+![](images/0b2fe1902257956f8e1f0aff6e39629e1d60d21ed734e740396b704826f0f390.jpg)  
+Figure S3: Distributions of a) logP, b) SA, c) QED and d) molecular weight for GA generated SELFIES (penalized logP objective function), molecules from the ZINC data set and molecules from the GuacaMol data set.
+
+![](images/f0a16e3dfe7a6ddbd1c5a21733c9c2a93729ff2b844168e7e49bf1ba32061192.jpg)  
+Figure S4: Distributions of a) logP, b) SA, c) QED and d) molecular weight for GA generated SELFIES (logP and QED as objective function), molecules from the ZINC data set and molecules from the GuacaMol data set.

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+        "type": "text",
+        "text": "AkshatKumar Nigam1,†, Pascal Friederich1,2,† Mario Krenn, 1,3,4, Alan Aspuru-Guzik ´ 1,3,4,5, $^ *$ ",
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+        "type": "text",
+        "text": "1Department of Computer Science, University of Toronto, Canada.   \n2Institute of Nanotechnology, Karlsruhe Institute of Technology, Germany.   \n3Department of Chemistry, University of Toronto, Canada.   \n4Vector Institute for Artificial Intelligence, Toronto, Canada.   \n5Canadian Institute for Advanced Research (CIFAR) Senior Fellow, Toronto, Canada ",
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+        "type": "text",
+        "text": "ABSTRACT ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Challenges in natural sciences can often be phrased as optimization problems. Machine learning techniques have recently been applied to solve such problems. One example in chemistry is the design of tailor-made organic materials and molecules, which requires efficient methods to explore the chemical space. We present a genetic algorithm (GA) that is enhanced with a neural network (DNN) based discriminator model to improve the diversity of generated molecules and at the same time steer the GA. We show that our algorithm outperforms other generative models in optimization tasks. We furthermore present a way to increase interpretability of genetic algorithms, which helped us to derive design principles. ",
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+        "type": "text",
+        "text": "Our open source implementation: https://github.com/aspuru-guzik-group/GA ",
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+    {
+        "type": "text",
+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "The design of optimal structures under constraints is an important problem spanning multiple domains in the physical sciences. Specifically, in chemistry, the design of tailor-made organic materials and molecules requires efficient methods to explore the chemical space. Purely experimental approaches are often time consuming and expensive. Reliable computational tools can accelerate and guide experimental efforts to find new materials faster. ",
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+    {
+        "type": "text",
+        "text": "We present a genetic algorithm (GA) (Davis, 1991; Devillers, 1996; Sheridan & Kearsley, 1995; Parrill, 1996) for molecular design that is enhanced with two features: ",
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+    {
+        "type": "text",
+        "text": "1. A neural network based adaptive penalty. This promotes exploratory behaviour of the GA and thus improve the diversity of generated molecules.   \n2. Exploiting the robustness of SELFIES (Krenn et al., 2019), we do not need to incorporate any expert based mutation or cross-over rules. ",
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+    {
+        "type": "text",
+        "text": "Starting from only simple methane molecules, our algorithm outperforms other generative models in optimization tasks for molecular design. By introducing machine learning (ML) techniques, the long term behaviour is not subject to stagnation, thus solving a significant problem in genetic algorithms (Paszkowicz, 2009). ",
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+    {
+        "type": "text",
+        "text": "No domain knowledge is required; thus, our approach is not limited to chemistry-specific questions but can be applied to a wide range of optimization problems. ",
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+    {
+        "type": "text",
+        "text": "2 RELATED WORKS ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Inverse design is the systematic development of structures with desired properties. In chemistry (Sanchez-Lengeling & Aspuru-Guzik, 2018), the challenge of inverse design has been tackled as an optimization problem, among others in the form of variational autoencoders (VAEs), generative adversarial networks (GANs) and genetic algorithms. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Variational autoencoders and generative adversarial networks VAEs (Kingma & Welling, 2013) are a widely used method for direct generation of molecular string or graph representations (Gomez- ´ Bombarelli et al., 2018). They encode discrete representations into a continuous (latent) space. Molecules resembling a known structure can be found by searching around the region of the encoded point. Making using of the continuous latent representation, it is possible to search via gradients or Bayesian Optimization (BO). However, the generation of semantically and syntactically valid molecules is a challenging task. Thus, several follow up works to the VAE have been proposed for inverse design in chemistry. Among them, CVAE (Gomez-Bombarelli et al., 2018), GVAE (Kusner ´ et al., 2017) and SD-VAE (Dai et al., 2018) work directly on string molecular representations. Alternatively, JT-VAE (Jin et al., 2018a) as well as CGVAE Liu et al. (2018) work on molecular graphs. Unlike latent space property optimization, the policy network (PN) based GCPN model (You et al., 2018) proposes a reinforcement learning (RL)-based method for direct optimization on molecular graphs. ORGAN (Guimaraes et al., 2017) demonstrate training string-based generative adversarial networks (GANs) (Goodfellow et al., 2014) via RL. Another method based on adversarial training is VJTNN (Jin et al., 2018b). Segler et al. (2017) first introduced molecule generating models based on language models and reinforcement learning, where actions in an environment are taken to construct a molecule, receiving reward from an external scoring function. This model has also shown strong performance in the GuacaMol benchmark (Brown et al. (2019)). ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "In all the approaches mentioned above, generative models are trained to mimic the reference data set distributions, thus limiting the exploration ability of VAEs and GANs. ",
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+    {
+        "type": "text",
+        "text": "Genetic algorithms & related methods There exist several examples of GA based molecule optimization algorithms in literature (O’Boyle et al., 2011; Virshup et al., 2013; Rupakheti et al., 2015; Jensen, 2019; Sheridan & Kearsley, 1995; Parrill, 1996)). While some of these examples pre-define mutations on a SMILES level to ensure validity of the molecules, other approaches use fragmentbased assembly of molecules. GAs are likely to get trapped in regions of local optima (Paszkowicz, 2009). Thus, for selection of the best molecules, (Rupakheti et al., 2015; Jensen, 2019) report multiple restarts upon stagnation. ",
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+        "type": "text",
+        "text": "We include the aforementioned models as baselines for numerical comparison. ",
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+    {
+        "type": "text",
+        "text": "3 GA-D ARCHITECTURE ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "3.1 OVERVIEW ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Our approach is illustrated in Figure 1. Our generator is a genetic algorithm with a population of molecules $m$ . In each generation, the fitness of all molecules is evaluated as a linear combination of molecular properties $J ( m )$ and the discriminator score $D ( m )$ : ",
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+    {
+        "type": "equation",
+        "img_path": "images/9d724121969189bfa2a1b1fe6b5ba05eefd8f2c8c6ed18fecfd2b720e64aaaa4.jpg",
+        "text": "$$\nF ( m ) = J ( m ) + \\beta \\cdot D ( m ) .\n$$",
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+    {
+        "type": "text",
+        "text": "Random mutations of high fitness (best performing) molecules replace inferior members, while bestperforming molecules continue to a subsequent generation. The probability of replacing a molecule is evaluated using a smooth logistic function based on a ranking of fitness among the molecules of a generation. At the end of each generation, a neural network based discriminator is trained jointly on molecules generated by the GA and a reference data set. The fitness evaluation accounts for the discriminator predictions for each molecule. Therefore, the discriminator plays a role in the selection of the subsequent population. ",
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+    {
+        "type": "text",
+        "text": "3.2 MUTATION & CROSS-OVER RULES ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Mutation of molecules to populate subsequent generations is an important element of the GA. A low degree of mutation can lead to a slow exploration of the chemical space, causing stagnation of the fitness function. Robustness of SELFIES allows us to do random mutations to molecular strings while preserving their validity. Thus, our mutations only include $50 \\%$ insertions or $50 \\%$ replacements of single SELFIES characters. To accelerate the exploration of the GA, we add one domain-specific mutation rule – the direct addition of phenyl groups in approximately $4 \\%$ of cases. Character deletion is implicitly taken into account in SELFIES mutations, and we do not use crossover rules. ",
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+    {
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+        "img_path": "images/cd8ba097b50038f6cdae830c10832404738ad3b8627fc5dca4f7f4fe13e99c02.jpg",
+        "image_caption": [
+            "Figure 1: Overview of our hybrid structure, which augments genetic algorithms with ML based neural networks. "
+        ],
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+        "type": "text",
+        "text": "",
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+    {
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+        "img_path": "images/1a7ea4f895854a7ad8f1e31c30dd5d557167d6d4a420117faffe1ea9a85edf30.jpg",
+        "image_caption": [
+            "Figure 2: Reducing Fitness of $o$ -terphenyl, initially possessing the largest fitness in generation 5 $( R a n k = O )$ ). Due to decreasing discriminator predictions $D ( m )$ , fitness decreases with an increased probability of getting killed (Kill Prob.). The molecule is completely replaced in generation 16. Rank denotes the position of the molecule in an increasing fitness list of generation molecules. "
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+    {
+        "type": "text",
+        "text": "3.3 ROLE OF THE DISCRIMINATOR ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "The fundamental role of the discriminator is to increase molecular diversity by removing longsurviving molecules. Consider the realistic scenario in which a GA has found a molecule close to a local optimum, where all mutations are lowering the fitness. As a result, this molecule survives for multiple generations while occupying a large fraction of the population. During such periods, the GA has limited view of the chemical space as it repeatedly explores mutations of the same high-fitness molecule. ",
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+        "type": "text",
+        "text": "A straightforward solution would be the addition of a linear penalty (Nanakorn & Meesomklin, 2001) in the fitness function that accounts for the number of successive generations a molecule survives. However, this method assigns independent scores to similar-looking molecules, which again results in less variety. ",
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+        "type": "text",
+        "text": "Our solution is the addition of an adaptive penalty (in our case a neural network based discriminator), thus resolving the problem of stagnation. Molecules with similar representation receive similar classification scores. Furthermore, long-surviving molecules are trained longer and receive weaker scores, resulting in decreasing fitness - reducing the chance of long periods of stagnation (illustrated in Figure 2). The task of the discriminator thus is to memorize families of high performing molecules and penalize their fitness to force the GA to explore different regions in chemical space. ",
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+    {
+        "type": "text",
+        "text": "4 EXPERIMENTS ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Comparing to the literature standard, we aim at maximizing the penalized logP objective $J ( m )$ proposed by (Gomez-Bombarelli et al., 2018). For molecule ´ $m$ , the penalized logP function is defined as ",
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+    {
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+        "img_path": "images/6d889c1e03d6921a8f0b1922653e80053166fe9db20c215e598cce9e6d01cf30.jpg",
+        "text": "$$\nJ ( m ) = \\log \\mathrm { P } ( m ) - \\mathrm { S A } ( m ) - \\mathrm { R i n g } \\mathrm { P e n a l t y } ( m ) ,\n$$",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "where logP indicates the water-octanol partition coefficient, SA (Ertl & Schuffenhauer, 2009) represents the synthetic accessibility and prevents the formation of chemically unfeasible molecules, and RingPenalty linearly penalizes the presence of rings of size larger than 6. Our reference data set consists of 250,000 commercially available molecules extracted from the ZINC database (Irwin et al., 2012). All three quantities in the above equation are normalized based on this data set. ",
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+    {
+        "type": "table",
+        "img_path": "images/aa7109a37b8dc337703cccf5bf54833ffdeafa92525d1fc0ba4b4cbf6eba4023.jpg",
+        "table_caption": [
+            "Table 1: Comparison of our model with maximum penalized logP scores reported in literature. Models in the upper part are forced to optimize within the distributions of given reference data sets while the GA based approaches in the lower part can freely explore chemical space. Direct comparisons need to take into account these different objectives and scopes. The parameter $\\beta$ in our GA can be used to balance exploration and exploitation (see Section 4.6). "
+        ],
+        "table_footnote": [
+            "1 average of three best molecules after performing Bayesian optimization on the latent representation of a trained VAE 2 two best molecules of a single run 3 averaged over 10 runs with 20 molecules per generation with a molecular weight (excl. hydrogen) smaller than $3 9 . 1 5 \\pm 3 . 5 0 \\mathrm { g / m o l }$ run for 50 generations 4 averaged over 10 runs with 500 molecules up to 81 characters per generation and 100 generations averaged over 5 runs with 1000 generations each "
+        ],
+        "table_body": "<table><tr><td>Model</td><td>Max. Penalized logP</td><td>Model</td></tr><tr><td>GVAE + BO (Kusner et al.,2017) 1</td><td>2.87 ± 0.06</td><td>VAE</td></tr><tr><td>SD-VAE (Dai et al., 2018) 1</td><td>3.50 ± 0.44</td><td>VAE</td></tr><tr><td>CVAE + BO (G6mez-Bombarelli et al., 2018) 2</td><td>4.85 ± 0.17</td><td>VAE</td></tr><tr><td>ORGAN (Guimaraes et al., 2017) 1</td><td>3.52 ± 0.08</td><td>GAN</td></tr><tr><td>JT-VAE (Jin et al., 2018a) 1</td><td>4.90 ± 0.33</td><td>VAE</td></tr><tr><td>ChemTS (Yang et al., 2017)</td><td>5.6 ± 0.5</td><td>RNN</td></tr><tr><td>GCPN(You et al., 2018) 1</td><td>7.87 ± 0.07</td><td>PN + GAN</td></tr><tr><td>Random SELFIES</td><td>6.19 ± 0.63</td><td>Random Search</td></tr><tr><td>GB-GA (Jensen, 2019) 3</td><td>7.4±0.9</td><td>GA</td></tr><tr><td>GB-GA (Jensen, 2019) 4</td><td>15.76 ± 5.71</td><td>GA</td></tr><tr><td>GA (here)</td><td>12.61 ± 0.81</td><td>GA</td></tr><tr><td>GA + D (here)</td><td>13.31 ± 0.63</td><td>GA+DNN</td></tr><tr><td>(GA + D(t) (here) 5</td><td>20.72 ± 3.14)</td><td>GA +DNN</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "4.1 UNCONSTRAINED OPTIMIZATION AND COMPARISON WITH OTHER GENERATIVE MODELS ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We define our fitness function according to Eq. 1 and 2 with $\\beta = 0$ and 10. The algorithm is run for 100 generations with a population size of 500. All generated molecules are constrained to a canonical smile length of 81 characters (as in (Yang et al., 2017; Jensen, 2019)). We train the discriminator (fully connected neural network with ReLU activation and sigmoid output layer, the input is a vector of chemical and geometrical properties characterizing the molecules) at the end of each generation for 10 epochs on 500 molecules proposed by the GA and 500 randomly drawn molecules from the ZINC data set. We report maximum $J ( m )$ scores, averaged over 10 independent runs. The highest $J ( m )$ achieved by our approach are $1 3 . 3 1 \\pm 0 . 6 3$ $\\beta = 1 0 $ ) and ",
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+        "text": "$1 2 . 6 1 \\pm 0 . 8 1$ $\\beta = 0 ,$ ), respectively, which is almost twice as high es the highest literature value of $7 . 8 7 { \\pm } 0 . 0 7$ (See Table 1). Furthermore, we compare to 50,000 random valid SELFIES strings, which surprisingly outperforms some existing generative models. The GA-D(t) results are explained in the next section. ",
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+    {
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+        "img_path": "images/05992edc307d774b967ad9610de9401894ae39f99f02815e3d93a335121cd6fb.jpg",
+        "image_caption": [
+            "4.2 LONG TERM EXPERIMENT WITH A TIME-DEPENDENT ADAPTIVE PENALTY",
+            "Figure 3: Maximum $J ( m )$ values found for 10 independent runs with no discriminator $\\mathcal { B } = 0 ,$ ) and 5 independent runs with the introduction of a time-dependent adaptive penalty. The full line is the average of all runs, the shaded areas are the boundaries of all runs and the dashed lines denote the average of all maximal $J ( m )$ values found at any generation. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In Figure 3, we show the results of runs where we use a time-dependent adaptive penalty. During periods of saturation, the weight of the discriminator predictions is switched from 0 to 1000 until stagnation is overcome. The genetic algorithm is hence forced to propose new families of molecules to increase $J ( m )$ . As it can be observed in Figure 3, even after steep decreases in max $J ( m )$ , the scores recover and potentially reach values higher than in previous plateaus. We observe that this approach significantly outperforms all previous methods in maximizing the objective $J ( m )$ . ",
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+    {
+        "type": "text",
+        "text": "Visual inspection of the highest performing molecules shows that the GA is exploiting deficiencies of the (penalized) logP metric by generating chemically irrelevant motifs such as sulfur chains. While being of limited relevance for application, this nonetheless shows the that the GA is very efficient in exploring the chemical space and finding solutions for a given task. Analysis of these solutions will help us to better understand and eventually improve objective functions. At the same time, surprising solutions found by an unbiased algorithm can lead to unexpected discovery or boost human creativity (Lehman et al. (2018)). While exploitative tasks that follow some reference database are significant for questions involving drug design, more explorative behaviour could be beneficial in domains such as solar cell design (Yan et al. (2018)), flow battery design (Yang et al. (2018)), and in particular for questions where datas sets are not available, such as design of targets in molecular beam interferometry (Fein et al. (2019)). ",
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+    {
+        "type": "text",
+        "text": "4.3 ANALYSIS OF MOLECULE CLASSES EXPLORED BY THE GA ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Figure 4 shows classes of molecules explored by the GA in a trajectory with 1000 generations and a generation size of 500 (see trajectories in Figure 3). A K-means clustering analysis based in the RDKit fingerprint bit-vectors with 20 clusters was used to automatically generate labels for the 50 best performing molecules (in terms of their properties $J ( m ) )$ in each generation. We find that the algorithm starts with a class of relatively small molecules $\\approx 4 0$ generations, see class 10), after which the algorithm explores several different classes of large molecules with e.g. aromatic rings and conjugates carbon chains (see class 15) and long linear sulfur chains (see class 1). Class 1 includes the molecules with the highest $J ( m )$ scores found in this work, exceeding values of 20. ",
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+    {
+        "type": "text",
+        "text": "The clustering analysis furthermore helps to analyze the large number of generated molecules. This allows us to learn from the data and derive design rules to achieve high target properties. In case of the penalized logP score, we find that representative examples (short distance to the cluster center) of high performing classes contain aromatic rings, conjugated carbon chains and linear sulfur chains, which can act as design rules for molecules with high penalized logP scores. Using these design rules to construct molecules of the maximally allowed length consisting of only sulfur chains, conjugated carbon chains and chains of benzene rings with sulfur bridges yields $J ( m )$ scores of 31.79, 8.58 and 10.02, respectively. The $J ( m )$ score reached by the linear sulfur chain outperforms the best scores found by the GA and other generative models. ",
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+        "image_caption": [
+            "Figure 4: Classes of molecules explored by the GA. "
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+        "type": "text",
+        "text": "To visualize the explorative behaviour of the GA, we did a two-dimensional principal component analysis (PCA) of the molecular fingerprint vectors of all molecules generated by the GA-D(t) in the trajectory shown in Figure 4. Five snapshots of the trajectory are shown in Figure 5, colored according to their chemical family. The property score $J ( m )$ of the trajectory is visualized in the images. We find that the GA sequentially explores different parts of the 2D projection of the chemical space, finding different families of high performing molecules, while the discriminator prevents the algorithm from searching in the same space repeatedly. ",
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+    {
+        "type": "text",
+        "text": "4.4 CONSTRAINED OPTIMIZATION ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In the previous sections, we aimed to maximize the penalized logP objective. Here, we consider two different tasks: firstly, generating molecules of specific chemical interest and secondly, modifying existing molecules to increase penalized logP scores. We used $\\beta = 0$ throughout Section 4.4. ",
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+    {
+        "type": "text",
+        "text": "4.4.1 GENERATING MOLECULES WITH SPECIFIC PROPERTIES",
+        "text_level": 1,
+        "bbox": [
+            181,
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+    {
+        "type": "text",
+        "text": "We run 250 instances of randomly selected sets of target properties (logP in the interval from -5 to 10, SA scores in the range from 1 to 5 and ring penalty for 0 to 3). The fitness function is modified to minimize the summed squared difference between the actual and desired properties. We compute the number of experiments that successfully proposed molecules with a squared difference less than 1.0. Each run is constrained to run for 100 generations with a maximum canonical SMILES length of 81 characters. In $9 0 . 0 \\%$ of the cases, our approach proposes the desired molecules. ",
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+    },
+    {
+        "type": "image",
+        "img_path": "images/6c84c0650154d15dd7d2a99e7ff938cd2a71d8e1ddedddfaa2617c1d53371d24.jpg",
+        "image_caption": [
+            "Figure 5: Two-dimensional PCA of five time snapshots of the molecular space explored by the GA-D(t). "
+        ],
+        "image_footnote": [],
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+    {
+        "type": "table",
+        "img_path": "images/243120b8e5bfc12f10608303fcb6e016f6084b2b73ef1508820579218de0a695.jpg",
+        "table_caption": [
+            "Table 2: Comparison on constrained improvement of penalized logP of specific molecules. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\"></td><td colspan=\"2\">δ=0.4</td><td colspan=\"2\">δ=0.6</td></tr><tr><td>Improvement</td><td>Success</td><td>Improvement</td><td> Success</td></tr><tr><td>JT-VAE (Jin et al., 2018a)</td><td>0.84± 1.45</td><td>83.6%</td><td>0.21 ± 0.71</td><td>46.4%</td></tr><tr><td>GCPN (You et al., 2018)</td><td>2.49 ± 1.30</td><td>100.0%</td><td>0.79 ± 0.63</td><td>100.0%</td></tr><tr><td>MMPA (Jin et al., 2018b)</td><td>3.29 ± 1.12</td><td>=</td><td>1.65 ± 1.44</td><td>=</td></tr><tr><td>DEFactor (Assouel et al., 2018)</td><td>3.41 ± 1.67</td><td>85.9%</td><td>1.55 ± 1.19</td><td>72.6%</td></tr><tr><td>VJTNN (Jin et al., 2018b)</td><td>3.55 ± 1.67</td><td></td><td>2.33 ± 1.17</td><td>=</td></tr><tr><td>GA (here)</td><td>5.93 ±1.41</td><td>100.0%</td><td>3.44 ±1.09</td><td>99.8%</td></tr></table>",
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+    {
+        "type": "image",
+        "img_path": "images/0c48f77a68a32c1f7df2c1b10e66a8aca5432b6c736808cfafc20c175d1d3669.jpg",
+        "image_caption": [
+            "Figure 6: Distributions of logP and QED for a) ZINC and b) GuacaMol data set compared to molecules generated using the GA. c) Examples of molecules generated by the GA with high logP and QED scores. "
+        ],
+        "image_footnote": [],
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+    },
+    {
+        "type": "text",
+        "text": "4.4.2 IMPROVING PENALIZED LOGP SCORES OF SPECIFIC MOLECULES",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In this experiment, we follow the experimental setup proposed by You et al. (2018). We optimize the penalized logP score of 800 low-scoring molecules from the ZINC data set. Our genetic algorithm is initiated with a molecule from the data set, and we run each experiment for 20 generations and a population size of 500 without the discriminator. For each run, we report the molecule $m$ that increases the penalized logP the greatest, while possessing a similarity $s i m ( m , m ^ { \\prime } ) > \\delta$ with the respective reference molecules $m ^ { \\prime }$ . We calculate molecular similarity based on Morgan Fingerprints of radius 2. To ensure generation of molecules possessing a certain similarity, for molecule $m$ we modify the fitness to: ",
+        "bbox": [
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+    },
+    {
+        "type": "equation",
+        "img_path": "images/0cbb169f8a5dd806c25c499811b112e66e5fbb614aaaf08886023ef35beae840.jpg",
+        "text": "$$\nF ( m ) = J ( m ) + \\mathrm { S i m i l a r i t y P e n a l t y } ( m ) .\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "Here, SimilarityPenalty $( m )$ is 0 if $s i m ( m , m ^ { \\prime } ) > \\delta$ and $- 1 0 ^ { 6 }$ otherwise. In Table 2, we report the average improvement for each molecule. Success is determined when the GA successfully improve upon the penalized logP score, while not violating the similarity constraint. Figure S1 shows examples of improved molecular structures. ",
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+    },
+    {
+        "type": "text",
+        "text": "4.5 SIMULTANEOUS LOGP AND QED OPTIMIZATION ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "To show the performance of the GA on a drug-discovery task (Brown et al., 2019; Polykovskiy et al., 2018), we modified the objective function to include the drug-likeness score QED (Bickerton et al., 2012). Solubility metric logP and drug-likeness cannot be maximized at the same time, which is shown in Figure 6 at the example of the ZINC and the GuacaMol data set (Brown et al., 2019). The experiment shows that the GA is able to efficiently and densely sample the edge of the property distributions of both data sets. Example molecules that simultaneously maximize logP and QED are shown in Figure 6c. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "4.6 MODIFICATION OF THE HYPERPARAMETER $\\beta$ ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "The definition of the fitness function used in this work (see Equation 1) has a free parameter $( \\beta )$ , that balances the relative importance of molecular target properties $J ( m )$ and discriminator score ",
+        "bbox": [
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+    },
+    {
+        "type": "image",
+        "img_path": "images/703febb1dd3aa996eac8e84ce805c1d68d5a2b27f94cbbda621b493c47357f89.jpg",
+        "image_caption": [
+            "Figure 7: Variation of the model parameter $\\beta$ that weights the discriminator score in the overall fitness function. a) Average $J ( m )$ as a function of the generation. b) Average discriminator score as a function of the generation. c) Distributions of $J ( m )$ and discriminator score $D$ for multiple values of $\\beta$ . d) Examples of molecules generated with $\\beta = 0$ and $\\beta = 5 0$ . "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "$D ( m )$ . Large values of $\\beta$ promote the generation of molecules that resemble the molecules from the reference data set, while small values of $\\beta$ let the GA explore molecules outside of the distribution of the reference data set. To systematically explore this behaviour, we varied the $\\beta$ parameter and analyzed the resulting values of $J ( m )$ , $D ( m )$ as well as their distributions. Figure 7 illustrates the results of this test, where each curve is obtained from averaging five independent runs with equal settings. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "In Figure 7a, we show the average property score $J ( m )$ for 11 different values $\\beta$ and observe, as expected, that low values of $\\beta$ on average lead to higher $J ( m )$ score while very high values of $\\beta$ limit the algorithm to stay inside the reference data set distribution, which, per definition, has a mean $J ( m )$ score of 0. Figure 7b illustrates the low average discriminator scores encountered after a few generations in case of low values of $\\beta$ . The curves shown in Figure 7a and b suggest that $\\beta$ allows us to interpolate between high and low $J ( m )$ and high and low resemblance with the reference data set. However, as shown in Figure $\\mathrm { 7 c }$ , this is not the case. At values of $\\beta \\approx 2 0$ , there is a rather fast transition from molecules with high values of $J ( m )$ of approximately 12-13 to a $J ( m )$ distribution centered around 0 which is similar to the $J ( m )$ distribution of the reference data set. The same abrupt change is visible in the distributions of the discriminator scores. Only at $\\beta \\approx 1 8$ , we find a slightly wider distribution of intermediate $J ( m )$ values, which we assume is partially related to the fact that the $\\beta = 1 8$ curve shown in Figure 7a is not converged yet. ",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Figure 7d shows examples of molecules generated with $\\beta = 0$ (upper panel) and $\\beta = 5 0$ (lower panel). While in the first case, the GA finds large molecules with many aromatic rings and long linear chains, that do not resemble the molecules in the reference data set, the latter case shows molecules with structures and properties resembling the reference data set. In this case, the distribution of $J ( m )$ is comparable to that of the data set (with 0 mean and unit standard deviation), while the discriminator encounters difficulty in correctly classification of the GA molecules, indicated by a mean discriminator score varying around 0.5 across many generations. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "5 CONCLUSIONS AND FUTURE WORK ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "We presented a hybrid GA and ML-based generative model and demonstrated its application in molecular design. The model outperforms literature approaches in generating molecules with desired properties. A detailed analysis of the data generated by the genetic algorithm allowed us to ",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "interpret the model and learn rules for the design of high performing molecules. This human expert design inspired from GA molecules outperformed all molecules created by generative models. ",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "For computationally more expensive property evaluations, we will extend our approach by the introduction of an on-the-fly trained ML property evaluation method, which will open new ways of solving the inverse design challenge in chemistry and materials sciences. ",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Our approach is independent of domain knowledge, thus applicable to design questions in other scientific disciplines beyond chemistry. We therefore plan to generalize the GA-D approach to make it a more general concept of generative modelling. ",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "ACKNOWLEDGMENTS ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "The authors thank Gabriel dos Passos Gomes & Andres Aguilar Granda for useful discussions. ´ A. A.-G. acknowledges generous support from the Canada 150 Research Chair Program, Tata Steel, Anders G. Froseth, and the Office of Naval Research. M.K. acknowledges support from the Austrian Science Fund (FWF) through the Erwin Schrodinger fellowship No. J4309. P.F. has received funding ¨ from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 795206. ",
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+    },
+    {
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+    },
+    {
+        "type": "text",
+        "text": "6 SUPPLEMENTARY INFORMATION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            103,
+            475,
+            117
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "image",
+        "img_path": "images/3549f3b7f48130e0d518e5f9934ce9d76c66fecc32988bf1c0754d09c73462b5.jpg",
+        "image_caption": [
+            "Figure S1 shows examples of the molecules optimized in Section 4.4. ",
+            "Figure S1: Molecular modifications resulting in increased penalized logP scores under similarity constraint $s i m ( m , m ^ { \\prime } ) > 0 . 4 , 0 . 6$ . We show the molecules that resulted in largest score improvement. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            187,
+            164,
+            810,
+            470
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Figures S2-S4 show comparisons between the property distributions observed in molecule data sets such as the ZINC and the GuacaMol data set and property distributions of molecules generated using random SELFIES (Figure S2), GA generated molecules with the penalized logP objective (Figure S3) and GA generated molecules with an objective function which includes logP and QED (Figure S4). While the average logP scores of average SELFIES are low, the tail of the distribution reaches to high values, explaining the surprisingly high penalized logP scores shown in Table 1. The QED and weight distributions of molecules optimized using the penalized logP objective significantly differ from the distributions of the ZINC and the GuacaMol data set (see Figure S3). As soon as the QED score is simultaneously optimized, the distributions of GA generated molecules and molecules from the reference data sets become more similar (see Figure S4). Figure 6 shows that the GA can simultaneously optimize logP and QED. ",
+        "bbox": [
+            173,
+            547,
+            825,
+            700
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "image",
+        "img_path": "images/98c1c4d7b4631aecc961db4861ae804b912dc18f02663ebd94fee1dd43123ff1.jpg",
+        "image_caption": [
+            "Figure S2: Distributions of a) logP, b) SA, c) QED and d) molecular weight for randomly generated SELFIES, molecules from the ZINC data set and molecules from the GuacaMol data set. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            222,
+            111,
+            771,
+            441
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "image",
+        "img_path": "images/0b2fe1902257956f8e1f0aff6e39629e1d60d21ed734e740396b704826f0f390.jpg",
+        "image_caption": [
+            "Figure S3: Distributions of a) logP, b) SA, c) QED and d) molecular weight for GA generated SELFIES (penalized logP objective function), molecules from the ZINC data set and molecules from the GuacaMol data set. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            222,
+            518,
+            771,
+            849
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "image",
+        "img_path": "images/f0a16e3dfe7a6ddbd1c5a21733c9c2a93729ff2b844168e7e49bf1ba32061192.jpg",
+        "image_caption": [
+            "Figure S4: Distributions of a) logP, b) SA, c) QED and d) molecular weight for GA generated SELFIES (logP and QED as objective function), molecules from the ZINC data set and molecules from the GuacaMol data set. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            243,
+            328,
+            750,
+            633
+        ],
+        "page_idx": 13
+    }
+]

parse/train/H1uP7ebAW/H1uP7ebAW.md

@@ -0,0 +1,283 @@
+# LEARNING TO DIAGNOSE FROM SCRATCH BY EXPLOIT-ING DEPENDENCIES AMONG LABELS
+
+Anonymous authors Paper under double-blind review
+
+# ABSTRACT
+
+The field of medical diagnostics contains a wealth of challenges which closely resemble classical machine learning problems; practical constraints, however, complicate the translation of these endpoints naively into classical architectures. Many tasks in radiology, for example, are largely problems of multi-label classification wherein medical images are interpreted to indicate multiple present or suspected pathologies. Clinical settings drive the necessity for high accuracy simultaneously across a multitude of pathological outcomes and greatly limit the utility of tools which consider only a subset. This issue is exacerbated by a general scarcity of training data and maximizes the need to extract clinically relevant features from available samples – ideally without the use of pre-trained models which may carry forward undesirable biases from tangentially related tasks. We present and evaluate a partial solution to these constraints in using LSTMs to leverage interdependencies among target labels in predicting 14 pathologic patterns from chest x-rays and establish state of the art results on the largest publicly available chest $\mathbf { X }$ -ray dataset from the NIH without pre-training. Furthermore, we propose and discuss alternative evaluation metrics and their relevance in clinical practice.
+
+# 1 INTRODUCTION
+
+Medical diagnostics have increasingly become a more interesting and viable endpoint for machine learning. A general scarcity of publicly available medical data, however, inhibits its rapid development. Pre-training on tangentially related datasets such as ImageNet (Deng et al., 2009) has been shown to help in circumstances where training data is limited, but may introduce unintended biases which are undesirable in a clinical setting. Furthermore, most clinical settings will drive a need for models which can accurately predict a large number of diagnostic outcomes. This essentially turns many medical problems into multi-label classification with a large number of targets, many of which may be subtle or poorly defined and are likely to be inconsistently labeled. In addition, unlike the traditional multi-label setting, predicting the absence of each label is as important as predicting its presence in order to minimize the possibility of misdiagnosis. Each of these challenges drive a need for architectures which consider clinical context to make the most of the data available.
+
+Chest $\mathbf { X }$ -rays are the most common type of radiology exam in the world and a particularly challenging example of multi-label classification in medical diagnostics. Making up nearly $45 \%$ of all radiological studies, the chest $\mathbf { X }$ -ray has achieved global ubiquity as a low-cost screening tool for a wealth of pathologies including lung cancer, tuberculosis, and pneumonia. Each scan can contain dozens of patterns corresponding to hundreds of potential pathologies and can thus be difficult to interpret, suffering from high disagreement rates between radiologists and often resulting in unnecessary follow-up procedures. Complex interactions between abnormal patterns frequently have significant clinical meaning that provides radiologists with additional context. For example, a study labeled to indicate the presence of cardiomegaly (enlargement of the cardiac silhouette) is more likely to additionally have pulmonary edema (abnormal fluid in the extravascular tissue of the lung) as the former may suggest left ventricular failure which often causes the latter. The presence of edema further predicates the possible presence of both consolidation (air space opacification) and a pleural effusion (abnormal fluid in the pleural space). Training a model to recognize the potential for these interdependencies could enable better prediction of pathologic outcomes across all categories while maximizing the data utilization and its statistical efficiency.
+
+Among the aforementioned challenges, this work firstly addresses the problem of predicting multiple labels simultaneously while taking into account their conditional dependencies during both the training and the inference. Similar problems have been raised and analyzed in the work of Wang et al. (2016); Chen et al. (2017) with the application of image tagging, both outside the medical context. The work of Shin et al. (2016); Wang et al. (2017) for chest $\mathbf { X }$ -ray annotations are closest to ours. All of them utilize out-of-the-box decoders based on recurrent neural networks (RNNs) to sequentially predict the labels. Such a naive adoption of RNNs is problematic and often fails to attend to peculiarities of the medical problem in their design, which we elaborate on in Section 2.3 and Section 3.3.1.
+
+In addition, we hypothesize that the need for pre-training may be safely removed when there are sufficient medical data available. To verify this, all our models are trained from scratch, without using any extra data from other domains. We directly compare our results with those of Wang et al. (2017) that are pre-trained on ImageNet. Furthermore, to address the issue of clinical interpretability, we juxtapose a collection of alternative metrics along with those traditionally used in machine learning, all of which are reported in our benchmark.
+
+# 1.1 MAIN CONTRIBUTIONS
+
+This work brings state-of-the-art machine learning models to bear on the problem of medical diagnosis with the hope that this will lead to better patient outcomes. We have advanced the existing research in three orthogonal directions:
+
+• This work experimentally verifies that without pre-training, a carefully designed baseline model that ignores the label dependencies is able to outperform the pre-trained state-ofthe-art by a large margin.   
+• A collection of metrics is investigated for the purpose of establishing clinically relevant and interpretable benchmarks for automatic chest $\mathbf { X }$ -ray diagnosis. We propose to explicitly exploit the conditional dependencies among abnormality labels for better diagnostic results. Existing RNNs are purposely modified to accomplish such a goal. The results on the proposed metrics consistently indicate their superiority over models that do not consider interdependencies.
+
+# 2 RELATED WORK
+
+# 2.1 NEURAL NETWORKS IN MEDICAL IMAGING
+
+The present work is part of a recent effort to harness advances in Artificial Intelligence and machine learning to improve computer-assisted diagnosis in medicine. Over the past decades, the volume of clinical data in machine-readable form has grown, particularly in medical imaging. While previous generations of algorithms struggled to make effective use of this high-dimensional data, modern neural networks have excelled at such tasks. Having demonstrated their superiority in solving difficult problems involving natural images and videos, recent surveys from Litjens et al. (2017); Shen et al. (2017); Qayyum et al. (2017) suggest that they are rapidly becoming the “de facto” standard for classification, detection, and segmentation tasks with input modalities such as CT, MRI, x-ray, and ultrasound. As further evidence, models based on neural networks dominate the leaderboard in most medical imaging challenges 1,2.
+
+Most successful applications of neural networks to medical images rely to a large extent on convolutional neural networks (ConvNets), which were first proposed in LeCun et al. (1998). This comes as no surprise since ConvNets are the basis of the top performing models for natural image understanding. For abnormality detection and segmentation, the most popular variants are UNets from Ronneberger et al. (2015) and VNets from Milletari et al. (2016), both built on the idea of fully convolutional neural networks introduced in Long et al. (2015). For classification, representative examples of neural network-based models from the medical literature include: Esteva et al. (2017) for skin cancer classification, Gulshan et al. (2016) for diabetic retinopathy, Lakhani & Sundaram (2017) for pulmonary tuberculosis detection in $\mathbf { X }$ -rays, and Huang et al. (2017b) for lung cancer diagnosis with chest CTs. All of the examples above employed 2D or 3D ConvNets and all of them provably achieved near-human level performance in their particular setup. Our model employs a 2D ConvNet as an image encoder to process chest $\mathbf { X }$ -rays.
+
+# 2.2 MULTI-LABEL CLASSIFICATION
+
+Given a finite set of possible labels, the multi-label classification problem is to associate each instance with a subset of those labels. Being relevant to applications in many domains, a variety of models have been proposed in the literature. The simplest approach, known as binary relevance, is to break the multi-label classification problem into independent binary classification problems, one for each label. A recent example from the medical literature is Wang et al. (2017). The appeal of binary relevance is its simplicity and the fact that it allows one to take advantage of a rich body of work on binary classification. However, it suffers from a potentially serious drawback: the assumption that the labels are independent. For many applications, such as the medical diagnostic application motivating this work, there are significant dependencies between labels that must be modeled appropriately in order to maximize the performance of the classifier.
+
+Researchers have sought to model inter-label dependencies by making predictions over the label power set (e.g. Tsoumakas & Vlahavas (2007) and Read et al. (2008)), by training classifiers with loss functions that implicitly represent dependencies (e.g. Li et al. (2017)), and by using a sequence of single-label classifiers, each of which receives a subset of the previous predictions along with the instance to be classified (e.g. Dembczynski et al. (2012)). The later approach is equivalent to ´ factoring the joint distribution of labels using a product of conditional distributions. Recent research has favored recurrent neural networks (RNNs), which rely on their state variables to encode the relevant information from the previous predictions (e.g. Wang et al. (2016) and Chen et al. (2017)). The present work falls into this category.
+
+# 2.3 KEY DIFFERENCES
+
+To detect and classify abnormalities in chest x-ray images, we propose using 2D ConvNets as encoders and decoders based on recurrent neural networks (RNNs). Recently, Lipton et al. (2016) proposed an RNN-based model for abnormality classification that, based on the title of their paper, bears much resemblance to ours. However, in their work the RNN is used to process the inputs rather than the outputs, which fails to capture dependencies between labels; something we set out to explicitly address. They also deal exclusively with time series data rather than high-resolution images.
+
+The work of Shin et al. (2016) also addresses the problem of chest $\mathbf { X }$ -ray annotation. They built a cascaded three-stage model using 2D ConvNets and RNNs to sequentially annotate both the abnormalities and their attributes (such as location and severity). Their RNN decoder resembles ours in its functionality, but differs in the way the sequence of abnormalities are predicted. In each RNN step, their model predicts one of $T$ abnormalities with softmax, and stops when reaching a predefined upper limit of total number of steps (5 is used in theirs). Instead, our model predicts the presence or absence of $t$ -th abnormality with sigmoid at time step $t$ and the total number of steps is the number of abnormalities. The choice of such a design is inspired by Neural Autoregressive Density Estimators (NADEs) of Larochelle & Murray (2011). Being able to predict the absence of an abnormality and feed to the next step, which is not possible with softmax and argmax, is preferable in the clinical setting to avoid any per-class overcall and false alarm. In addition, the absence of a certain abnormality may be a strong indication of the presence or absence of others. Beyond having a distinct approach to decoding, their model was trained on the $\mathrm { O p e n I } ^ { 3 }$ dataset with 7000 images, which is smaller and less representative than the dataset that we used (see below). In addition, we propose a different set of metrics to use in place of BLEU (Papineni et al., 2002), commonly used in machine translation, for better clinical interpretation.
+
+In the non-medical setting, Wang et al. (2016) proposed a similar ConvNet–RNN architecture. Their choice of using an RNN decoder was also motivated by the desire to model label dependencies. However, they perform training and inference in the manner of Shin et al. (2016). Another example of this combination of application, architecture, and inference comes from Chen et al. (2017) whose work focused on eliminating the need to use a pre-defined label order for training. We show in the experiments that ordering does not seem to impose as a significant constraint when models are sufficiently trained.
+
+Finally, Wang et al. (2017) proposed a 2D ConvNet for classifying abnormalities in chest x-ray images. However, they used a simple binary relevance approach to predict the labels. As we mentioned earlier, there is strong clinical evidence to suggest that labels do in fact exhibit dependencies that we attempt to model. They also presented the largest public $\mathbf { X }$ -ray dataset to date (“ChestX-ray8”). Due to its careful curation and large volume, such a collection is a more realistic retrospective clinical study than OpenI and therefore better suited to developing and benchmarking models. Consequently, we use “ChestX-ray8” to train and evaluate our model. And it should be noted that unlike Wang et al. (2017), we train our models from scratch to ensure that the image encoding best captures the features of $\mathbf { X }$ -ray images as opposed to natural images.
+
+# 3 MODELS
+
+The following notations are used throughout the paper. Denote $\mathbf { x }$ as an input image, and ${ \textbf { x } } \in$ $\mathcal { R } ^ { w \times h \times c }$ where $w$ , $h$ and $c$ represent width, height, and channel. Denote $\mathbf { y }$ as a binary vector of dimensionality $T$ , the total number of abnormalities. We used superscripts to indicate a specific dimensionality. Thus, given a specific abnormality $t$ , $\mathbf { y } ^ { t } = 0$ indicates its absence and $\mathbf { y } ^ { t } = 1$ its presence. We use subscripts to index a particular example, for instance, $\left\{ \mathbf { x } _ { i } , \mathbf { y } _ { i } \right\}$ is the $i$ -th example. In addition, $\theta$ denotes the union of parameters in a model. We also use $\mathbf { m }$ to represent a vector with each element $\mathbf { m } ^ { t }$ as the mean of a Bernoulli distribution.
+
+# 3.1 DENSELY CONNECTED IMAGE ENCODER
+
+A recent variant of Convolutional Neural Network (ConvNet) is proposed in Huang et al. (2017a), dubbed as Densely Connected Networks (DenseNet). As a direct extension of Deep Residual Networks (He et al., 2016) and Highway Networks (Srivastava et al., 2015), the key idea behind DenseNet is to establish shortcut connections from all pairs of layers at different depth of a very deep neural network. It has been argued in Huang et al. (2017a) that, as the result of the extensive and explicit feature reuse in DenseNets, they are both computationally and statistically more efficient. This property is particularly desirable in dealing with medical imaging problems where the number of training examples are usually limited and overfitting tends to prevail in models with more than tens of millions of parameters.
+
+We therefore propose a model based on the design of DenseNets while taking into account the peculiarity of medical problems at hand. Firstly, the inputs of the model are of much higher resolutions. Lower resolution, typically with $2 5 6 \times 2 5 6$ , may be sufficient in dealing with problems related to natural images, photos and videos, a higher resolution, however, is often necessary to faithfully represent regions in images that are small and localized. Secondly, the proposed model is much smaller in network depth. While there is ample evidence suggesting the use of hundreds of layers, such models typically require hundreds of thousands to millions of examples to train. Large models are prone to overfitting with one tenth the training data. Figure 1 highlights such a design.
+
+# 3.2 INDEPENDENT PREDICTION OF LABELS
+
+Ignoring the nature of conditional dependencies among the indicators, $\mathbf { y } ^ { t }$ , one could establish the following probabilistic model:
+
+$$
+P ( \mathbf { y } | \mathbf { x } ) = \prod _ { t = 1 } ^ { T } P ( \mathbf { y } ^ { t } | \mathbf { x } ) .
+$$
+
+Equ (1) assumes that knowing one label does not provide any additional information about any other label. Therefore, in principle, one could build a separate model for each $\mathbf { y } ^ { t }$ which do not share any parameters. However, it is common in the majority of multi-class settings to permit a certain degree of parameter sharing among individual classifiers, which encourages the learned features to be reused among them. Furthermore, sharing alleviates the effect of overfitting as the exampleparameter ratio is much higher.
+
+![](images/5394bb64e113ca2ad553721a50f5a44ef4e56b256555081290680542f22af0e4.jpg)  
+Figure 1: The input image is encoded by a densely connected convolutional neural network (top). Similar to DenseNets from Huang et al. (2017a), our variant consists of DenseBlocks and TransitionBlocks. Within each DenseBlock, there are several ConvBlocks. The resulting encoded representation of the input is a vector that captures the higher-order semantics that are useful for the decoding task. $K$ is the growth rate in Huang et al. (2017a), $S$ is the stride. We also include the filter and pooling dimensionality when applicable. Unlike a DenseNet that has 16 to 32 ConvBlock within a DenseBlock, our model uses 4 in order to keep the total number of parameters small. Our proposed RNN decoder is illustrated on the bottom right.
+
+# 3.2.1 TRAINING
+
+During training, the model optimizes the following Maximum Log-likelihood Estimate (MLE) criteria:
+
+$$
+\mathcal { L } _ { \alpha } = \underset { \theta } { \arg \operatorname* { m a x } } \sum _ { t = 1 } ^ { T } \log P ( \mathbf { y } ^ { t } | \mathbf { x } , \theta )
+$$
+
+where $P ( \mathbf { y } ^ { t } | \mathbf { x } , \theta )$ is a Bernoulli distribution with its mean $\mathbf { m } ^ { t }$ parameterized by the model. In particular, $\mathbf { m } ^ { t } = \mathrm { s i g m o i d } ( f ( \mathbf { x } , \theta ) )$ .
+
+# 3.2.2 INFERENCE
+
+As labels are considered independent and during the inference, a binary label is generated for each factor independently with $\mathbf { y } ^ { t ^ { * } } = \arg \operatorname* { m a x } P ( \mathbf { y } ^ { t } | \mathbf { x } , \boldsymbol { \theta } )$ . This is equivalent to setting the classification threshold to 0.5.
+
+# 3.3 EXPLOITING HIGHER-ORDER DEPENDENCIES AMONG LABELS
+
+As discussed in length in Section 1, it is hardly true that abnormalities are independent from each other. Hence the assumption made by Equ (1) is undoubtably too restrictive. In order to treat the multi-label problem in its full generality, we can begin with the following factorization, which makes no assumption of independence:
+
+$$
+P ( \mathbf { y } | \mathbf { x } ) = P ( \mathbf { y } ^ { 0 } | \mathbf { x } ) P ( \mathbf { y } ^ { 1 } | \mathbf { y } ^ { 0 } , \mathbf { x } ) \dots P ( \mathbf { y } ^ { T } | \mathbf { y } ^ { 0 } , \dots , \mathbf { y } ^ { T - 1 } , \mathbf { x } ) .
+$$
+
+Here, the statistical dependencies among the indicators, $\mathbf { y } ^ { t }$ , are explicitly modeled within each factor so the absence or the presence of a particular abnormality may suggest the absence or presence of others.
+
+The factorization in Equ (3) has been the central study of many recent models. Bengio & Bengio (2000) proposed the first neural network based model, refined by Larochelle & Murray (2011) and Gregor et al. (2014), all of which used the model in the context of unsupervised learning in small discrete data or small image patches. Recently Sutskever et al. (2014); Cho et al. (2014) popularized the so-called “sequence-to-sequence” model where a Recurrent Neural Network (RNN) decoder models precisely the same joint distribution while conditioned on the output of an encoder. Compared with the previous work, RNNs provide a more general framework to model Equ (3) and an unmatched proficiency in capturing long term dependencies when $K$ is large.
+
+We therefore adopt the Long-short Term Memory Networks (LSTM) (Hochreiter & Schmidhuber, 1997) and treat the multi-label classification as sequence prediction with a fixed length. The formulation of our LSTM is particularly similar to those used in image and video captioning (Xu et al., 2015; Yao et al., 2015), but without the use of an attention mechanism and without the need of learning when to stop.
+
+Given an input $\mathbf { x }$ , the same DenseNet-based encoder of Section 3.2 is applied to produce a lower dimensional vector representation of it with
+
+$$
+\mathbf { x } _ { \mathrm { e n c } } = f _ { \mathrm { e n c } } ( \mathbf { x } )
+$$
+
+For the decoder, $\mathbf { x e n c }$ is used to initialize both the states and memory of an LSTM with
+
+$$
+\begin{array} { r } { \mathbf { h } _ { 0 } = f _ { h _ { 0 } } ( \mathbf { x } _ { \mathrm { e n c } } ) \qquad \mathbf { c } _ { 0 } = f _ { c _ { 0 } } ( \mathbf { x } _ { \mathrm { e n c } } ) } \end{array}
+$$
+
+where $f _ { h _ { 0 } }$ and $f _ { c _ { 0 } }$ are standard feedforward neural networks with one hidden layer. With $\mathbf { h } _ { 0 }$ and $\mathbf { c } _ { 0 }$ the LSTM decoder is parameterized as
+
+$$
+\begin{array} { r l } & { \mathbf { g } _ { i } ^ { t } = \mathrm { s i g m o i d } ( \mathbf { x } _ { \mathrm { e n c } } \mathbf { W } _ { i } + \mathbf { h } ^ { t - 1 } \mathbf { U } _ { i } + \mathbf { y } ^ { t - 1 } \mathbf { V } _ { i } + \mathbf { b } _ { i } ) } \\ & { \mathbf { g } _ { o } ^ { t } = \mathrm { s i g m o i d } ( \mathbf { x } _ { \mathrm { e n c } } \mathbf { W } _ { o } + \mathbf { h } ^ { t - 1 } \mathbf { U } _ { o } + \mathbf { y } ^ { t - 1 } \mathbf { V } _ { o } + \mathbf { b } _ { o } ) } \\ & { \mathbf { g } _ { f } ^ { t } = \mathrm { s i g m o i d } ( \mathbf { x } _ { \mathrm { e n c } } \mathbf { W } _ { f } + \mathbf { h } ^ { t - 1 } \mathbf { U } _ { f } + \mathbf { y } ^ { t - 1 } \mathbf { V } _ { f } + \mathbf { b } _ { f } ) } \\ & { \mathbf { g } _ { g } ^ { t } = \mathbf { x } _ { \mathrm { e n c } } \mathbf { W } _ { g } + \mathbf { h } ^ { t - 1 } \mathbf { U } _ { g } + \mathbf { y } ^ { t - 1 } \mathbf { V } _ { g } + \mathbf { b } _ { g } } \\ & { \mathbf { c } ^ { t } = \mathbf { g } _ { f } ^ { t } \odot \mathbf { c } ^ { t - 1 } + \mathbf { g } _ { i } ^ { t } \odot \mathrm { t a n h } ( \mathbf { g } _ { g } ^ { t } ) } \\ & { \mathbf { h } ^ { t } = \mathbf { g } _ { o } ^ { t } \odot \mathrm { t a n h } ( \mathbf { c } ^ { t } ) } \\ & { \mathbf { m } ^ { t } = \mathrm { s i g m o i d } ( \mathbf { h } ^ { t } \mathbf { q } ^ { T } + b _ { l } ) } \end{array}
+$$
+
+where model parameters consist of three matrices Ws, Us, Vs, vectors bs and a scalar $b _ { l }$ . y is a vector code of the ground truth labels that respects a fixed ordering, with each element being either 0 or 1. All the vectors, including hs, gs, cs, bs, $\mathbf { q }$ and $\mathbf { y }$ are row vectors such that the vector-matrix multiplication makes sense. $\odot$ denotes the element-wise multiplication. Both sigmoid and tanh are element-wise nonlinearities. For brevity, we summarize one step of decoder computation as
+
+$$
+\mathbf { m } ^ { t } = f _ { \mathrm { d e c } } ( \mathbf { x } _ { \mathrm { e n c } } , \mathbf { y } ^ { t - 1 } , \mathbf { h } ^ { t - 1 } )
+$$
+
+where the decoder LSTM computes sequentially the mean of a Bernoulli distribution. With Equ (3), each of its factor may be rewritten as
+
+$$
+P ( \mathbf { y } ^ { t } | \mathbf { y } ^ { 0 } , \ldots , \mathbf { y } ^ { t - 1 } , \mathbf { x } ) = P ( \mathbf { y } ^ { t } = 1 ) ^ { \mathbf { m } ^ { t } } P ( \mathbf { y } ^ { t } = 0 ) ^ { ( 1 - \mathbf { m } ^ { t } ) }
+$$
+
+# 3.3.1 THE DESIGN CHOICE OF SIGMOID
+
+The choice of using sigmoid to predict $\mathbf { y } _ { t }$ is by design. Standard sequence-to-sequence models often use softmax to predict one out of $\mathrm { T }$ classes and thus need to learn explicitly an “end-ofsequence” class. This is not desirable in our context due to the sparseness of the labels, resulting in the learned decoder being strongly biased towards predicting “end-of-sequence” while missing infrequently appearing abnormalities. Secondly, during the inference of the softmax based RNN decoder, the prediction at the current step is largely based on the presence of abnormalities at all previous steps due to the use of argmax. However, in the medical setting, the absence of previously predicted abnormalities may also be important. Sigmoid conveniently addresses these issues by explicitly predicting 0 or 1 at each step and it does not require the model to learn when to stop; the decoder always runs for the same number of steps as the total number of classes. Figure 1 contains the overall architecture of the decoder.
+
+# 3.3.2 TRAINING
+
+During training, the model optimizes
+
+$$
+\mathcal { L } _ { \beta } = \mathop { \arg \operatorname* { m a x } } _ { \theta } \sum _ { t = 1 } ^ { T } \log P ( \mathbf { y } ^ { k } | \mathbf { y } ^ { 0 } , \dots , \mathbf { y } ^ { t - 1 } ,  { \mathbf { x } } , \theta )
+$$
+
+Compared with Equ (1), the difference is the explicit dependencies among $\mathbf { y } ^ { t } \mathbf { s }$ . One may also notice that such a factorization is not unique – in fact, there exist $T !$ different orderings. Although mathematically equivalent, in practice, some of the orderings may result in a model that is easier to train. We investigate in Section 4 the impact of such decisions with two distinct orderings.
+
+# 3.3.3 INFERENCE
+
+The inference of such a model is unfortunately intractable as $\mathbf { y } ^ { * } = \arg \operatorname* { m a x } _ { \mathbf { y } } P ( \mathbf { y } ^ { 0 } , \ldots , \mathbf { y } ^ { T } | \mathbf { x } )$ . Beam search (Sutskever et al., 2014) is often used as an approximation. We have found in practice that greedy search, which is equivalent to beam search with size 1, results in similar performance due to the binary sampling nature of each $\mathbf { y } ^ { t }$ , and use it throughout the experiments. It is equivalent to setting 0.5 as the discretization threshold on each of the factors.
+
+# 4 EXPERIMENTS
+
+# 4.1 DATASET
+
+To verify the efficacy of the proposed models in medical diagnosis, we conduct experiments on the dataset introduced in Wang et al. (2017). It is to-date the largest collection of chest $\mathbf { X }$ -rays that is publicly available. It contains in total 112,120 frontal-view chest x-rays each of which is associated with the absence or presence of 14 abnormalities. The dataset is originally released in PNG format, with each image rescaled to $1 0 2 4 \times 1 0 2 4$ .
+
+As there is no standard split for this dataset, we follow the guideline in Wang et al. (2017) to randomly split the entire dataset into $70 \%$ for training, $10 \%$ for validation and $20 \%$ for training. The authors of Wang et al. (2017) noticed insignificant performance difference with different random splits, as confirmed in our experiments by the observation that the performance on validation and test sets are consistent with each other.
+
+# 4.2 PERFORMANCE METRICS
+
+As the dataset is relatively new, the complete set of metrics have yet to be established. In this work, the following metrics are considered, and their advantage and drawbacks outlined below.
+
+1. Negative log-probability of the test set (NLL). This metric has a direct and intuitive probabilistic interpretation: The lower the NLL, the more likely the ground truth label. However, it is difficult to associate it with a clinical interpretation. Indeed, it does not directly reflect how accurate the model is at diagnosing cases with or without particular abnormalities.
+
+2. Area under the ROC curves (AUC). This is the reported metric of Wang et al. (2017) and it is widely used in modern biostatistics to measure collectively the rate of true detections and false alarms. In particular, we define 4 quantities: (1) true positive as TP: model predicts 1 with ground truth 1. (2) true negative as TN: model predicts 0 with ground truth 0. (3) false positive as FP: model predicts 1 with ground truth 0. (4) false negative as FN: model predicts 0 with ground truth 1. Sensitivity (or recall) is computed as $\mathrm { \bar { T P } / ( T P + F N ) }$ that measures the success of identifying abnormal cases. Specificity is $\mathrm { T N } / ( \mathrm { T N } + \mathrm { F P } )$ that measures the success of not flagging normal cases as abnormal. The ROC curve has typically horizontal axis as (1-specificity) and vertical axis as sensitivity. Once $P ( \mathbf { y } _ { i } | \mathbf { x } )$ is available, the curve is generated by varying the decision threshold to discretize the probability into either 0 or 1. Despite of its clinical relevance, $P ( \mathbf { y } _ { i } | \mathbf { x } )$ is intractable to compute with the model of Equ (3) due to the need of marginalizing out other binary random variables. It is however straightforward to compute with the model of Equ (1) due the independent factorization.
+
+3. DICE coefficient. As a similarity measure over two sets, DICE coefficient is formulated as $\mathrm { D I C E } ( { \bf y } _ { \alpha } , { \bf y } _ { \beta } ) = ( 2 { \bf y } _ { \alpha } { \bf y } _ { \beta } ) / ( { \bf \dot { y } } _ { \alpha } ^ { 2 } + { \bf y } _ { \beta } ^ { 2 } ) = 2 \mathrm { T P } / ( 2 \mathrm { T P } + \mathrm { F P } + \mathrm { F N } )$ with the maxima at 1 when ${ \bf y } _ { \alpha } \equiv { \bf y } _ { \beta }$ . Such a metric may be generalized in cases where $\mathbf { y } _ { \alpha }$ is a predicted probability with ${ \bf y } _ { \alpha } = { \cal P } ( { \bf y } | { \bf x } )$ and $\mathbf { y } _ { \beta }$ is the binary-valued ground truth, as is used in image segmentation tasks such as in Ronneberger et al. (2015); Milletari et al. (2016). We adopt such a generalization as our models naturally output probabilities.
+
+4. Per-example sensitivity and specificity (PESS). The following formula is used to compute PESS
+
+$$
+\mathrm { P E S S } = \frac { 1 } { N } \sum _ { i = 1 } ^ { N } \frac { \mathrm { s e n s i t i v i t y } ( \hat { \bf y } _ { i } , { \bf y } _ { i } ) + \mathrm { s p e c i f i c i t y } ( \hat { \bf y } _ { i } , { \bf y } _ { i } ) } { 2 }
+$$
+
+where $N$ is the size of the test set. Notice that the computation of sensitivity and specificity requires a binary prediction vector. Therefore, without introducing any thresholding bias, we use
+
+$$
+\hat { \mathbf { y } } _ { i } = \left\{ \begin{array} { l l } { 1 } & { P ( \mathbf { y } _ { i } | \mathbf { x } _ { i } ) > 0 . 5 } \\ { 0 } & { \mathrm { o t h e r w i s e } } \end{array} \right.
+$$
+
+5. Per-class sensitivity and specificity (PCSS). Unlike PESS, the following formula is used to compute PCSS
+
+$$
+\mathrm { P C S S } = \frac { 1 } { T } \sum _ { t = 1 } ^ { T } \frac { \mathrm { s e n s i t i v i t y } ( \hat { \mathbf { y } } _ { i } ^ { t } , \mathbf { y } _ { i } ^ { t } ) + \mathrm { s p e c i f i c i t y } ( \hat { \mathbf { y } } _ { i } ^ { t } , \mathbf { y } _ { i } ^ { t } ) } { 2 }
+$$
+
+where $\hat { \mathbf { y } } _ { i } ^ { t }$ follows the same threshold of 0.5 as in PESS. Unlike PCSS where the average is over examples, PCSS averages over abnormalities instead.
+
+# 4.3 TRAINING PROCEDURES
+
+Three types of models are tuned on the training set. We have found that data augmentation is crucial in combatting the overfitting in all of our experiments despite their relatively small size. In particular, the input image of resolution $5 1 2 \times 5 1 2$ is randomly translated in 4 directions by 25 pixels, randomly rotated from -15 to 15 degrees, and randomly scaled between $80 \%$ and $120 \%$ . Furthermore, the ADAM optimizer Kingma & Ba (2015) is used with an initial learning rate of 0.001 which is multiplied by 0.9 whenever the performance on the validation set does not improve during training. Early stop is applied when the performance on the validation set does not improve for 10,000 parameter updates. All the reported metrics are computed on the test set with models selected with the metric in question on the validation set.
+
+In order to ensure a fair comparison, we constrain all models to have roughly the same number of parameters. For $\mathrm { m o d e l } _ { a }$ , where labels are considered independent, a much higher network growth rate is used for the encoder. For $\mathrm { m o d e l } _ { b _ { 1 } }$ and $\mathrm { m o d e l } _ { b _ { 2 } }$ where LSTMs are used as decoders, the encoders are narrower. The exact configuration of three models is shown in Table 1. In addition, we investigate the effect of ordering in the factorization of Equ (3). In particular, $\mathrm { m o d e l } _ { b _ { 1 } }$ sorts labels by their frequencies in the training set while $\mathrm { m o d e l } _ { b _ { 1 } }$ orders them alphabetically. All models are trained with MLE with the weighted cross-entropy loss introduced in Wang et al. (2017). All models are trained end-to-end from scratch, without any pre-training on ImageNet data.
+
+Table 1: Hyper-parameter configuration of three models. To ensure the fairness of the comparison, we deliberately reduce the capacity of the encoder for $\mathrm { m o d e l } _ { b _ { 1 } }$ and $\mathrm { m o d e l } _ { b _ { 2 } }$ to match the total number of parameters of mode $^ { - a }$ .   
+
+<table><tr><td></td><td># of dense block × # of conv block</td><td>growth rate</td><td>LSTM dim.</td><td>total # of params</td></tr><tr><td>modela</td><td>4×3</td><td>38</td><td>1</td><td>1,007K</td></tr><tr><td>modelb1,b2</td><td>4×3</td><td>19</td><td>100</td><td>1,016K</td></tr></table>
+
+# 4.4 QUANTITATIVE RESULTS
+
+The AUC per abnormality is shown in Table 2, computed based on the marginal distribution of $P ( \mathbf { y } | \mathbf { x } )$ . Only mode $^ { - a }$ is included as such marginals are in general intractable for the other two due to the dependencies among $\mathbf { y } ^ { t } \mathbf { s }$ . In addition, Table 3 compares all three models based on the proposed metrics from Section 4.2. It can be observed that our baseline model significantly outperformed the previous state-of-the-art. According to Table 3, considering label dependencies brings significant benefits in all 4 metrics and the impact of ordering seems to be marginal when the model is sufficiently trained.
+
+Table 2: Fifteen abnormalities and their AUCs, including the average AUC over all abnormalities. The model is trained without pre-training or feature extraction from ImageNet. The model corresponds to the one in Section 3.2 where $\mathbf { \bar { y } } ^ { t } \mathbf { s }$ are considered independent. This table excludes the model from Section 3.3 because AUC requires $P ( \mathbf { y } ^ { t } | \mathbf { x } )$ , which is in general intractable.
+
+<table><tr><td>abnormality</td><td>Wang et al. (2017)</td><td>modela</td></tr><tr><td>atelectasis cardiomegaly</td><td>0.716</td><td>0.772</td></tr><tr><td>effusion</td><td>0.807 0.784</td><td>0.904 0.859</td></tr><tr><td>infiltration</td><td>0.609</td><td>0.695</td></tr><tr><td>mass</td><td>0.706</td><td>0.792</td></tr><tr><td>nodule</td><td>0.671</td><td>0.717</td></tr><tr><td>pneumonia</td><td>0.633</td><td>0.713</td></tr><tr><td>pneumothorax</td><td>0.806</td><td></td></tr><tr><td>consolidation</td><td></td><td>0.841</td></tr><tr><td>edema</td><td>0.708</td><td>0.788</td></tr><tr><td>emphysema</td><td>0.835</td><td>0.882</td></tr><tr><td>fibrosis</td><td>0.815</td><td>0.829</td></tr><tr><td></td><td>0.769</td><td>0.767</td></tr><tr><td>PT</td><td>0.708</td><td>0.765</td></tr><tr><td>hernia</td><td>0.767</td><td>0.914</td></tr><tr><td>A.V.G.</td><td>0.738</td><td>0.798</td></tr><tr><td>no finding</td><td>-</td><td>0.762</td></tr></table>
+
+Table 3: Test set performance on negative log-probability (NLL), DICE, per-example sensitivity (PESS) at a threshold 0.5 and per-class sensitivity and specificity (PCSS) at a threshold of 0.5. See Section 4.2 for explanations of the metrics. In addition to $\mathrm { m o d e l } _ { a }$ used in Table 2, $\mathrm { m o d e l } _ { b 1 }$ and $\mathrm { m o d e l } _ { b 2 }$ corresponds to the model introduced in Section 3.3, with the difference in the ordering of the factorization in Equ (3). $\mathrm { m o d e l } _ { b 1 }$ sorts labels by their frequency in the training set in ascending order. As a comparison, $\mathrm { m o d e l } _ { b 2 }$ orders labels alphabetically according to the name of the abnormality.
+
+<table><tr><td></td><td>NLL</td><td>DICE</td><td>PESS0.5</td><td>PCSS0.5</td></tr><tr><td>modela</td><td>4.474</td><td>0.261</td><td>0.752</td><td>0.665</td></tr><tr><td>modelb1</td><td>4.099</td><td>0.310</td><td>0.765</td><td>0.676</td></tr><tr><td>modelb2</td><td>3.848</td><td>0.310</td><td>0.767</td><td>0.677</td></tr></table>
+
+# 5 CONCLUSION
+
+To improve the quality of computer-assisted diagnosis of chest $\mathbf { X }$ -rays, we proposed a two-stage end-to-end neural network model that combines a densely connected image encoder with a recurrent neural network decoder. The first stage was chosen to address the challenges to learning presented by high-resolution medical images and limited training set sizes. The second stage was designed to allow the model to exploit statistical dependencies between labels in order to improve the accuracy of its predictions. Finally, the model was trained from scratch to ensure that the best application-specific features were captured. Our experiments have demonstrated both the feasibility and effectiveness of this approach. Indeed, our baseline model significantly outperformed the current state-of-the-art. The proposed set of metrics provides a meaningful quantification of this performance and will facilitate comparisons with future work.
+
+While a limited exploration into the value of learning interdependencies among labels yields promising results, additional experimentation will be required to further explore the potential of this methodology both as it applies specifically to chest $\mathbf { X }$ -rays and to medical diagnostics as a whole. One potential concern with this approach is the risk of learning biased interdependencies from a limited training set which does not accurately represent a realistic distribution of pathologies – if every example of cardiomegaly is also one of cardiac failure, the model may learn to depend too much on the presence of other patterns such as edemas which do not always accompany enlargement of the cardiac silhouette. This risk is heightened when dealing with data labeled with a scheme which mixes pathologies, such as pneumonia, with patterns symptomatic of those pathologies, such as consolidation. The best approach to maximizing feature extraction and leveraging interdependencies among target labels likely entails training from data labeled with an ontology that inherently poses some consistent known relational structure. This will be the endpoint of a future study.
+
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+        "text": "The field of medical diagnostics contains a wealth of challenges which closely resemble classical machine learning problems; practical constraints, however, complicate the translation of these endpoints naively into classical architectures. Many tasks in radiology, for example, are largely problems of multi-label classification wherein medical images are interpreted to indicate multiple present or suspected pathologies. Clinical settings drive the necessity for high accuracy simultaneously across a multitude of pathological outcomes and greatly limit the utility of tools which consider only a subset. This issue is exacerbated by a general scarcity of training data and maximizes the need to extract clinically relevant features from available samples – ideally without the use of pre-trained models which may carry forward undesirable biases from tangentially related tasks. We present and evaluate a partial solution to these constraints in using LSTMs to leverage interdependencies among target labels in predicting 14 pathologic patterns from chest x-rays and establish state of the art results on the largest publicly available chest $\\mathbf { X }$ -ray dataset from the NIH without pre-training. Furthermore, we propose and discuss alternative evaluation metrics and their relevance in clinical practice. ",
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+        "type": "text",
+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
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+        "text": "Medical diagnostics have increasingly become a more interesting and viable endpoint for machine learning. A general scarcity of publicly available medical data, however, inhibits its rapid development. Pre-training on tangentially related datasets such as ImageNet (Deng et al., 2009) has been shown to help in circumstances where training data is limited, but may introduce unintended biases which are undesirable in a clinical setting. Furthermore, most clinical settings will drive a need for models which can accurately predict a large number of diagnostic outcomes. This essentially turns many medical problems into multi-label classification with a large number of targets, many of which may be subtle or poorly defined and are likely to be inconsistently labeled. In addition, unlike the traditional multi-label setting, predicting the absence of each label is as important as predicting its presence in order to minimize the possibility of misdiagnosis. Each of these challenges drive a need for architectures which consider clinical context to make the most of the data available. ",
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+        "text": "Chest $\\mathbf { X }$ -rays are the most common type of radiology exam in the world and a particularly challenging example of multi-label classification in medical diagnostics. Making up nearly $45 \\%$ of all radiological studies, the chest $\\mathbf { X }$ -ray has achieved global ubiquity as a low-cost screening tool for a wealth of pathologies including lung cancer, tuberculosis, and pneumonia. Each scan can contain dozens of patterns corresponding to hundreds of potential pathologies and can thus be difficult to interpret, suffering from high disagreement rates between radiologists and often resulting in unnecessary follow-up procedures. Complex interactions between abnormal patterns frequently have significant clinical meaning that provides radiologists with additional context. For example, a study labeled to indicate the presence of cardiomegaly (enlargement of the cardiac silhouette) is more likely to additionally have pulmonary edema (abnormal fluid in the extravascular tissue of the lung) as the former may suggest left ventricular failure which often causes the latter. The presence of edema further predicates the possible presence of both consolidation (air space opacification) and a pleural effusion (abnormal fluid in the pleural space). Training a model to recognize the potential for these interdependencies could enable better prediction of pathologic outcomes across all categories while maximizing the data utilization and its statistical efficiency. ",
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+        "type": "text",
+        "text": "Among the aforementioned challenges, this work firstly addresses the problem of predicting multiple labels simultaneously while taking into account their conditional dependencies during both the training and the inference. Similar problems have been raised and analyzed in the work of Wang et al. (2016); Chen et al. (2017) with the application of image tagging, both outside the medical context. The work of Shin et al. (2016); Wang et al. (2017) for chest $\\mathbf { X }$ -ray annotations are closest to ours. All of them utilize out-of-the-box decoders based on recurrent neural networks (RNNs) to sequentially predict the labels. Such a naive adoption of RNNs is problematic and often fails to attend to peculiarities of the medical problem in their design, which we elaborate on in Section 2.3 and Section 3.3.1. ",
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+        "type": "text",
+        "text": "In addition, we hypothesize that the need for pre-training may be safely removed when there are sufficient medical data available. To verify this, all our models are trained from scratch, without using any extra data from other domains. We directly compare our results with those of Wang et al. (2017) that are pre-trained on ImageNet. Furthermore, to address the issue of clinical interpretability, we juxtapose a collection of alternative metrics along with those traditionally used in machine learning, all of which are reported in our benchmark. ",
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+    {
+        "type": "text",
+        "text": "1.1 MAIN CONTRIBUTIONS ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "This work brings state-of-the-art machine learning models to bear on the problem of medical diagnosis with the hope that this will lead to better patient outcomes. We have advanced the existing research in three orthogonal directions: ",
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+        "text": "• This work experimentally verifies that without pre-training, a carefully designed baseline model that ignores the label dependencies is able to outperform the pre-trained state-ofthe-art by a large margin.   \n• A collection of metrics is investigated for the purpose of establishing clinically relevant and interpretable benchmarks for automatic chest $\\mathbf { X }$ -ray diagnosis. We propose to explicitly exploit the conditional dependencies among abnormality labels for better diagnostic results. Existing RNNs are purposely modified to accomplish such a goal. The results on the proposed metrics consistently indicate their superiority over models that do not consider interdependencies. ",
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+        "type": "text",
+        "text": "2 RELATED WORK ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "2.1 NEURAL NETWORKS IN MEDICAL IMAGING ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "The present work is part of a recent effort to harness advances in Artificial Intelligence and machine learning to improve computer-assisted diagnosis in medicine. Over the past decades, the volume of clinical data in machine-readable form has grown, particularly in medical imaging. While previous generations of algorithms struggled to make effective use of this high-dimensional data, modern neural networks have excelled at such tasks. Having demonstrated their superiority in solving difficult problems involving natural images and videos, recent surveys from Litjens et al. (2017); Shen et al. (2017); Qayyum et al. (2017) suggest that they are rapidly becoming the “de facto” standard for classification, detection, and segmentation tasks with input modalities such as CT, MRI, x-ray, and ultrasound. As further evidence, models based on neural networks dominate the leaderboard in most medical imaging challenges 1,2. ",
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+    {
+        "type": "text",
+        "text": "Most successful applications of neural networks to medical images rely to a large extent on convolutional neural networks (ConvNets), which were first proposed in LeCun et al. (1998). This comes as no surprise since ConvNets are the basis of the top performing models for natural image understanding. For abnormality detection and segmentation, the most popular variants are UNets from Ronneberger et al. (2015) and VNets from Milletari et al. (2016), both built on the idea of fully convolutional neural networks introduced in Long et al. (2015). For classification, representative examples of neural network-based models from the medical literature include: Esteva et al. (2017) for skin cancer classification, Gulshan et al. (2016) for diabetic retinopathy, Lakhani & Sundaram (2017) for pulmonary tuberculosis detection in $\\mathbf { X }$ -rays, and Huang et al. (2017b) for lung cancer diagnosis with chest CTs. All of the examples above employed 2D or 3D ConvNets and all of them provably achieved near-human level performance in their particular setup. Our model employs a 2D ConvNet as an image encoder to process chest $\\mathbf { X }$ -rays. ",
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+        "type": "text",
+        "text": "",
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+        "type": "text",
+        "text": "2.2 MULTI-LABEL CLASSIFICATION ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Given a finite set of possible labels, the multi-label classification problem is to associate each instance with a subset of those labels. Being relevant to applications in many domains, a variety of models have been proposed in the literature. The simplest approach, known as binary relevance, is to break the multi-label classification problem into independent binary classification problems, one for each label. A recent example from the medical literature is Wang et al. (2017). The appeal of binary relevance is its simplicity and the fact that it allows one to take advantage of a rich body of work on binary classification. However, it suffers from a potentially serious drawback: the assumption that the labels are independent. For many applications, such as the medical diagnostic application motivating this work, there are significant dependencies between labels that must be modeled appropriately in order to maximize the performance of the classifier. ",
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+        "type": "text",
+        "text": "Researchers have sought to model inter-label dependencies by making predictions over the label power set (e.g. Tsoumakas & Vlahavas (2007) and Read et al. (2008)), by training classifiers with loss functions that implicitly represent dependencies (e.g. Li et al. (2017)), and by using a sequence of single-label classifiers, each of which receives a subset of the previous predictions along with the instance to be classified (e.g. Dembczynski et al. (2012)). The later approach is equivalent to ´ factoring the joint distribution of labels using a product of conditional distributions. Recent research has favored recurrent neural networks (RNNs), which rely on their state variables to encode the relevant information from the previous predictions (e.g. Wang et al. (2016) and Chen et al. (2017)). The present work falls into this category. ",
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+        "type": "text",
+        "text": "2.3 KEY DIFFERENCES ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "To detect and classify abnormalities in chest x-ray images, we propose using 2D ConvNets as encoders and decoders based on recurrent neural networks (RNNs). Recently, Lipton et al. (2016) proposed an RNN-based model for abnormality classification that, based on the title of their paper, bears much resemblance to ours. However, in their work the RNN is used to process the inputs rather than the outputs, which fails to capture dependencies between labels; something we set out to explicitly address. They also deal exclusively with time series data rather than high-resolution images. ",
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+    {
+        "type": "text",
+        "text": "The work of Shin et al. (2016) also addresses the problem of chest $\\mathbf { X }$ -ray annotation. They built a cascaded three-stage model using 2D ConvNets and RNNs to sequentially annotate both the abnormalities and their attributes (such as location and severity). Their RNN decoder resembles ours in its functionality, but differs in the way the sequence of abnormalities are predicted. In each RNN step, their model predicts one of $T$ abnormalities with softmax, and stops when reaching a predefined upper limit of total number of steps (5 is used in theirs). Instead, our model predicts the presence or absence of $t$ -th abnormality with sigmoid at time step $t$ and the total number of steps is the number of abnormalities. The choice of such a design is inspired by Neural Autoregressive Density Estimators (NADEs) of Larochelle & Murray (2011). Being able to predict the absence of an abnormality and feed to the next step, which is not possible with softmax and argmax, is preferable in the clinical setting to avoid any per-class overcall and false alarm. In addition, the absence of a certain abnormality may be a strong indication of the presence or absence of others. Beyond having a distinct approach to decoding, their model was trained on the $\\mathrm { O p e n I } ^ { 3 }$ dataset with 7000 images, which is smaller and less representative than the dataset that we used (see below). In addition, we propose a different set of metrics to use in place of BLEU (Papineni et al., 2002), commonly used in machine translation, for better clinical interpretation. ",
+        "bbox": [
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "In the non-medical setting, Wang et al. (2016) proposed a similar ConvNet–RNN architecture. Their choice of using an RNN decoder was also motivated by the desire to model label dependencies. However, they perform training and inference in the manner of Shin et al. (2016). Another example of this combination of application, architecture, and inference comes from Chen et al. (2017) whose work focused on eliminating the need to use a pre-defined label order for training. We show in the experiments that ordering does not seem to impose as a significant constraint when models are sufficiently trained. ",
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+        "type": "text",
+        "text": "",
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+        "type": "text",
+        "text": "Finally, Wang et al. (2017) proposed a 2D ConvNet for classifying abnormalities in chest x-ray images. However, they used a simple binary relevance approach to predict the labels. As we mentioned earlier, there is strong clinical evidence to suggest that labels do in fact exhibit dependencies that we attempt to model. They also presented the largest public $\\mathbf { X }$ -ray dataset to date (“ChestX-ray8”). Due to its careful curation and large volume, such a collection is a more realistic retrospective clinical study than OpenI and therefore better suited to developing and benchmarking models. Consequently, we use “ChestX-ray8” to train and evaluate our model. And it should be noted that unlike Wang et al. (2017), we train our models from scratch to ensure that the image encoding best captures the features of $\\mathbf { X }$ -ray images as opposed to natural images. ",
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+    {
+        "type": "text",
+        "text": "3 MODELS ",
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+        "type": "text",
+        "text": "The following notations are used throughout the paper. Denote $\\mathbf { x }$ as an input image, and ${ \\textbf { x } } \\in$ $\\mathcal { R } ^ { w \\times h \\times c }$ where $w$ , $h$ and $c$ represent width, height, and channel. Denote $\\mathbf { y }$ as a binary vector of dimensionality $T$ , the total number of abnormalities. We used superscripts to indicate a specific dimensionality. Thus, given a specific abnormality $t$ , $\\mathbf { y } ^ { t } = 0$ indicates its absence and $\\mathbf { y } ^ { t } = 1$ its presence. We use subscripts to index a particular example, for instance, $\\left\\{ \\mathbf { x } _ { i } , \\mathbf { y } _ { i } \\right\\}$ is the $i$ -th example. In addition, $\\theta$ denotes the union of parameters in a model. We also use $\\mathbf { m }$ to represent a vector with each element $\\mathbf { m } ^ { t }$ as the mean of a Bernoulli distribution. ",
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+        "type": "text",
+        "text": "3.1 DENSELY CONNECTED IMAGE ENCODER ",
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+        "type": "text",
+        "text": "A recent variant of Convolutional Neural Network (ConvNet) is proposed in Huang et al. (2017a), dubbed as Densely Connected Networks (DenseNet). As a direct extension of Deep Residual Networks (He et al., 2016) and Highway Networks (Srivastava et al., 2015), the key idea behind DenseNet is to establish shortcut connections from all pairs of layers at different depth of a very deep neural network. It has been argued in Huang et al. (2017a) that, as the result of the extensive and explicit feature reuse in DenseNets, they are both computationally and statistically more efficient. This property is particularly desirable in dealing with medical imaging problems where the number of training examples are usually limited and overfitting tends to prevail in models with more than tens of millions of parameters. ",
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+        "type": "text",
+        "text": "We therefore propose a model based on the design of DenseNets while taking into account the peculiarity of medical problems at hand. Firstly, the inputs of the model are of much higher resolutions. Lower resolution, typically with $2 5 6 \\times 2 5 6$ , may be sufficient in dealing with problems related to natural images, photos and videos, a higher resolution, however, is often necessary to faithfully represent regions in images that are small and localized. Secondly, the proposed model is much smaller in network depth. While there is ample evidence suggesting the use of hundreds of layers, such models typically require hundreds of thousands to millions of examples to train. Large models are prone to overfitting with one tenth the training data. Figure 1 highlights such a design. ",
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+    {
+        "type": "text",
+        "text": "3.2 INDEPENDENT PREDICTION OF LABELS ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Ignoring the nature of conditional dependencies among the indicators, $\\mathbf { y } ^ { t }$ , one could establish the following probabilistic model: ",
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+    {
+        "type": "equation",
+        "img_path": "images/f170c7d2ba7cb3710f70bdad82e8c9b5249185f0fee448a6a6296a6a48186588.jpg",
+        "text": "$$\nP ( \\mathbf { y } | \\mathbf { x } ) = \\prod _ { t = 1 } ^ { T } P ( \\mathbf { y } ^ { t } | \\mathbf { x } ) .\n$$",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "Equ (1) assumes that knowing one label does not provide any additional information about any other label. Therefore, in principle, one could build a separate model for each $\\mathbf { y } ^ { t }$ which do not share any parameters. However, it is common in the majority of multi-class settings to permit a certain degree of parameter sharing among individual classifiers, which encourages the learned features to be reused among them. Furthermore, sharing alleviates the effect of overfitting as the exampleparameter ratio is much higher. ",
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+        "image_caption": [
+            "Figure 1: The input image is encoded by a densely connected convolutional neural network (top). Similar to DenseNets from Huang et al. (2017a), our variant consists of DenseBlocks and TransitionBlocks. Within each DenseBlock, there are several ConvBlocks. The resulting encoded representation of the input is a vector that captures the higher-order semantics that are useful for the decoding task. $K$ is the growth rate in Huang et al. (2017a), $S$ is the stride. We also include the filter and pooling dimensionality when applicable. Unlike a DenseNet that has 16 to 32 ConvBlock within a DenseBlock, our model uses 4 in order to keep the total number of parameters small. Our proposed RNN decoder is illustrated on the bottom right. "
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+    {
+        "type": "text",
+        "text": "3.2.1 TRAINING ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "During training, the model optimizes the following Maximum Log-likelihood Estimate (MLE) criteria: ",
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+    {
+        "type": "equation",
+        "img_path": "images/52f6968dd7628dba6be14005b92070c3cfd96cda69550fb08fa2eda46df8c425.jpg",
+        "text": "$$\n\\mathcal { L } _ { \\alpha } = \\underset { \\theta } { \\arg \\operatorname* { m a x } } \\sum _ { t = 1 } ^ { T } \\log P ( \\mathbf { y } ^ { t } | \\mathbf { x } , \\theta )\n$$",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "where $P ( \\mathbf { y } ^ { t } | \\mathbf { x } , \\theta )$ is a Bernoulli distribution with its mean $\\mathbf { m } ^ { t }$ parameterized by the model. In particular, $\\mathbf { m } ^ { t } = \\mathrm { s i g m o i d } ( f ( \\mathbf { x } , \\theta ) )$ . ",
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+    {
+        "type": "text",
+        "text": "3.2.2 INFERENCE ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "As labels are considered independent and during the inference, a binary label is generated for each factor independently with $\\mathbf { y } ^ { t ^ { * } } = \\arg \\operatorname* { m a x } P ( \\mathbf { y } ^ { t } | \\mathbf { x } , \\boldsymbol { \\theta } )$ . This is equivalent to setting the classification threshold to 0.5. ",
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+    {
+        "type": "text",
+        "text": "3.3 EXPLOITING HIGHER-ORDER DEPENDENCIES AMONG LABELS",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "As discussed in length in Section 1, it is hardly true that abnormalities are independent from each other. Hence the assumption made by Equ (1) is undoubtably too restrictive. In order to treat the multi-label problem in its full generality, we can begin with the following factorization, which makes no assumption of independence: ",
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+        "type": "equation",
+        "img_path": "images/0fa8e64a96a441516139665d133c5e5f6ce4b8f98b7b97e0a0a14a0164de0211.jpg",
+        "text": "$$\nP ( \\mathbf { y } | \\mathbf { x } ) = P ( \\mathbf { y } ^ { 0 } | \\mathbf { x } ) P ( \\mathbf { y } ^ { 1 } | \\mathbf { y } ^ { 0 } , \\mathbf { x } ) \\dots P ( \\mathbf { y } ^ { T } | \\mathbf { y } ^ { 0 } , \\dots , \\mathbf { y } ^ { T - 1 } , \\mathbf { x } ) .\n$$",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "Here, the statistical dependencies among the indicators, $\\mathbf { y } ^ { t }$ , are explicitly modeled within each factor so the absence or the presence of a particular abnormality may suggest the absence or presence of others. ",
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+    {
+        "type": "text",
+        "text": "The factorization in Equ (3) has been the central study of many recent models. Bengio & Bengio (2000) proposed the first neural network based model, refined by Larochelle & Murray (2011) and Gregor et al. (2014), all of which used the model in the context of unsupervised learning in small discrete data or small image patches. Recently Sutskever et al. (2014); Cho et al. (2014) popularized the so-called “sequence-to-sequence” model where a Recurrent Neural Network (RNN) decoder models precisely the same joint distribution while conditioned on the output of an encoder. Compared with the previous work, RNNs provide a more general framework to model Equ (3) and an unmatched proficiency in capturing long term dependencies when $K$ is large. ",
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+        "text": "",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We therefore adopt the Long-short Term Memory Networks (LSTM) (Hochreiter & Schmidhuber, 1997) and treat the multi-label classification as sequence prediction with a fixed length. The formulation of our LSTM is particularly similar to those used in image and video captioning (Xu et al., 2015; Yao et al., 2015), but without the use of an attention mechanism and without the need of learning when to stop. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Given an input $\\mathbf { x }$ , the same DenseNet-based encoder of Section 3.2 is applied to produce a lower dimensional vector representation of it with ",
+        "bbox": [
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+    {
+        "type": "equation",
+        "img_path": "images/ffa6197b22d46f6dc493ea986f76ca7e3035fb87072fc374b724a222fbb32126.jpg",
+        "text": "$$\n\\mathbf { x } _ { \\mathrm { e n c } } = f _ { \\mathrm { e n c } } ( \\mathbf { x } )\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 5
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+    {
+        "type": "text",
+        "text": "For the decoder, $\\mathbf { x e n c }$ is used to initialize both the states and memory of an LSTM with ",
+        "bbox": [
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+        "page_idx": 5
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+    {
+        "type": "equation",
+        "img_path": "images/6aa95304fb920488b2d1a729c5ac13601691253b8a9eb7209298b37173acb899.jpg",
+        "text": "$$\n\\begin{array} { r } { \\mathbf { h } _ { 0 } = f _ { h _ { 0 } } ( \\mathbf { x } _ { \\mathrm { e n c } } ) \\qquad \\mathbf { c } _ { 0 } = f _ { c _ { 0 } } ( \\mathbf { x } _ { \\mathrm { e n c } } ) } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where $f _ { h _ { 0 } }$ and $f _ { c _ { 0 } }$ are standard feedforward neural networks with one hidden layer. With $\\mathbf { h } _ { 0 }$ and $\\mathbf { c } _ { 0 }$ the LSTM decoder is parameterized as ",
+        "bbox": [
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+    {
+        "type": "equation",
+        "img_path": "images/6ccd69006ff12ca977be80411b2e219f42d9e54fcc0e5986dc2a9681802bf233.jpg",
+        "text": "$$\n\\begin{array} { r l } & { \\mathbf { g } _ { i } ^ { t } = \\mathrm { s i g m o i d } ( \\mathbf { x } _ { \\mathrm { e n c } } \\mathbf { W } _ { i } + \\mathbf { h } ^ { t - 1 } \\mathbf { U } _ { i } + \\mathbf { y } ^ { t - 1 } \\mathbf { V } _ { i } + \\mathbf { b } _ { i } ) } \\\\ & { \\mathbf { g } _ { o } ^ { t } = \\mathrm { s i g m o i d } ( \\mathbf { x } _ { \\mathrm { e n c } } \\mathbf { W } _ { o } + \\mathbf { h } ^ { t - 1 } \\mathbf { U } _ { o } + \\mathbf { y } ^ { t - 1 } \\mathbf { V } _ { o } + \\mathbf { b } _ { o } ) } \\\\ & { \\mathbf { g } _ { f } ^ { t } = \\mathrm { s i g m o i d } ( \\mathbf { x } _ { \\mathrm { e n c } } \\mathbf { W } _ { f } + \\mathbf { h } ^ { t - 1 } \\mathbf { U } _ { f } + \\mathbf { y } ^ { t - 1 } \\mathbf { V } _ { f } + \\mathbf { b } _ { f } ) } \\\\ & { \\mathbf { g } _ { g } ^ { t } = \\mathbf { x } _ { \\mathrm { e n c } } \\mathbf { W } _ { g } + \\mathbf { h } ^ { t - 1 } \\mathbf { U } _ { g } + \\mathbf { y } ^ { t - 1 } \\mathbf { V } _ { g } + \\mathbf { b } _ { g } } \\\\ & { \\mathbf { c } ^ { t } = \\mathbf { g } _ { f } ^ { t } \\odot \\mathbf { c } ^ { t - 1 } + \\mathbf { g } _ { i } ^ { t } \\odot \\mathrm { t a n h } ( \\mathbf { g } _ { g } ^ { t } ) } \\\\ & { \\mathbf { h } ^ { t } = \\mathbf { g } _ { o } ^ { t } \\odot \\mathrm { t a n h } ( \\mathbf { c } ^ { t } ) } \\\\ & { \\mathbf { m } ^ { t } = \\mathrm { s i g m o i d } ( \\mathbf { h } ^ { t } \\mathbf { q } ^ { T } + b _ { l } ) } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where model parameters consist of three matrices Ws, Us, Vs, vectors bs and a scalar $b _ { l }$ . y is a vector code of the ground truth labels that respects a fixed ordering, with each element being either 0 or 1. All the vectors, including hs, gs, cs, bs, $\\mathbf { q }$ and $\\mathbf { y }$ are row vectors such that the vector-matrix multiplication makes sense. $\\odot$ denotes the element-wise multiplication. Both sigmoid and tanh are element-wise nonlinearities. For brevity, we summarize one step of decoder computation as ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "img_path": "images/c47255c0fb258b4eaa555b7a282a4cc626ef23775e54d3dd651420f5bec42e29.jpg",
+        "text": "$$\n\\mathbf { m } ^ { t } = f _ { \\mathrm { d e c } } ( \\mathbf { x } _ { \\mathrm { e n c } } , \\mathbf { y } ^ { t - 1 } , \\mathbf { h } ^ { t - 1 } )\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where the decoder LSTM computes sequentially the mean of a Bernoulli distribution. With Equ (3), each of its factor may be rewritten as ",
+        "bbox": [
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+    },
+    {
+        "type": "equation",
+        "img_path": "images/478a95163eb13b6939245bb23898e1cce8c4cbe2e498d8917d67e5ffe0a98c11.jpg",
+        "text": "$$\nP ( \\mathbf { y } ^ { t } | \\mathbf { y } ^ { 0 } , \\ldots , \\mathbf { y } ^ { t - 1 } , \\mathbf { x } ) = P ( \\mathbf { y } ^ { t } = 1 ) ^ { \\mathbf { m } ^ { t } } P ( \\mathbf { y } ^ { t } = 0 ) ^ { ( 1 - \\mathbf { m } ^ { t } ) }\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "3.3.1 THE DESIGN CHOICE OF SIGMOID ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "The choice of using sigmoid to predict $\\mathbf { y } _ { t }$ is by design. Standard sequence-to-sequence models often use softmax to predict one out of $\\mathrm { T }$ classes and thus need to learn explicitly an “end-ofsequence” class. This is not desirable in our context due to the sparseness of the labels, resulting in the learned decoder being strongly biased towards predicting “end-of-sequence” while missing infrequently appearing abnormalities. Secondly, during the inference of the softmax based RNN decoder, the prediction at the current step is largely based on the presence of abnormalities at all previous steps due to the use of argmax. However, in the medical setting, the absence of previously predicted abnormalities may also be important. Sigmoid conveniently addresses these issues by explicitly predicting 0 or 1 at each step and it does not require the model to learn when to stop; the decoder always runs for the same number of steps as the total number of classes. Figure 1 contains the overall architecture of the decoder. ",
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+    {
+        "type": "text",
+        "text": "3.3.2 TRAINING ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "During training, the model optimizes ",
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+    },
+    {
+        "type": "equation",
+        "img_path": "images/e9d426f86475d1543f0fe818bde3da28ebebdec12122d2501d2039e22f87f666.jpg",
+        "text": "$$\n\\mathcal { L } _ { \\beta } = \\mathop { \\arg \\operatorname* { m a x } } _ { \\theta } \\sum _ { t = 1 } ^ { T } \\log P ( \\mathbf { y } ^ { k } | \\mathbf { y } ^ { 0 } , \\dots , \\mathbf { y } ^ { t - 1 } ,  { \\mathbf { x } } , \\theta )\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Compared with Equ (1), the difference is the explicit dependencies among $\\mathbf { y } ^ { t } \\mathbf { s }$ . One may also notice that such a factorization is not unique – in fact, there exist $T !$ different orderings. Although mathematically equivalent, in practice, some of the orderings may result in a model that is easier to train. We investigate in Section 4 the impact of such decisions with two distinct orderings. ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "3.3.3 INFERENCE ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "The inference of such a model is unfortunately intractable as $\\mathbf { y } ^ { * } = \\arg \\operatorname* { m a x } _ { \\mathbf { y } } P ( \\mathbf { y } ^ { 0 } , \\ldots , \\mathbf { y } ^ { T } | \\mathbf { x } )$ . Beam search (Sutskever et al., 2014) is often used as an approximation. We have found in practice that greedy search, which is equivalent to beam search with size 1, results in similar performance due to the binary sampling nature of each $\\mathbf { y } ^ { t }$ , and use it throughout the experiments. It is equivalent to setting 0.5 as the discretization threshold on each of the factors. ",
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+    {
+        "type": "text",
+        "text": "4 EXPERIMENTS ",
+        "text_level": 1,
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.1 DATASET ",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "To verify the efficacy of the proposed models in medical diagnosis, we conduct experiments on the dataset introduced in Wang et al. (2017). It is to-date the largest collection of chest $\\mathbf { X }$ -rays that is publicly available. It contains in total 112,120 frontal-view chest x-rays each of which is associated with the absence or presence of 14 abnormalities. The dataset is originally released in PNG format, with each image rescaled to $1 0 2 4 \\times 1 0 2 4$ . ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "As there is no standard split for this dataset, we follow the guideline in Wang et al. (2017) to randomly split the entire dataset into $70 \\%$ for training, $10 \\%$ for validation and $20 \\%$ for training. The authors of Wang et al. (2017) noticed insignificant performance difference with different random splits, as confirmed in our experiments by the observation that the performance on validation and test sets are consistent with each other. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "4.2 PERFORMANCE METRICS ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "As the dataset is relatively new, the complete set of metrics have yet to be established. In this work, the following metrics are considered, and their advantage and drawbacks outlined below. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "1. Negative log-probability of the test set (NLL). This metric has a direct and intuitive probabilistic interpretation: The lower the NLL, the more likely the ground truth label. However, it is difficult to associate it with a clinical interpretation. Indeed, it does not directly reflect how accurate the model is at diagnosing cases with or without particular abnormalities. ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "2. Area under the ROC curves (AUC). This is the reported metric of Wang et al. (2017) and it is widely used in modern biostatistics to measure collectively the rate of true detections and false alarms. In particular, we define 4 quantities: (1) true positive as TP: model predicts 1 with ground truth 1. (2) true negative as TN: model predicts 0 with ground truth 0. (3) false positive as FP: model predicts 1 with ground truth 0. (4) false negative as FN: model predicts 0 with ground truth 1. Sensitivity (or recall) is computed as $\\mathrm { \\bar { T P } / ( T P + F N ) }$ that measures the success of identifying abnormal cases. Specificity is $\\mathrm { T N } / ( \\mathrm { T N } + \\mathrm { F P } )$ that measures the success of not flagging normal cases as abnormal. The ROC curve has typically horizontal axis as (1-specificity) and vertical axis as sensitivity. Once $P ( \\mathbf { y } _ { i } | \\mathbf { x } )$ is available, the curve is generated by varying the decision threshold to discretize the probability into either 0 or 1. Despite of its clinical relevance, $P ( \\mathbf { y } _ { i } | \\mathbf { x } )$ is intractable to compute with the model of Equ (3) due to the need of marginalizing out other binary random variables. It is however straightforward to compute with the model of Equ (1) due the independent factorization. ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "3. DICE coefficient. As a similarity measure over two sets, DICE coefficient is formulated as $\\mathrm { D I C E } ( { \\bf y } _ { \\alpha } , { \\bf y } _ { \\beta } ) = ( 2 { \\bf y } _ { \\alpha } { \\bf y } _ { \\beta } ) / ( { \\bf \\dot { y } } _ { \\alpha } ^ { 2 } + { \\bf y } _ { \\beta } ^ { 2 } ) = 2 \\mathrm { T P } / ( 2 \\mathrm { T P } + \\mathrm { F P } + \\mathrm { F N } )$ with the maxima at 1 when ${ \\bf y } _ { \\alpha } \\equiv { \\bf y } _ { \\beta }$ . Such a metric may be generalized in cases where $\\mathbf { y } _ { \\alpha }$ is a predicted probability with ${ \\bf y } _ { \\alpha } = { \\cal P } ( { \\bf y } | { \\bf x } )$ and $\\mathbf { y } _ { \\beta }$ is the binary-valued ground truth, as is used in image segmentation tasks such as in Ronneberger et al. (2015); Milletari et al. (2016). We adopt such a generalization as our models naturally output probabilities. ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "4. Per-example sensitivity and specificity (PESS). The following formula is used to compute PESS ",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "equation",
+        "img_path": "images/46067c87b09e3974b4c33c5bd9bcd671a4262c9b7a3faf8668e92e94e28627c9.jpg",
+        "text": "$$\n\\mathrm { P E S S } = \\frac { 1 } { N } \\sum _ { i = 1 } ^ { N } \\frac { \\mathrm { s e n s i t i v i t y } ( \\hat { \\bf y } _ { i } , { \\bf y } _ { i } ) + \\mathrm { s p e c i f i c i t y } ( \\hat { \\bf y } _ { i } , { \\bf y } _ { i } ) } { 2 }\n$$",
+        "text_format": "latex",
+        "bbox": [
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+            161,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "where $N$ is the size of the test set. Notice that the computation of sensitivity and specificity requires a binary prediction vector. Therefore, without introducing any thresholding bias, we use ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "equation",
+        "img_path": "images/0463942fc2d9447281c87626f3e11d3c1a2361b71dcb879fbeb550242ba7e843.jpg",
+        "text": "$$\n\\hat { \\mathbf { y } } _ { i } = \\left\\{ \\begin{array} { l l } { 1 } & { P ( \\mathbf { y } _ { i } | \\mathbf { x } _ { i } ) > 0 . 5 } \\\\ { 0 } & { \\mathrm { o t h e r w i s e } } \\end{array} \\right.\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "5. Per-class sensitivity and specificity (PCSS). Unlike PESS, the following formula is used to compute PCSS ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "equation",
+        "img_path": "images/67b9453d555ac7521717a4c7017b1463b002191538dfa8895c4822a96539e5bc.jpg",
+        "text": "$$\n\\mathrm { P C S S } = \\frac { 1 } { T } \\sum _ { t = 1 } ^ { T } \\frac { \\mathrm { s e n s i t i v i t y } ( \\hat { \\mathbf { y } } _ { i } ^ { t } , \\mathbf { y } _ { i } ^ { t } ) + \\mathrm { s p e c i f i c i t y } ( \\hat { \\mathbf { y } } _ { i } ^ { t } , \\mathbf { y } _ { i } ^ { t } ) } { 2 }\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "where $\\hat { \\mathbf { y } } _ { i } ^ { t }$ follows the same threshold of 0.5 as in PESS. Unlike PCSS where the average is over examples, PCSS averages over abnormalities instead. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "4.3 TRAINING PROCEDURES ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Three types of models are tuned on the training set. We have found that data augmentation is crucial in combatting the overfitting in all of our experiments despite their relatively small size. In particular, the input image of resolution $5 1 2 \\times 5 1 2$ is randomly translated in 4 directions by 25 pixels, randomly rotated from -15 to 15 degrees, and randomly scaled between $80 \\%$ and $120 \\%$ . Furthermore, the ADAM optimizer Kingma & Ba (2015) is used with an initial learning rate of 0.001 which is multiplied by 0.9 whenever the performance on the validation set does not improve during training. Early stop is applied when the performance on the validation set does not improve for 10,000 parameter updates. All the reported metrics are computed on the test set with models selected with the metric in question on the validation set. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "In order to ensure a fair comparison, we constrain all models to have roughly the same number of parameters. For $\\mathrm { m o d e l } _ { a }$ , where labels are considered independent, a much higher network growth rate is used for the encoder. For $\\mathrm { m o d e l } _ { b _ { 1 } }$ and $\\mathrm { m o d e l } _ { b _ { 2 } }$ where LSTMs are used as decoders, the encoders are narrower. The exact configuration of three models is shown in Table 1. In addition, we investigate the effect of ordering in the factorization of Equ (3). In particular, $\\mathrm { m o d e l } _ { b _ { 1 } }$ sorts labels by their frequencies in the training set while $\\mathrm { m o d e l } _ { b _ { 1 } }$ orders them alphabetically. All models are trained with MLE with the weighted cross-entropy loss introduced in Wang et al. (2017). All models are trained end-to-end from scratch, without any pre-training on ImageNet data. ",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/9815995895288433b3e80076e3fbf377a8eb9730c4c7c1584671b76c24b24bd5.jpg",
+        "table_caption": [
+            "Table 1: Hyper-parameter configuration of three models. To ensure the fairness of the comparison, we deliberately reduce the capacity of the encoder for $\\mathrm { m o d e l } _ { b _ { 1 } }$ and $\\mathrm { m o d e l } _ { b _ { 2 } }$ to match the total number of parameters of mode $^ { - a }$ . "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td># of dense block × # of conv block</td><td>growth rate</td><td>LSTM dim.</td><td>total # of params</td></tr><tr><td>modela</td><td>4×3</td><td>38</td><td>1</td><td>1,007K</td></tr><tr><td>modelb1,b2</td><td>4×3</td><td>19</td><td>100</td><td>1,016K</td></tr></table>",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "4.4 QUANTITATIVE RESULTS ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "The AUC per abnormality is shown in Table 2, computed based on the marginal distribution of $P ( \\mathbf { y } | \\mathbf { x } )$ . Only mode $^ { - a }$ is included as such marginals are in general intractable for the other two due to the dependencies among $\\mathbf { y } ^ { t } \\mathbf { s }$ . In addition, Table 3 compares all three models based on the proposed metrics from Section 4.2. It can be observed that our baseline model significantly outperformed the previous state-of-the-art. According to Table 3, considering label dependencies brings significant benefits in all 4 metrics and the impact of ordering seems to be marginal when the model is sufficiently trained. ",
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+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Table 2: Fifteen abnormalities and their AUCs, including the average AUC over all abnormalities. The model is trained without pre-training or feature extraction from ImageNet. The model corresponds to the one in Section 3.2 where $\\mathbf { \\bar { y } } ^ { t } \\mathbf { s }$ are considered independent. This table excludes the model from Section 3.3 because AUC requires $P ( \\mathbf { y } ^ { t } | \\mathbf { x } )$ , which is in general intractable. ",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/befd89220d0231586d4ef7a7d6c969dc49c731f13606177008f400c6ab345a50.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>abnormality</td><td>Wang et al. (2017)</td><td>modela</td></tr><tr><td>atelectasis cardiomegaly</td><td>0.716</td><td>0.772</td></tr><tr><td>effusion</td><td>0.807 0.784</td><td>0.904 0.859</td></tr><tr><td>infiltration</td><td>0.609</td><td>0.695</td></tr><tr><td>mass</td><td>0.706</td><td>0.792</td></tr><tr><td>nodule</td><td>0.671</td><td>0.717</td></tr><tr><td>pneumonia</td><td>0.633</td><td>0.713</td></tr><tr><td>pneumothorax</td><td>0.806</td><td></td></tr><tr><td>consolidation</td><td></td><td>0.841</td></tr><tr><td>edema</td><td>0.708</td><td>0.788</td></tr><tr><td>emphysema</td><td>0.835</td><td>0.882</td></tr><tr><td>fibrosis</td><td>0.815</td><td>0.829</td></tr><tr><td></td><td>0.769</td><td>0.767</td></tr><tr><td>PT</td><td>0.708</td><td>0.765</td></tr><tr><td>hernia</td><td>0.767</td><td>0.914</td></tr><tr><td>A.V.G.</td><td>0.738</td><td>0.798</td></tr><tr><td>no finding</td><td>-</td><td>0.762</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Table 3: Test set performance on negative log-probability (NLL), DICE, per-example sensitivity (PESS) at a threshold 0.5 and per-class sensitivity and specificity (PCSS) at a threshold of 0.5. See Section 4.2 for explanations of the metrics. In addition to $\\mathrm { m o d e l } _ { a }$ used in Table 2, $\\mathrm { m o d e l } _ { b 1 }$ and $\\mathrm { m o d e l } _ { b 2 }$ corresponds to the model introduced in Section 3.3, with the difference in the ordering of the factorization in Equ (3). $\\mathrm { m o d e l } _ { b 1 }$ sorts labels by their frequency in the training set in ascending order. As a comparison, $\\mathrm { m o d e l } _ { b 2 }$ orders labels alphabetically according to the name of the abnormality. ",
+        "bbox": [
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+    {
+        "type": "table",
+        "img_path": "images/61acc6b2d6d6ba483109ee282b1481593e9c4dd6156e16162d8b571b66ce6d37.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>NLL</td><td>DICE</td><td>PESS0.5</td><td>PCSS0.5</td></tr><tr><td>modela</td><td>4.474</td><td>0.261</td><td>0.752</td><td>0.665</td></tr><tr><td>modelb1</td><td>4.099</td><td>0.310</td><td>0.765</td><td>0.676</td></tr><tr><td>modelb2</td><td>3.848</td><td>0.310</td><td>0.767</td><td>0.677</td></tr></table>",
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+    },
+    {
+        "type": "text",
+        "text": "5 CONCLUSION ",
+        "text_level": 1,
+        "bbox": [
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+            318,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "To improve the quality of computer-assisted diagnosis of chest $\\mathbf { X }$ -rays, we proposed a two-stage end-to-end neural network model that combines a densely connected image encoder with a recurrent neural network decoder. The first stage was chosen to address the challenges to learning presented by high-resolution medical images and limited training set sizes. The second stage was designed to allow the model to exploit statistical dependencies between labels in order to improve the accuracy of its predictions. Finally, the model was trained from scratch to ensure that the best application-specific features were captured. Our experiments have demonstrated both the feasibility and effectiveness of this approach. Indeed, our baseline model significantly outperformed the current state-of-the-art. The proposed set of metrics provides a meaningful quantification of this performance and will facilitate comparisons with future work. ",
+        "bbox": [
+            174,
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "While a limited exploration into the value of learning interdependencies among labels yields promising results, additional experimentation will be required to further explore the potential of this methodology both as it applies specifically to chest $\\mathbf { X }$ -rays and to medical diagnostics as a whole. One potential concern with this approach is the risk of learning biased interdependencies from a limited training set which does not accurately represent a realistic distribution of pathologies – if every example of cardiomegaly is also one of cardiac failure, the model may learn to depend too much on the presence of other patterns such as edemas which do not always accompany enlargement of the cardiac silhouette. This risk is heightened when dealing with data labeled with a scheme which mixes pathologies, such as pneumonia, with patterns symptomatic of those pathologies, such as consolidation. The best approach to maximizing feature extraction and leveraging interdependencies among target labels likely entails training from data labeled with an ontology that inherently poses some consistent known relational structure. This will be the endpoint of a future study. ",
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+    {
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parse/train/HJg2b0VYDr/HJg2b0VYDr.md

@@ -0,0 +1,348 @@
+# SELECTION VIA PROXY: EFFICIENT DATA SELECTION FOR DEEP LEARNING
+
+Cody Coleman∗, Christopher Yeh, Stephen Mussmann, Baharan Mirzasoleiman,   
+Peter Bailis, Percy Liang, Jure Leskovec, Matei Zaharia   
+Stanford University
+
+# ABSTRACT
+
+Data selection methods, such as active learning and core-set selection, are useful tools for machine learning on large datasets. However, they can be prohibitively expensive to apply in deep learning because they depend on feature representations that need to be learned. In this work, we show that we can greatly improve the computational efficiency by using a small proxy model to perform data selection (e.g., selecting data points to label for active learning). By removing hidden layers from the target model, using smaller architectures, and training for fewer epochs, we create proxies that are an order of magnitude faster to train. Although these small proxy models have higher error rates, we find that they empirically provide useful signals for data selection. We evaluate this “selection via proxy” (SVP) approach on several data selection tasks across five datasets: CIFAR10, CIFAR100, ImageNet, Amazon Review Polarity, and Amazon Review Full. For active learning, applying SVP can give an order of magnitude improvement in data selection runtime (i.e., the time it takes to repeatedly train and select points) without significantly increasing the final error (often within $0 . 1 \%$ ). For core-set selection on CIFAR10, proxies that are over $1 0 \times$ faster to train than their larger, more accurate targets can remove up to $50 \%$ of the data without harming the final accuracy of the target, leading to a $1 . 6 \times$ end-to-end training time improvement.
+
+# 1 INTRODUCTION
+
+Data selection methods, such as active learning and core-set selection, improve the data efficiency of machine learning by identifying the most informative training examples. To quantify informativeness, these methods depend on semantically meaningful features or a trained model to calculate uncertainty. Concretely, active learning selects points to label from a large pool of unlabeled data by repeatedly training a model on a small pool of labeled data and selecting additional examples to label based on the model’s uncertainty (e.g., the entropy of predicted class probabilities) or other heuristics (Lewis & Gale, 1994; Rosenberg et al., 2005; Settles, 2011; 2012). Conversely, core-set selection techniques start with a large labeled or unlabeled dataset and aim to find a small subset that accurately approximates the full dataset by selecting representative examples (Har-Peled & Kushal, 2007; Tsang et al., 2005; Huggins et al., 2016; Campbell & Broderick, 2017; 2018; Sener & Savarese, 2018).
+
+Unfortunately, classical data selection methods are often prohibitively expensive to apply in deep learning (Shen et al., 2017; Sener & Savarese, 2018; Kirsch et al., 2019). Deep learning models learn complex internal semantic representations (hidden layers) from raw inputs (e.g., pixels or characters) that enable them to achieve state-of-the-art performance but result in substantial training times. Many core-set selection and active learning techniques require some feature representation before they can accurately identify informative points either to take diversity into account or as part of a trained model to quantify uncertainty. As a result, new deep active learning methods request labels in large batches to avoid retraining the model too many times (Shen et al., 2017; Sener & Savarese, 2018; Kirsch et al., 2019). However, batch active learning still requires training a full deep model for every batch, which is costly for large models (He et al., 2016b; Jozefowicz et al., 2016; Vaswani et al., 2017). Similarly, core-set selection applications mitigate the training time of deep learning models by using bespoke combinations of hand-engineered features and simple models (e.g., hidden Markov models) pretrained on auxiliary tasks (Wei et al., 2013; 2014; Tschiatschek et al., 2014; Ni et al., 2015).
+
+In this paper, we propose selection via proxy (SVP) as a way to make existing data selection methods more computationally efficient for deep learning. SVP uses the feature representation from a separate, less computationally intensive proxy model in place of the representation from the much larger and more accurate target model we aim to train. SVP builds on the idea of heterogeneous uncertainty sampling from Lewis & Catlett (1994), which showed that an inexpensive classifier (e.g., naïve Bayes) can select points to label for a much more computationally expensive classifier (e.g., decision tree). In our work, we show that small deep learning models can similarly serve as an inexpensive proxy for data selection in deep learning, significantly accelerating both active learning and core-set selection across a range of datasets and selection methods. To create these cheap proxy models, we can scale down deep learning models by removing layers, using smaller model architectures, and training them for fewer epochs. While these scaled-down models achieve significantly lower accuracy than larger models, we surprisingly find that they still provide useful representations to rank and select points. Specifically, we observe high Spearman’s and Pearson’s correlations between the rankings from small proxy models and the larger, more accurate target models on metrics including uncertainty (Settles, 2012), forgetting events (Toneva et al., 2019), and submodular algorithms such as greedy $\mathbf { k }$ -centers (Wolf, 2011). Because these proxy models are quick to train (often $1 0 \times$ faster), we can identify which points to select nearly as well as the larger target model but significantly faster.
+
+We empirically evaluated SVP for active learning and core-set selection on five datasets: CIFAR10, CIFAR100 (Krizhevsky & Hinton, 2009), ImageNet (Russakovsky et al., 2015), Amazon Review Polarity, and Amazon Review Full (Zhang et al., 2015). For active learning, we considered both least confidence uncertainty sampling (Settles, 2012; Shen et al., 2017; Gal et al., 2017) and the greedy $\mathbf { k }$ -centers approach from Sener & Savarese (2018) with a variety of proxies. Across all datasets, we found that SVP matches the accuracy of the traditional approach of using the same large model for both selecting points and the final prediction task. Depending on the proxy, SVP yielded up to a $7 \times$ speed-up on CIFAR10 and CIFAR100, $4 1 . 9 \times$ speed-up on Amazon Review Polarity and Full, and $2 . 9 \times$ speed-up on ImageNet in data selection runtime (i.e., the time it takes to repeatedly train and select points). For core-set selection, we tried three methods to identify a subset of points: max entropy uncertainty sampling (Settles, 2012), greedy $\mathbf { k }$ -centers as a submodular approach (Wolf, 2011), and the recent approach of forgetting events (Toneva et al., 2019). For each method, we found that smaller proxy models have high Spearman’s rank-order correlations with models that are $1 0 \times$ larger and performed as well as these large models at identifying subsets of points to train on that yield high test accuracy. On CIFAR10, SVP applied to forgetting events removed $50 \%$ of the data without impacting the accuracy of ResNet164 with pre-activation (He et al., 2016b), using a $1 0 \times$ faster model than ResNet164 to make the selection. This substitution yielded an end-to-end training time improvement of about $1 . 6 \times$ for ResNet164 (including the time to train and use the proxy). Taken together, these results demonstrate that SVP is a promising, yet simple approach to make data selection methods computationally feasible for deep learning. While we focus on active learning and core-set selection, SVP is widely applicable to methods that depend on learned representations.
+
+# 2 METHODS
+
+In this section, we describe SVP and show how it can be incorporated into active learning and core-set selection. Figure 1 shows an overview of SVP: in active learning, we retrain a proxy model $A _ { k } ^ { P }$ in place of the target model $A _ { k } ^ { T }$ after each batch is selected, and in core-set selection, we train the proxy $A _ { [ n ] } ^ { P }$ rather than the target $A _ { [ n ] } ^ { T }$ over all the data to learn a feature representation and select points.
+
+# 2.1 ACTIVE LEARNING
+
+Pool-based active learning starts with a large pool of unlabeled data $U = \{ \mathbf { x } _ { i } \} _ { i \in [ n ] }$ where $[ n ] =$ $\{ 1 , \ldots , n \}$ . Each example is from the space $\mathcal { X }$ with an unknown label from the label space $\mathcal { V }$ and is sampled i.i.d. over the space ${ \mathcal { Z } } = { \mathcal { X } } \times { \mathcal { Y } }$ as $( \mathbf { x } _ { i } , y _ { i } ) \sim p _ { \mathcal { Z } }$ . Initially, methods label a small pool of points $s ^ { 0 } = \{ s _ { j } ^ { 0 } \in [ n ] \} _ { j \in [ m ] }$ chosen uniformly at random. Given $U$ , a loss function $\ell$ , and the labels $\{ y _ { s _ { j } ^ { 0 } } \} _ { j \in [ m ] }$ for the initial random subset, the goal of active learning is to select up to a budget of $b$ points $s = s ^ { 0 } \cup \{ s _ { j } \in [ n ] \setminus s ^ { 0 } \} _ { j \in [ b - m ] }$ to label that produces a model $A _ { s }$ with low error.
+
+![](images/d2e1999295459ae03026407e0764655a52cb8c17d5862d15837f858eeff535c2.jpg)  
+Figure 1: SVP applied to active learning (left) and core-set selection (right). In active learning, we followed the same iterative procedure of training and selecting points to label as traditional approaches but replaced the target model with a cheaper-to-compute proxy model. For core-set selection, we learned a feature representation over the data using a proxy model and used it to select points to train a larger, more accurate model. In both cases, we found the proxy and target model have high rank-order correlation, leading to similar selections and downstream results.
+
+Baseline. In this paper, we apply SVP to least confidence uncertainty sampling (Settles, 2012; Shen et al., 2017; Gal et al., 2017) and the recent greedy $\mathrm { k }$ -centers approach from Sener & Savarese (2018). Like recent work for deep active learning (Shen et al., 2017; Sener & Savarese, 2018; Kirsch et al., 2019), we consider a batch setting with $K$ rounds where we select $\textstyle { \frac { b } { K } }$ points in every round. Following Gal et al. (2017); Sener & Savarese (2018); Kirsch et al. (2019), we reinitialize the target model and retrain on all of the labeled data from the previous $k$ rounds to avoid any correlation between selections (Frankle $\&$ Carbin, 2018; Kirsch et al., 2019). We denote this trained model as $A _ { s ^ { 0 } \cup \ldots \cup s ^ { k } } ^ { T }$ or just $A _ { k } ^ { T }$ for simplicity. Then using $A _ { k } ^ { T }$ , we either calculate the model’s confidence as:
+
+$$
+f _ { \mathrm { c o n f i d e n c e } } ( \mathbf { x } ; A _ { k } ^ { T } ) = 1 - \operatorname* { m a x } _ { \hat { y } } P ( { \hat { y } } | \mathbf { x } ; A _ { k } ^ { T } )
+$$
+
+and select the examples with the lowest confidence or extract a feature representation from the model’s final hidden layer and compute the distance between examples (i.e., $\Delta ( \mathbf { x } _ { i } , \mathbf { x } _ { j } ; A _ { k } ^ { T } ) )$ to select points according to the greedy $\mathbf { k }$ -centers method from Wolf (2011); Sener & Savarese (2018) (Algorithm 1). The same model is trained on the final $b$ labeled points to yield the final model, $A _ { K } ^ { T }$ , which is then tested on a held-out set to evaluate error and quantify the quality of the selected data.
+
+Although other selection approaches exist, least confidence uncertainty sampling and greedy $\mathbf { k }$ -centers cover the spectrum of uncertainty-based and representativeness-based approaches for deep active learning. Other uncertainty metrics such as entropy or margin were highly correlated with confidence when using the same trained model (i.e., above a 0.96 Spearman’s correlation in our experiments on CIFAR). Query-by-committee (Seung et al., 1992) can be prohibitively expensive in deep learning, where training a single model is already costly. BALD (Houlsby et al., 2011) has seen success in deep learning (Gal et al., 2017; Shen et al., 2017) but is restricted to Bayesian neural networks or networks with dropout (Srivastava et al., 2014) as an approximation (Gal & Ghahramani, 2016).
+
+<table><tr><td>Algorithm1GREEDYK-CENTERS</td></tr></table>
+
+Input: data $\mathbf { x } _ { i }$ , existing pool $s ^ { 0 }$ , trained model $A _ { 0 } ^ { T }$ , and a budget $b$   
+1: Initialize $s = \bar { s ^ { 0 } }$   
+2: repeat   
+3: $\begin{array} { r } { \hat { u _ { { \mathbf { \xi } } } } = \arg \operatorname* { m a x } _ { i \in [ n ] \setminus s } \operatorname* { m i n } _ { j \in s } \Delta \left( \mathbf { x } _ { i } , \mathbf { x } _ { j } ; A _ { 0 } ^ { T } \right) } \end{array}$   
+4: s = s ∪ {u}   
+5: until $| s | = \grave { b } + | s ^ { 0 } |$   
+6: return s \ s0
+
+# Algorithm 2 FORGETTING EVENTS (TONEVA ET AL., 2019)
+
+1: Initialize prev_ $\mathsf { a c c } _ { i } = 0 , i \in [ n ]$   
+2: Initialize forgetting_event $\mathsf { i } _ { i } = 0 , i \in [ n ]$   
+3: while training is not done do   
+4: Sample mini-batch $B$ from $L$   
+5: for example $i \in B$ do   
+6: Compute $\operatorname { a c c } _ { i }$   
+7: if prev_ $\mathrm { a c c } _ { i } >$ acci then   
+8: forgetting_eventsi $+ = 1$   
+9: pre $\vartriangle { \mathbf { a c c } } _ { i } = \mathrm { a c c } _ { i }$   
+10: Gradient update classifier on $B$   
+11: return forgetting_events
+
+# 2.2 CORE-SET SELECTION
+
+Core-set selection can be broadly defined as techniques that find a subset of data points that maintain a similar level of quality (e.g., generalization error of a trained model or minimum enclosing ball) as the full dataset. Specifically, we start with a labeled dataset $L = \{ { \bf x } _ { i } , y _ { i } \} _ { i \in [ n ] }$ sampled i.i.d. from $\mathcal { Z }$ with $p _ { \mathcal { Z } }$ and want to find a subset of $m \leq n$ points $s = \{ s _ { j } \in [ n ] \} _ { j \in [ m ] }$ that achieves comparable quality to the full dataset: $\begin{array} { r } { \operatorname* { m i n } _ { s : | s | = m } E _ { \mathbf { x } , y \sim p _ { \mathbb { Z } } } \left[ \ell ( \mathbf { x } , y ; A _ { s } ) \right] - E _ { \mathbf { x } , y \sim p _ { \mathbb { Z } } } \left[ \ell ( \mathbf { x } , y ; A _ { [ n ] } ) \right] } \end{array}$
+
+Baseline. To find $s$ for a given budget $m$ , we implement three core-set selection techniques: greedy kcenters (Wolf, 2011; Sener & Savarese, 2018), forgetting events (Toneva et al., 2019), and max entropy uncertainty sampling (Lewis & Gale, 1994; Settles, 2012). Greedy $\mathbf { k }$ -centers is described above and in Algorithm 1. Forgetting events are defined as the number of times an example is incorrectly classified after having been correctly classified earlier during training a model, as described in Algorithm 2. To select points, we follow the same procedure as Toneva et al. (2019): we keep the points with the $m$ highest number of forgetting events. Points that are never correctly classified are treated as having an target infinite number of forgetting events. Similarly, we rank examples based on the entropy from a trained $A _ { [ n ] } ^ { T }$ as:
+
+$$
+f _ { \mathrm { e n t r o p y } } ( \mathbf { x } ; A _ { [ n ] } ^ { T } ) = - \sum _ { \hat { y } } P ( \hat { y } | \mathbf { x } ; A _ { [ n ] } ^ { T } ) \log P ( \hat { y } | \mathbf { x } ; A _ { [ n ] } ^ { T } )
+$$
+
+and keep the $m$ examples with the highest entropy. To evaluate core-set quality, we compare the performance of training the large target model on the selected subset $A _ { s } ^ { T }$ to training the target model on the entire dataset $\bar { A _ { [ n ] } ^ { T } }$ by measuring error on a held-out test set.
+
+# 2.3 APPLYING SELECTION VIA PROXY
+
+In general, SVP can be applied by replacing the models used to compute data selection metrics such as uncertainty with proxy models. In this paper, we applied SVP to the active learning and core-set selection methods described in Sections 2.1 and 2.2 as follows:
+
+• For active learning, we replaced the model trained at each batch $( A _ { k } ^ { T } )$ with a proxy $( A _ { k } ^ { P } )$ , but then trained the same final model $A _ { K } ^ { T }$ once the budget $b$ was reached. • For core-set selection, we used a proxy $A _ { [ n ] } ^ { P }$ instead of $A _ { [ n ] } ^ { T }$ to compute metrics and select $s$ .
+
+We explored two main methods to create our proxy models:
+
+Scaling down. For deep models with many layers, reducing the dimension or the number of hidden layers is an easy way to trade-off accuracy to reduce training time. For example, deep ResNet models come in a variety of depths (He et al., 2016b;a) and widths (Zagoruyko & Komodakis, 2016) that represent many points on the accuracy and training time curve. As shown in Figure 4a in the Appendix, a ResNet20 model achieves a top-1 error of $7 . 6 \%$ on CIFAR10 in 26 minutes, while a larger ResNet164 model takes 4 hours and reduces error by $2 . 5 \%$ . Similar results have been shown for many other tasks, including neural machine translation (Vaswani et al., 2017), text classification (Conneau et al., 2016), and recommendation (He et al., 2017). Looking across architectures gives even more options to reduce computational complexity. We exploit the limitless model architectures in deep learning to trade-off between accuracy and complexity to scale down to a proxy that can be trained quickly but still provides a good approximation of the target’s decision boundary.
+
+Training for fewer epochs. Similarly, a significant amount of training is spent on a relatively small reduction in error. While training ResNet20, almost half of the training time (i.e., 12 minutes out of 26 minutes) is spent on a $1 . 4 \%$ improvement in test error, as shown in Figure 4a in the Appendix. Based on this observation, we also explored training proxy models for a smaller number of epochs to get good approximations of the decision boundary of the target model even faster.
+
+# 3 RESULTS
+
+We applied SVP to data selection methods from active learning and core-set selection on five datasets. After a brief description of the datasets and models in Section 3.1, Section 3.2 evaluates SVP’s impact on active learning and shows that across labeling budgets SVP achieved similar or higher accuracy and up to a $4 1 . 9 \times$ improvement in data selection runtime (i.e., the time it takes to repeatedly train and select points). Next, we applied SVP to the core-set selection problem (Section 3.3). For all selection methods, the target model performed nearly as well as or better with SVP than the oracle that trained the target model on all of the data before selecting examples. On CIFAR10, a small proxy model trained for 50 epochs instead of 181 epochs took only 7 minutes compared to the 4 hours for training the target model for all 181 epochs, making SVP feasible for end-to-end training time speed-ups. Finally, Section 3.4 illustrates why proxy models performed so well by evaluating how varying models and methods rank examples.
+
+# 3.1 EXPERIMENTAL SETUP
+
+Datasets. We focused on classification as a well-studied task in the active learning literature (see Section A.1 for more detail). Our experiments included three image classification datasets: CIFAR10, CIFAR100 (Krizhevsky & Hinton, 2009), and ImageNet (Russakovsky et al., 2015); and two text classification datasets: Amazon Review Polarity and Full (Zhang & LeCun, 2015; Zhang et al., 2015). CIFAR10 is a coarse-grained classification task over 10 classes, and CIFAR100 is a fine-grained task with 100 classes. Both datasets contain 50,000 images for training and 10,000 images for testing. ImageNet has 1.28 million training images and 50,000 validation images that belong to 1 of 1,000 classes. Amazon Review Polarity has 3.6 million reviews split evenly between positive and negative ratings with an additional 400,000 reviews for testing. Amazon Review Full has 3 million reviews split evenly between the 5 stars with an additional 650,000 reviews for testing.
+
+Models. For CIFAR10 and CIFAR100, we used ResNet164 with pre-activation from He et al. (2016b) as our large target model. The smaller, proxy models are also ResNet architectures with preactivation, but they use pairs of $3 \times 3$ convolutional layers as their residual unit rather than bottlenecks. For ImageNet, we used the original ResNet architecture from He et al. (2016a) implemented in PyTorch 1 (Paszke et al., 2017) with ResNet50 as the target and ResNet18 as the proxy. For Amazon Review Polarity and Amazon Review Full, we used VDCNN (Conneau et al., 2017) and fastText (Joulin et al., 2016) with VDCNN29 as the target and fastText and VDCNN9 as proxies. In general, we followed the same training procedure as the original papers (more details in Section A.2).
+
+# 3.2 ACTIVE LEARNING
+
+We explored the impact of SVP on two active learning techniques: least confidence uncertainty sampling and the greedy $\mathbf { k }$ -centers approach from Sener & Savarese (2018). Starting with an initial random subset of $2 \%$ of the data, we selected $8 \%$ of the remaining unlabeled data for the first round and $10 \%$ for subsequent rounds until the labeled data reached the budget $b$ and retrained the models from scratch between rounds as described in Section 2.1. Across datasets, SVP sped up data selection without significantly impacting the final predictive performance of the target.
+
+CIFAR10 and CIFAR100. For least confidence uncertainty sampling and greedy k-centers, SVP sped-up data selection by up to $7 \times$ and $3 . 8 \times$ respectively without impacting data efficiency (see Tables 1 and 3) despite the proxy achieving substantially higher top-1 error than the target ResNet164 model (see Figure 6 in the Appendix). The speed-ups for least confidence were a direct reflection of the difference in training time between the proxy in the target models. As shown in Figures 4 and 5 in the Appendix, ResNet20 was about $8 \times$ faster to train than ResNet164, taking 30 minutes to train rather than 4 hours. Larger budgets required more rounds of selection and, in turn, more training, which led to larger speed-ups as training became a more significant fraction of the total time. Training for fewer epochs provided a significant error reduction compared to random sampling but was not as good as training for the full schedule (see Table 4 in the Appendix). For greedy $\mathbf { k }$ -centers, the speed-ups increased more slowly because executing the selection algorithm added more overhead.
+
+ImageNet. For least confidence uncertainty sampling, SVP sped-up data selection by up to $1 . 6 \times$ (Table 1) despite ResNet18’s higher error compared to ResNet50 (Figure $6 \mathrm { g }$ in the Appendix). Training for fewer epochs increased the speed-up to $2 . 9 \times$ without increasing the error rate of ResNet50 (Table 4). Greedy k-centers was too slow on ImageNet due to the quadratic complexity of Algorithm 1.
+
+Table 1: SVP performance on active learning. Average $\geq 1$ std.) data selection speed-ups from 3 runs of active learning using least confidence uncertainty sampling with varying proxies and labeling budgets on four datasets. Bold speed-ups indicate settings that either achieve lower error or are within 1 std. of the mean top-1 error for the baseline approach of using the same model for selection and the final predictions. Across datasets, SVP sped up selection without significantly increasing the error of the final target. Additional results and details are in Table 3.
+
+<table><tr><td colspan="2"></td><td colspan="5">Data Selection Speed-up 30%</td></tr><tr><td>Dataset</td><td>Budget (b/n) SelectionModel</td><td colspan="3">10% 20%</td><td>40%</td><td>50%</td></tr><tr><td>CIFAR10</td><td>ResNet164 (Baseline)</td><td colspan="4">1.0× 1.0× 1.0×</td><td>1.0×</td></tr><tr><td rowspan="4">CIFAR100</td><td>ResNet110</td><td>1.8×</td><td>1.9×</td><td>1.9×</td><td>1.0× 1.8×</td><td>1.8×</td></tr><tr><td>ResNet56</td><td>2.6×</td><td>2.9×</td><td>3.0×</td><td>3.1×</td><td>3.1×</td></tr><tr><td>ResNet20</td><td>3.8×</td><td>5.8×</td><td>6.7×</td><td>7.0×</td><td>7.2×</td></tr><tr><td>ResNet164 (Baseline)</td><td>1.0× 1.0×</td><td>1.0×</td><td></td><td>1.0×</td><td>1.0x</td></tr><tr><td rowspan="4"></td><td>ResNet110</td><td>1.5×</td><td>1.6×</td><td>1.6×</td><td>1.6×</td><td>1.6×</td></tr><tr><td>ResNet56</td><td>2.4×</td><td></td><td></td><td></td><td></td></tr><tr><td></td><td></td><td>2.7× 5.8×</td><td>3.0×</td><td>2.9×</td><td>3.1×</td></tr><tr><td>ResNet20 ResNet50 (Baseline)</td><td>4.0× 1.0×</td><td>1.0×</td><td>6.6× 1.0×</td><td>7.0× 1.0×</td><td>7.2× 1.0×</td></tr><tr><td>ImageNet</td><td>ResNet18</td><td>1.2×</td><td>1.3×</td><td>1.4×</td><td>1.5×</td><td>1.6×</td></tr><tr><td>Amazon</td><td>VDCNN29 (Baseline)</td><td>1.0×</td><td>1.0×</td><td>1.0×</td><td>1.0×</td><td>1.0x</td></tr><tr><td>Review</td><td>VDCNN9</td><td>1.9×</td><td>1.8×</td><td>1.8×</td><td>1.8×</td><td>1.8×</td></tr><tr><td>Polarity</td><td>fastText</td><td>10.6×</td><td>20.6×</td><td>32.2×</td><td>41.9×</td><td>51.3×</td></tr></table>
+
+Amazon Review Polarity and Amazon Review Full. On Amazon Review Polarity, SVP with a fastText proxy for VDCNN29 led to up to a relative error reduction of $14 \%$ over random sampling for large budgets (Table 3), while being up to $4 1 . 9 \times$ faster at data selection than the baseline approach (Table 1). Despite fastText’s architectural simplicity compared to VDCNN29 and higher error (Figure 6e), the calculated confidences signaled which examples would be the most informative. For all budgets, VDCNN9 was within $0 . 1 \%$ top-1 error of VDCNN29, giving a consistent $1 . 8 \times$ speed-up. On Amazon Review Full, neither the baseline least confidence uncertainty sampling approach nor the application of SVP outperformed random sampling (see Table 3 in the Appendix), so the data selection speed-ups were uninteresting even though they were similar to Amazon Review Polarity. For both datasets, greedy $\mathrm { k }$ -centers was too slow as mentioned above in the ImageNet experiments.
+
+# 3.3 CORE-SET SELECTION
+
+CIFAR10 and CIFAR100. For all methods on both CIFAR10 and CIFAR100, SVP proxy models performed as well as or better than an oracle where ResNet164 itself is used as the core-set selection model, as shown in Figure 2 (and Figure 7 in the Appendix). Using forgetting events on CIFAR10, SVP with ResNet20 as the proxy removed $50 \%$ of the data without a significant increase in error from ResNet164. The entire process of training ResNet20 on all the data, selecting which examples to keep, and training ResNet164 on the subset only took 2 hours and 20 minutes (see Table 6 in the Appendix), which was a $1 . 6 \times$ speed-up compared to training ResNet164 over all of the data. If we stopped training ResNet56 early and removed $50 \%$ of the data based on forgetting events from the first 50 epochs, SVP achieved an end-to-end training time speed-up of $1 . 8 \times$ with only a slightly higher top-1 error from ResNet164 $5 . 4 \%$ vs. $5 . 1 \%$ ) as shown in Table 7 in the Appendix. In general, training the proxy for fewer epochs also maintained the accuracy of the target model on CIFAR10 because the ranking quickly converged (Figure 11a and 12a in the Appendix). On CIFAR100, partial training did not work as well for proxies at large subset sizes because the ranking took longer to stabilize and were less correlated (Figure 11b and Figure 12b in the Appendix). On small $30 \%$ subsets with forgetting events, partial training improved accuracy on CIFAR100.
+
+ImageNet. Neither the baseline approach nor SVP was able to remove a significant percentage of the data without increasing the final error of ResNet50, as shown in Table 5 in the Appendix. However, the selected subsets from both ResNet18 and ResNet50 outperformed random sampling with up to a $1 \%$ drop in top-1 error using forgetting events. Note, due to the quadratic computational complexity of Algorithm 1, we were unable to run greedy k-centers in a reasonable amount of time.
+
+![](images/b49ae592f5c3826a11ab7bd55028f05d951b6ce39fb9d4ece92d471131b27969.jpg)  
+Figure 2: SVP performance on core-set selection. Average $\pm 1$ std.) top-1 error of ResNet164 over 5 runs of core-set selection with different selection methods, proxies, and subset sizes on CIFAR10. We found subsets using forgetting events (left), entropy (middle), and greedy $\mathbf { k }$ -centers (right) from a proxy model trained over the entire dataset. Across datasets and selection methods, SVP performed as well as an oracle baseline but significantly faster (speed-ups in parentheses).
+
+![](images/b42767111d4bb37e1564616acb98610ea044d53840f77df96333ea5f31fe6e6c.jpg)  
+Figure 3: Comparing selection across model sizes and methods on CIFAR10. Average Spearman’s correlation between different runs of ResNet (R) models and at varying depths. We computed rankings based on forgetting events (left), entropy (middle), and greedy k-centers (right). We saw a similarly high correlation across model architectures (off-diagonal) as between different runs of the same architecture (on-diagonal), suggesting that small models are good proxies for data selection.
+
+Amazon Review Polarity and Amazon Review Full. On Amazon Review Polarity, we were able to remove $20 \%$ of the dataset with only a $0 . 1 \%$ increase in VDCNN29’s top-1 error using fastText as the proxy (see Table 5). In comparison to VDCNN29, which took 16 hours and 40 minutes to train over the entire dataset on a Titan V GPU, fastText was two orders of magnitude faster, taking less than 10 minutes on a CPU to train over the same data and compute output probabilities. This difference allowed us to train VDCNN29 to nearly the same error in 13 and a half hours. However, on Amazon Review Full, both the baseline approach and SVP failed to outperform random sampling. Similar to ImageNet, we were unable to run greedy $\mathbf { k }$ -centers in a reasonable amount of time, and additionally, Facebook’s fastText implementation 2 did not allow us to compute forgetting events.
+
+# 3.4 RANKING CORRELATION BETWEEN MODELS
+
+Models with fewer layers. Figure 3 (and Figure 9 in the appendix) shows the Spearman’s rankorder correlation between ResNets of varying depth for three selection methods on CIFAR10 (and CIFAR100). For greedy k-centers, we started with 1,000 randomly selected points and ranked the remaining points based on the order they are added to set $s$ in Algorithm 1. Across models, there was a positive correlation similar to the correlation between runs of the same model. For forgetting events and entropy, we ranked points in descending order based on the number of forgetting events and the entropy of the output predictions from the trained model, respectively. Both metrics had comparable positive correlations between different models and different runs of the same model. We also looked at the Pearson correlation coefficient for the number of forgetting events and entropy in Figure 15 in the Appendix and found a similar positive correlation. The consistent positive correlation between varying depths illustrates why small models are good proxies for larger models in data selection.
+
+Models with different architectures. We further investigated different model architectures by calculating the Spearman’s correlation between pretrained ImageNet models and found that correlations were high across a wide range of models (Figure 8 in the Appendix). For example, MobileNet V2’s (Sandler et al., 2018) entropy-based rankings were highly correlated to ResNet50 (on par with ResNet18), even though the model had far fewer parameters (3.5M vs. 25.6M). In concert with our fastText and VDCNN results, the high correlations between different model architectures suggest that SVP might be widely applicable. While there are likely limits to how different architectures can be, there is a wide range of trade-offs between accuracy and computational complexity, even within a narrow spectrum of models.
+
+# 4 RELATED WORK
+
+Active learning. There are examples in the active learning literature that address the computational efficiency of active learning methods by using one model to select points for a different, more expensive model. For instance, Lewis & Catlett (1994) proposed heterogeneous uncertainty sampling and used a Naïve Bayes classifier to select points to label for a more expensive decision tree target model. Tomanek et al. (2007) uses a committee-based active learning algorithm for an NLP task and notes that the set of selected points are “reusable” across different models (maximum entropy, conditional random field, naive Bayes). In our work, we showed that this can be generalized to deep learning by either using smaller models or fewer training epochs, where it can significantly reduce the running time of uncertainty-based (Settles, 2012; Shen et al., 2017; Gal et al., 2017) and recent representativeness-based (Sener & Savarese, 2018) methods.
+
+Core-set selection. Core-set selection attempts to find a representative subset of points to speed up learning or clustering; such as $k$ -means and $k$ -medians (Har-Peled & Kushal, 2007), SVM (Tsang et al., 2005), Bayesian logistic regression (Huggins et al., 2016), and Bayesian inference (Campbell & Broderick, 2017; 2018). However, these examples generally require ready-to-use features as input, and do not directly apply to deep neural networks unless a feature representation is first learned, which usually requires training the full target model itself. There is also a body of work on data summarization based on submodular maximization (Wei et al., 2013; 2014; Tschiatschek et al., 2014; Ni et al., 2015), but these techniques depend on a combination of hand-engineered features and simple models (e.g., hidden Markov models and Gaussian mixture models) pretrained on auxiliary tasks. In comparison, our work demonstrated that we can use the feature representations of smaller, faster-to-train proxy models as an effective way to select core-sets for deep learning tasks.
+
+Recently, Toneva et al. (2019) showed that a large number of “unforgettable” examples that are rarely incorrectly classified once learned (i.e., $30 \%$ on CIFAR10) could be omitted without impacting generalization, which can be viewed as a core-set selection method. They also provide initial evidence that forgetting events are transferable across models and throughout training by using the forgetting events from ResNet18 to select a subset for WideResNet (Zagoruyko & Komodakis, 2016) and by computing the Spearman’s correlation of forgetting events during training compared to their final values. In our work, we evaluated a similar idea of using proxy models to approximate various properties of a large model, and showed that proxy models closely match the rankings of large models in the entropy, greedy $\mathbf { k }$ -centers, and example forgetting metrics.
+
+# 5 CONCLUSION
+
+In this work, we introduced selection via proxy (SVP) to improve the computational efficiency of active learning and core-set selection in deep learning by substituting a cheaper proxy model’s representation for an expensive model’s during data selection. Applied to least confidence uncertainty sampling and Sener & Savarese (2018)’s greedy k-centers approach, SVP achieved up to a $4 1 . 9 \times$ and $3 . 8 \times$ improvement in runtime respectively with no significant increase in error (often within $0 . 1 \%$ ). For core-set selection, we found that SVP can remove up to $50 \%$ of the data from CIFAR10 in $1 0 \times$ less time than it takes to train the target model, achieving a $1 . 6 \times$ speed-up in end-to-end training.
+
+# ACKNOWLEDGMENTS
+
+This research was supported in part by affiliate members and other supporters of the Stanford DAWN project—Ant Financial, Facebook, Google, Infosys, NEC, and VMware—as well as Toyota Research Institute, Northrop Grumman, Amazon Web Services, Cisco, and the NSF under CAREER grant CNS-1651570. Jure Leskovec is a Chan Zuckerberg Biohub investigator. We also gratefully acknowledge the support of DARPA under Nos. FA865018C7880 (ASED), N660011924033 (MCS); ARO under Nos. W911NF-16-1-0342 (MURI), W911NF-16-1-0171 (DURIP); NSF under Nos. OAC1835598 (CINES), OAC-1934578 (HDR), DGE-1656518 (GRFP), DGE-114747 (GRFP); SNSF under Nos. P2EZP2_172187; Stanford Data Science Initiative, Wu Tsai Neurosciences Institute, Chan Zuckerberg Biohub, JD.com, Amazon, Boeing, Docomo, Huawei, Hitachi, Observe, Siemens, UST Global. The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright notation thereon. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views, policies, or endorsements, either expressed or implied, of SNSF, NSF, DARPA, NIH, ARO, or the U.S. Government.
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+
+# A APPENDIX
+
+# A.1 CHOICE OF DATASETS
+
+For our experimental evaluation in Section 3, we focused on classification because it is a widely studied task in active learning (Lewis & Gale, 1994; Lewis & Catlett, 1994; Settles, 2012; Sener & Savarese, 2018; Kirsch et al., 2019; Mussmann & Liang, 2018; Gal et al., 2017; Houlsby et al., 2011). While there are a few bespoke solutions for machine translation (Peris & Casacuberta, 2018) and named entity recognition (Shen et al., 2017), we wanted to compare against the broader body of active learning research. Many popular active learning methods like uncertainty sampling (e.g., entropy, least confidence, and max-margin) assume a single categorical probability distribution for each example, which makes it hard to adapt to other domains. Instead of tackling open challenges for active learning like machine translation, we applied SVP to many classification datasets; however, the simplicity of SVP means that the core ideas of this paper can be applied more broadly in future work.
+
+Specifically, we performed experiments on three image classification datasets: CIFAR10, CIFAR100 (Krizhevsky & Hinton, 2009), and ImageNet (Russakovsky et al., 2015); and two text classification datasets: Amazon Review Polarity and Full (Zhang & LeCun, 2015; Zhang et al., 2015). While multiple tasks on roughly the same data distribution may seem redundant, the data efficiency of active learning depends on error (Mussmann & Liang, 2018). We included both CIFAR10 (low-error) and CIFAR100 (high-error) to demonstrate that our approach performs as well as standard active learning at different points on the error and data efficiency curve. The same rationale is also valid for Amazon Review Polarity (low-error) and Full (high-error). However, the Amazon Review dataset adds a medium (text) and a much larger scale (3.6M and 3M examples, respectively). Adding ImageNet further allows us to investigate scale in the number of examples, but also the number of classes and the dimension of the input. To the best of our knowledge, we are the first active learning paper to present results on the full ImageNet classification task.
+
+# A.2 IMPLEMENTATION DETAILS
+
+CIFAR10 and CIFAR100. We used ResNet164 with pre-activation from He et al. (2016b) as our large target model for both CIFAR10 and CIFAR100. Note that as originally proposed in He et al. (2016a), the smaller, proxy models are also ResNet architectures with pre-activation, but they use pairs of $3 \times 3$ convolutional layers as their residual unit rather than bottlenecks and achieve lower accuracy as shown in Figure 4. As with He et al. (2016b), the ResNets we used were much narrower when applied to CIFAR rather than ImageNet (256 filters rather than 2048 in the final layer of the last bottleneck) and have fewer sections, which means far fewer weights despite the increased depth. For example, ResNet50 on ImageNet has $\sim 2 5 \mathbf { M }$ weights while ResNet164 on CIFAR has $\mathord { \sim } 1 . 7 \mathbf { M }$ (see Table 2). More recent networks such as Wide Residual Networks (Zagoruyko & Komodakis, 2016), ResNeXt (Xie et al., 2017), and DenseNets (Huang et al., 2017) use models with more than 25M parameters on CIFAR10, making ResNet164 relatively small in comparison. Core-set selection experiments used a single Nvidia P100 GPU, while the active learning experiments used a Titan V GPU. We followed the same training procedure, initialization, and hyperparameters as He et al. (2016b) with the exception of weight decay, which was set to 0.0005 and decreased the model’s validation error in all conditions.
+
+ImageNet. we used the original ResNet architecture from He et al. (2016a) implemented in PyTorch 3 (Paszke et al., 2017) with ResNet50 as the target and ResNet18 as the proxy. For training, we used a custom machine with 4 Nvidia Titan V GPUs and followed Nvidia’s optimized implementation 4 with a larger batch size, appropriately scaled learning rate (Goyal et al., 2017), a 5-epoch warm-up period, and mixed precision training (Micikevicius et al., 2017) with the apex 5 library. For active learning, we used the same batch size of 768 images for both ResNet18 and ResNet50 for simplicity, which was the maximum batch size that could fit into memory for ResNet50. However, ResNet18 with a batch size of 768 underutilized the GPU and yielded a lower speed-up. With separate batch sizes for ResNet18 and ResNet50, we would have seen speed-ups closer to $2 . 7 \times$ .
+
+Table 2: Number of parameters in each model.   
+
+<table><tr><td>Dataset</td><td>Model</td><td colspan="2">Number of Parameters (millions)</td></tr><tr><td rowspan="6">CIFAR10</td><td>ResNet164</td><td></td><td>1.7</td></tr><tr><td>ResNet110</td><td></td><td>1.73</td></tr><tr><td>ResNet56</td><td></td><td>0.86</td></tr><tr><td>ResNet20</td><td></td><td>0.27</td></tr><tr><td>ResNet14</td><td></td><td>0.18</td></tr><tr><td>ResNet8</td><td></td><td>0.08</td></tr><tr><td rowspan="6">CIFAR100</td><td>ResNet164</td><td></td><td>1.73</td></tr><tr><td>ResNet110</td><td></td><td>1.74</td></tr><tr><td>ResNet56</td><td></td><td>0.86</td></tr><tr><td>ResNet20</td><td></td><td>0.28</td></tr><tr><td>ResNet14</td><td></td><td>0.18</td></tr><tr><td>ResNet8</td><td></td><td>0.08</td></tr><tr><td rowspan="2">ImageNet</td><td>ResNet50</td><td></td><td>25.56 11.69</td></tr><tr><td>ResNet18</td><td></td><td></td></tr><tr><td rowspan="2">Amazon Review Polarity</td><td>VDCNN29</td><td></td><td>16.64</td></tr><tr><td>VDCNN9</td><td></td><td>14.17</td></tr><tr><td rowspan="2">AmazonReviewFull</td><td>VDCNN29</td><td></td><td>16.64</td></tr><tr><td>VDCNN9</td><td></td><td>14.18</td></tr></table>
+
+Amazon Review Polarity (2-classes) and Full (5-classes). For Amazon Review Polarity and Amazon Review Full, we used VDCNN (Conneau et al., 2017) and fastText (Joulin et al., 2016) with VDCNN29 as the target and fastText and VDCNN9 as proxies. For Amazon Review Polarity, core-set selection experiments used a single Nvidia P100 GPU, while the active learning experiments used a Nvidia Titan V GPU to train VDCNN models. For Amazon Review Full, core-set selection and active learning experiments both used a Nvidia Titan V GPU. In all settings, we used the same training procedure from Conneau et al. (2017) for VDCNN9 and VDCNN29. For fastText, we used Facebook’s implementation 6 and followed the same training procedure from Joulin et al. (2016).
+
+# A.3 MOTIVATION FOR CREATING PROXIES
+
+(a) Top-1 test error and training time on CIFAR10 for ResNet with pre-activation and a varying number of layers. There is a diminishing return in accuracy by increasing the number of layers.
+
+![](images/3acbaf560ec46f3f87160eb3d7438049069a4886e072ff9816174357c3a21310.jpg)  
+(b) Top-1 test error during training of ResNet20 with pre-activation. In the first 14 minutes, ResNet20 reaches $9 . 0 \%$ top-1 error, while the remaining $1 2 \mathrm { m i n }$ - utes are spent on decreasing error to $7 . 6 \%$
+
+![](images/8b7d2cdf692dc9a0476aa1a93c28940d8f4ad9cca3eb1f3355648005dc9e1475.jpg)
+
+Figure 4: Top-1 test error on CIFAR10 for varying model sizes (left) and over the course of training a single model (right), demonstrating a large amount of time is spent on small changes in accuracy.
+
+(a) Top-1 test error and training time on CIFAR100 for ResNet with pre-activation and a varying number of layers. There are diminishing returns in accuracy from increasing the number of layers.
+
+![](images/315e58532f8a07d413f1dc5a9d0ff5c21d6ec5e0aca5d8401ab7d7ace2f3d6a3.jpg)  
+(b) Top-1 test error during training of ResNet20 with pre-activation. In the first 15 minutes, ResNet20 reaches $3 3 . 9 \%$ top-1 error, while the remaining 12 minutes are spent on decreasing error to $3 1 . 1 \%$
+
+![](images/1c301851468f5d4bdc70480ed16bff416cb7242b5705a6efa5d1899e2c07d5c5.jpg)
+
+Figure 5: Top-1 test error on CIFAR100 for varying model sizes (left) and over the course of training a single model (right), demonstrating a large amount of time is spent on small changes in accuracy.
+
+![](images/f5f2e7977dcdf73da31b9ffe9da46484851bc70bb27e292913d649d864ae0bca.jpg)  
+Figure 6: Quality of proxies compared to target models. Average ( $\pm 1$ std.) top-1 error from 3 runs of active learning with varying proxies, selection methods, and budgets on five classification datasets. Dotted lines show the top-1 error of the proxy models, while solid lines show the top-1 error of the target models. CIFAR10 and CIFAR100 experiments used varying depths of pre-activation ResNet (R) models as proxies and ResNet164 (R164) as the target model (e.g., R20-R164 is ResNet20 selecting for ResNet164). ImageNet used ResNet18 (R18) as the proxy and ResNet50 (R50) as the target. Amazon Review Polarity and Amazon Review Full used VDCNN9 (V9) and fastText (FT) as proxies and VDCNN29 (V29) as the target. Across datasets, proxies, methods, and budgets, smaller proxies had higher top-1 error than the target model, but selecting points that were nearly as good as the points selected by the target that did not harm the final target model’s predictive performance.
+
+<table><tr><td rowspan="10">50 dn-peede eenesee eeg %04 %00 320 00 350 13：511 %04 770318 （%) TP neJ-do %00 11014 0 1703675 100 2003331</td><td rowspan="10">1 130335 730553 91051 130干11 80-505 1105181</td><td rowspan="10">区 8 X0L 8 3 X0I ×6 X0I X6 3 区 ×8 9039 700339</td><td rowspan="10">8 3 XL X0I 6 5 3 X0% x0&#x27;s</td><td rowspan="10"></td><td>x0I 区 6 X32 1 ×91 X0℃ 8</td><td>x0I ×91 区 xI</td><td>X0I 8 区 8</td><td>332 区 ×8 X64 X0I ×81</td></tr><tr><td>1 区 2 3 X0I 28</td><td>X0I 1 2 1 区 1 X33 6 1 X0I 1 X0 ×9&#x27;9 区 8 X1 5</td><td>X0I X4 X0I</td><td>8 8222</td><td>3323 X0I ×8I X97</td></tr><tr><td>5 区 8 2 ×94 2 8 区 2 3 X8℃</td><td>X0I ×9 2 ×8s 修 2 3 X5S 1 区 国 2 ×04 区 3 3 5</td><td>区 1 1 区 1</td><td>X0I ×8 ×907 区 0 ×9&#x27;01</td><td>X0I ×6 XLLI X0I 2 8</td></tr><tr><td>85099 1052 5099 91075 61119</td><td>810干1&#x27;9 9700166 2707.97 22:022:22 325.55 45.17.914 2222222 2201</td><td>851581 213.25 9503377 25.05.95</td><td>100-25 20 2035</td><td>1230 01006.20 30039.20 33032.20</td></tr><tr><td>61069 61072 90&#x27;0干1&#x27;9 17099 0105&#x27;9 11093&#x27;9</td><td>27:03:22 850310 810667 201.61 0108.67 3303503 95033:30 2708:30 800167</td><td>200665 3333731 2303385 2523585</td><td>1006V 200 401 10030</td><td>70.532.23 5513580 3303583 60589 9005.89</td></tr><tr><td>2752 77054 910干1&#x27;8 1058 130388</td><td>200310 55003.90 3303333 8303350 3303223 33.333.3 2107.50 522710</td><td>55333.73 3333770 31000.10 3515511</td><td>20079 7000 10090 10090</td><td>60000.60 010988 600189</td></tr><tr><td>1</td><td></td><td>2702355</td><td>200午99 1008 1006V 247777</td><td>533533 3.038.70</td></tr><tr><td>9009:00 1710355 10101 [11115 910干9I1 910干911 1114</td><td>1203555 290774 2502375 2400 112425 2202575 22227 2409</td><td>3303721 2703370 670599</td><td></td><td>03330 77:03160 37038.33</td></tr><tr><td>[111.11 111785 87118 2000555 1503565 650861</td><td>709.66 18&#x27;0F2:09 601719 807:09 97:051.35 22:14477 0013555 8/09.69</td><td>80&#x27;[干6&#x27;09 20:07:07 440585 11:035.85 33333.55</td><td>600399 80089</td><td>33.081 18&#x27;0干6&#x27;9 6101V 906</td><td>20 22277</td></tr><tr><td rowspan="2">(u/9) tpng Pepeo nogeeget Pereed Jatetee</td><td>raegrtaegsr Brreetseee EreeTr PrNr Pse555 PrNESR</td><td>Braegtaaeee PrnNr Pse55 HrS2ES0 Psse55 eouepguoe</td><td>rregrtsaeea PrNr HHS2220 Peee5e EHNESR eetetcr</td><td>Braseg sseer Hesr couepguog</td><td>CGTag S4ess GNNICA xssttet coeepeuee</td><td>(GTg G61isg 6NNDCA xssttet eoeeeeee</td></tr><tr><td>coeepeeee aopurm Ttees CIRIIIO</td><td>sreeetrr FAP1TrHOrrorom Cpeeig</td><td>Cpeegg seer</td><td>aopuam Jaeet 1ee8e</td><td>iopuer teet 1Azeae Brreer Poirrlr</td><td>Fapuer Tees AAzaav Rrreer </td></tr></table>
+
+. 1std)top-1erroranddataselectionspeed-upsfrom3runsofactivelear
+
+<table><tr><td rowspan=2 colspan=1>50Ppeeet eeeeereteieg%04%00%07100</td><td></td><td rowspan=2 colspan=1>11</td><td rowspan=2 colspan=1>X0I839€X0I839℃X0I8×9℃X0I839℃区8342</td><td rowspan=2 colspan=1>X7L×39271222XX93327X8915051464区×89141</td><td rowspan=2 colspan=1>区5X25区52区×41区X40区区1</td><td rowspan=2 colspan=1>X2区2区2区88区1</td><td rowspan=2 colspan=1>×97×84×88x84×48区8×I82452G￥9</td><td rowspan=1 colspan=1>区×7012X0S19&#x27;51</td><td rowspan=1 colspan=1>11</td><td rowspan=1 colspan=1>X0I839%区83</td><td rowspan=1 colspan=1>X15X527X225</td><td rowspan=1 colspan=1>X0I6×9X0I55</td><td rowspan=2 colspan=1>X9I2X0&#x27;S45×8I25X6I2X0S区X35</td><td rowspan=2 colspan=1>区5×76区区8区48￥948</td><td rowspan=1 colspan=1>×1&#x27;9×60125x001×091</td><td rowspan=1 colspan=1>1</td><td rowspan=1 colspan=1>×0I1X018</td><td rowspan=1 colspan=1>区X1区×6</td></tr><tr><td></td><td rowspan=1 colspan=1>X8481231424×III51</td><td rowspan=1 colspan=1>11</td><td rowspan=1 colspan=1>区83区83区83</td><td rowspan=1 colspan=1>×99×0248X401X6&#x27;818X.1</td><td rowspan=1 colspan=1>X0I53区42区11</td><td rowspan=1 colspan=1>X8s54422×9&#x27;11区×498</td><td rowspan=1 colspan=1>111</td><td rowspan=1 colspan=1>×0I8区×8X0I1</td><td rowspan=1 colspan=1>区2区2区1</td></tr><tr><td rowspan=8 colspan=1>5%04（%) TP nrr J o%002000</td><td></td><td rowspan=7 colspan=1>110552710元788101111103.05</td><td rowspan=7 colspan=1>900393107555055170019910干0&#x27;92372910800829105811050511077011115135</td><td rowspan=8 colspan=1>42119106933.353.76117933.03.760&#x27;0干8&#x27;92225211111610干9810101241110100111553511158511158518&#x27;08&#x27;8]</td><td rowspan=8 colspan=1>100元99010干1&#x27;9110-&#x27;17:057301&#x27;0干8&#x27;9070086107&#x27;877018670干6&#x27;61113315800午6111333358000505[1&#x27;06.6171.13.55</td><td rowspan=7 colspan=1>1109920089710干6.9200干5990&#x27;0干6&#x27;9710干0&#x27;8610干1&#x27;8V10干9&#x27;818:0F2.611151111115151110755</td><td rowspan=8 colspan=1>120292107&#x27;91000.201079610干02610干I&#x27;8810干887072397&#x27;0干9&#x27;6[1190097011411010481016188026110.055.55</td><td rowspan=7 colspan=1>9005391109910干126107220527053373032880°0干1&#x27;6110511700.77111770171573</td><td rowspan=5 colspan=1>272256037033703335730</td><td rowspan=8 colspan=1>37.36.75706.94225228106.672708.670007.31330333303083032.：32.532222775205161719657171</td><td rowspan=2 colspan=1>45.19.7122:00.2270.22108.709006780.005.3</td><td rowspan=1 colspan=1>20252520252.22.55</td><td rowspan=1 colspan=1>22237.2723021.17815.6</td><td rowspan=1 colspan=1>20727900822733535</td><td rowspan=1 colspan=1>27021822:07.858500700</td><td rowspan=1 colspan=1>27133.5</td><td rowspan=1 colspan=1>75253.75450777</td><td rowspan=1 colspan=1>205908009&#x27;9%</td></tr><tr><td></td><td rowspan=1 colspan=1>300353035033302222222</td><td rowspan=2 colspan=1>33333.3330.033.30252445</td><td rowspan=2 colspan=1>330333020007.3037.0元.7.51</td><td rowspan=1 colspan=1>25011033335333500350</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>23033853507787</td><td rowspan=1 colspan=1>231785</td></tr><tr><td></td><td rowspan=6 colspan=1>9006733333332713350323520111527227773733535203577711617041T119</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>2</td></tr><tr><td></td><td rowspan=2 colspan=1>20552606003.053.33</td><td rowspan=2 colspan=1>2215030333.0037.335.79</td><td rowspan=2 colspan=1>5733353333335033.33533</td><td rowspan=2 colspan=1>39335337535507.337.17</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>31101303733330</td><td rowspan=1 colspan=1>710T511</td></tr><tr><td></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>3110130</td><td rowspan=1 colspan=1></td></tr><tr><td></td><td rowspan=3 colspan=1>2031771000057</td><td rowspan=1 colspan=1>207220200431000</td><td rowspan=3 colspan=1>222272417.138.1137333.3009&#x27;0干1&#x27;09593775</td><td rowspan=3 colspan=1>201248303535212451202.0920&#x27;1干6&#x27;09271干109</td><td rowspan=3 colspan=1>21287023007551711575690干0:0910&#x27;1干6&#x27;19990949</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>70377033333.33</td><td rowspan=1 colspan=1>3515579</td></tr><tr><td></td><td rowspan=2 colspan=1>06:09:09991092000507</td><td rowspan=2 colspan=1>1098</td><td rowspan=2 colspan=1>13:23735170T18</td><td rowspan=2 colspan=1>130518533.333.55</td></tr><tr><td></td><td rowspan=1 colspan=1>2022540</td><td rowspan=1 colspan=1>1001811715851113535</td><td rowspan=1 colspan=1>190061V109611700.07</td><td rowspan=1 colspan=1>110033530.00511271975</td></tr><tr><td rowspan=1 colspan=1>(u/9)1png</td><td rowspan=1 colspan=4>ppporg  区1050810501BregteegPepeo nrneeaet    PS2EERcoeepeueePhreeaaapaerJeeesPatetetCIRIIII</td><td rowspan=1 colspan=1>81050rsaegrtraeesrCpeegeeeetrr</td><td rowspan=1 colspan=1>81050FINr</td><td rowspan=1 colspan=2>1050区1050P5s58    PPS220</td><td rowspan=1 colspan=5>8105081050区105081050Bregteeg           rsaegteeeeRSS0ES0    PrNTYcoeepgueeEITPTTrTTooooom         CpeegeeerrrTaeer</td><td rowspan=1 colspan=2>区1050810050Pse8    PSNEER</td><td rowspan=1 colspan=3>0450451Brreg reesr  JrooeepeeeeaapaersaeetNe</td></tr></table>
+
+. 1std)top-1erroranddataselectionspeed-upsfro
+
+A.5 ADDITIONAL CORE-SET SELECTION RESULTS
+
+![](images/5bca31bbd02679d6f14e18fd2d064d6f3903113bbb9991e2df61c29d47876987.jpg)  
+Figure 7: SVP performance on core-set selection. Average $\pm 1$ std.) top-1 error of ResNet164 over 5 runs of core-set selection with different selection methods, proxies, and subset sizes on CIFAR100. We found subsets using forgetting events (left), entropy (middle), and greedy $\mathbf { k }$ -centers (right) from a proxy model trained over the entire dataset. Across datasets and selection methods, SVP performed as well as an oracle baseline but significantly faster (speed-ups in parentheses).
+
+Table 5: Average top-1 error $\pm \nobreakspace 1 \nobreakspace$ std.) from 3 runs of core-set selection with varying selection methods on ImageNet, Amazon Review Polarity, and Amazon Review Full.   
+
+<table><tr><td rowspan="2"></td><td rowspan="2"></td><td colspan="4">Top-1Error(%)</td></tr><tr><td>Subset Size</td><td>40% 60%</td><td>80%</td><td>100%</td></tr><tr><td>Dataset</td><td>Method</td><td>Selection Model</td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="5">ImageNet</td><td>Random</td><td>-</td><td>32.2± 0.12</td><td>28.0±0.15</td><td>25.8±0.06</td><td>23.3± 0.11</td></tr><tr><td>Entropy</td><td>ResNet50 (Baseline)</td><td>34.9±0.08</td><td>28.8±0.03</td><td>25.9 ±0.04</td><td>-</td></tr><tr><td>Entropy</td><td>ResNet18</td><td>32.2 ± 0.04</td><td>27.0± 0.01</td><td>25.1 ± 0.07</td><td>-</td></tr><tr><td>Forgetting Events</td><td>ResNet50 (Baseline)</td><td>31.9± 0.07</td><td>26.7±0.06</td><td>24.8±0.03</td><td>=</td></tr><tr><td>Forgetting Events</td><td>ResNet18</td><td>31.6 ± 0.07</td><td>27.1 ± 0.10</td><td>25.3±0.18</td><td>-</td></tr><tr><td rowspan="4">Amazon Review Polarity</td><td>Random</td><td></td><td>4.9±0.02</td><td>4.5± 0.05</td><td>4.3± 0.01</td><td>4.1 ± 0.04</td></tr><tr><td>Entropy</td><td>VDCNN29 (Baseline)</td><td>4.4± 0.03</td><td>4.2 ±0.02</td><td>4.2±0.02</td><td>-</td></tr><tr><td>Entropy</td><td>VDCNN9</td><td>4.4± 0.02</td><td>4.2 ± 0.01</td><td>4.2 ± 0.00</td><td>-</td></tr><tr><td>Entropy</td><td>fastText</td><td>4.4± 0.02</td><td>4.2± 0.02</td><td>4.2 ±0.02</td><td>-</td></tr><tr><td rowspan="4">AmazonReviewFull</td><td>Random</td><td>-</td><td>38.4±0.03</td><td>37.6± 0.03</td><td>37.0± 0.05</td><td>36.6±0.06</td></tr><tr><td>Entropy</td><td>VDCNN29 (Baseline)</td><td>42.7 ± 1.14</td><td>39.3± 0.14</td><td>37.6± 0.10</td><td>-</td></tr><tr><td>Entropy</td><td>VDCNN9</td><td>41.1 ± 0.24</td><td>38.8±0.03</td><td>37.7±0.09</td><td>=</td></tr><tr><td>Entropy</td><td>fastText</td><td>39.0±0.18</td><td>37.8±0.06</td><td>37.1 ±0.06</td><td></td></tr></table>
+
+<table><tr><td>R Tihrir nrirntrgeetn %0s</td><td>12 19干36 323337 953739 113185 116955 8181 83050 15</td><td>797 333733</td><td>∠061 2957 169F09V 9861 333335</td><td>933333 2580 [&#x27;9 61 2872 22335 12088 28335 29353 98 83335 22394 2208</td></tr><tr><td>%00 %0L</td><td>222272 60 </td><td>9184 273833 733555 97101 21965</td><td>1780 181139 11：315 11185 720 8 2703638 11104 287</td><td>985 6981 29867 113555 23257 723275 2I干90I 6</td></tr><tr><td>aarrernrernrrrnrnaeateiet %0s</td><td>2094 20 89 167 936988 8 829 21817</td><td>099 27817 0599 21817 </td><td>099 70996 79 13333 09 28713770 8 6[干99 113333</td><td>3977 20 61干79 271 2922 2097 61干79 11： 39177 2097 9779 172271 22274 2097 81干79</td></tr><tr><td>%00</td><td>2853990 6399 87</td><td>35339 187 </td><td>35335 2293890 80 [干59 233777 297 0 9</td><td>1121 2721 2924 90 179 1250</td></tr><tr><td>10</td><td>60059 35077 700339 1510.7</td><td>10059 600.9 61099 60039</td><td>210717 2044 22055 20 2122250 2323777 2322511 8203335</td><td>2203535 2323555 22 2745 23335.74</td></tr><tr><td>（h） DeTY JT .G-TG %0S</td><td>370555 11051 170午57 13071</td><td>33211 6079 17059 3725</td><td>60&#x27;0干9&#x27;9 6700766 2722735 8709.67 25257:35 50127 45511</td><td>20:00-25 2707.757 7103100 24026 1509.65 2303533</td></tr><tr><td>%00</td><td>6706.8 £3.0556 60&#x27;0干6&#x27;8 6102:2</td><td>8109.7 270干22 910干9&#x27;6 81&#x27;0干6&#x27;8</td><td>67&#x27;0干6.6 27080 3333573 680800 2221 93338.90 37.：37.28</td><td>3713533 39.335.31 35095.35 40194 12.2.955 4224725</td></tr><tr><td>ss sset</td><td>ree5aeeese Braeragsr sepenninoes</td><td>reetaeeee</td><td>reeteeer reetaeee</td><td>raerrtatesr HreTr</td></tr><tr><td></td><td>HSsS2ESD Lee55 Ferrilieg Prreea CIRIIII Jareter</td><td>ESsS2ESD Peee5 ErSN0 aerg Bunearr donug</td><td>HrN220 Pe55 Pner HS5s55 aerg Bunerg TTeTriierLrrirom</td><td>Pee5 EreLTr EPSS2LSD P5555 ES2LSY Pdonu</td></tr></table>
+
+<table><tr><td rowspan=1 colspan=1>%0Linnir nrlrnanrlrtn%0s%0</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>957881131851840I干6911758335041：39319412335297101917607988&#x27;0干08</td><td rowspan=1 colspan=1>333353120065£19116[干691∠&#x27;0干99132333111997：2375517335917686&#x27;0干18</td><td rowspan=1 colspan=2>王5881&#x27;9 干6180159132339933669901155223253985511123：3235318411553111干851130029867102555∠0干76918II干I8226721干90I9&#x27;0干1610干9850干08</td></tr><tr><td rowspan=1 colspan=1>gaarrir erlrnrrrerneeaeteiet%OL%0S%00</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>23：7150干2870023160干</td><td rowspan=1 colspan=1>9187001870021800</td><td rowspan=1 colspan=2>397790干80V222400干839770090干8029220029177000干82222490000</td></tr><tr><td rowspan=1 colspan=1>%OL（%) DeTr Jo r G-t%0S%0</td><td></td><td rowspan=1 colspan=1>15101120191111.791T7515133127113177426096409610∠281&#x27;0 干9&#x27;910干81072210干82</td><td rowspan=1 colspan=1>7517796003950713:055551311771573222210979093533.035.791&#x27;0干96810干6&#x27;8105861101：12</td><td rowspan=1 colspan=2>773707232252205522.953335.7127259522071222022.203.00220120272224272223725.8555155212506599.0373522000.0030137.3333333332237:2235333.10353333385333.8035095.334/71.1427035352333352373335</td></tr><tr><td rowspan=1 colspan=1>szis sssshe</td><td rowspan=1 colspan=1>ppooesssernineeetPrriedaatese</td><td rowspan=1 colspan=1>18188105025BrreegtaeerEs22SEEITITI3</td><td rowspan=1 colspan=1>881105025FPegtaeeePr220Fdonug</td><td rowspan=1 colspan=1>81881005025BraeetaeerHrSNE5Rrgernrree</td><td rowspan=1 colspan=1>区81105025hsasegtaeegEse5Rdonug</td></tr></table>
+
+A.6 ADDITIONAL CORRELATION RESULTS
+
+![](images/4913bb8962175fe0c05bf59ec64b03dc1f4973bfcc5ad6c1f7bb3e1fee923c59.jpg)  
+Figure 8: Comparing selection across model architectures on ImageNet. Spearman’s correlation between max entropy rankings from PyTorch (Paszke et al., 2017) pretrained models on ImageNet. Correlations are high across a wide range of model architectures (Xie et al., 2017; He et al., 2016a; Sandler et al., 2018; Huang et al., 2017; Szegedy et al., 2015; Simonyan & Zisserman, 2014; Iandola et al., 2016; Krizhevsky et al., 2012). For example, MobileNet V2’s entropy-based rankings were highly correlated to ResNet50, even though the model had far fewer parameters (3.5M vs. 25.6M). In concert with our fastText and VDCNN results from Section 3.2, the high correlations between different model architectures suggest that SVP might be widely applicable.
+
+![](images/8ebfd91596117c390532fa258ff604630bf72a6c36741c6d59e61955b8b9f786.jpg)  
+Figure 9: Comparing selection across model sizes and methods on CIFAR100. Average Spearman’s correlation between different runs of ResNet (R) models and a varying depths. We computed rankings based on forgetting events (left), entropy (middle), and greedy $\mathbf { k }$ -centers (right). We saw a similarly high correlation across model architectures (off-diagonal) as between runs of the same architecture (on-diagonal), suggesting that small models are good proxies for data selection.
+
+![](images/173edc63bfe701570c058f678fa25430e14ff9cd87060ba20aef9a32024be975.jpg)  
+Figure 10: Spearman’s rank-order correlation between different runs of ResNet (R) with pre-activation and a varying number of layers on CIFAR10 (left) and CIFAR100 (right). For each combination, we compute the average from 20 pairs of runs. For each run, we compute rankings based on the order examples are added in facility location using the same initial subset of 1,000 randomly selected examples. The results are consistent with Figure 3c and Figure 9c, demonstrating that most of the variation is due to stochasticity in training rather than the initial subset.
+
+![](images/f1a632959169aba60e389816cc6a4b99b464cd5fcabd37fd672f7abbff6562f7.jpg)  
+Figure 11: Average ( $\pm 1$ std.) Spearman’s rank-order correlation with ResNet164 during 5 training runs of varying ResNet architectures on CIFAR10 (left) and CIFAR100 (right), where rankings were based on forgetting events.
+
+![](images/a8eeb085fe80812913a2815f676e7f520e5d5c7dd526169e447c3ec424fb628e.jpg)  
+Figure 12: Average ( $\pm 1$ std.) Spearman’s rank-order correlation with ResNet164 during 5 training runs of varying ResNet architectures on CIFAR10 (left) and CIFAR100 (right), where rankings were based on entropy.
+
+![](images/17b58d06b1b9a06faffd136bdf6bb9df925ce7e3e38ecd46a3ba390ea6ae0586.jpg)  
+Figure 13: Average ( $\pm 1$ std.) Spearman’s rank-order correlation between epochs during 5 training runs of varying ResNet architectures on CIFAR10 (left) and CIFAR100 (right), where rankings were based on forgetting events.
+
+![](images/132f67ab277aed9b5761873a2bc40f7486ba93c2fb1139d4bfa053c786577b6c.jpg)  
+Figure 14: Average ( $\pm 1$ std.) Spearman’s rank-order correlation between epochs during 5 training runs of varying ResNet architectures on CIFAR10 (left) and CIFAR100 (right), where rankings were based on entropy.
+
+![](images/7711d439e9b790460097cf03c072c47dad645b677428d43caecee95376340fc3.jpg)  
+Figure 15: Pearson correlation coefficient between different runs of ResNet (R) with pre-activation and a varying number of layers on CIFAR10 (top) and CIFAR100 (bottom). For each combination, we compute the average from 20 pairs of runs. For each run, we compute rankings based on the number of forgetting events (left), and entropy of the final model (right). Generally, we see a similarly high correlation across model architectures (off-diagonal) as between runs of the same architecture (on-diagonal), providing further evidence that small models are good proxies for data selection.
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+![](images/18d9cbd79fa9a9e1786c42a0757521a06fc8b6b1783dabbd7f6e54ae2b6bd016.jpg)  
+Figure 16: 2D t-SNE plots from the final hidden layer of a fully trained ResNet164 model on CIFAR10 and a $30 \%$ subset selected (black). The top row uses another run of ResNet164 to select the subset and the bottom row uses ResNet20. Rankings are computed using forgetting events (left), entropy (middle), and greedy k-centers (right).
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+![](images/ede7a5f78d4a88f314e7e1d700f01a1d4cb31394bdc50fb2e937cb986e8875d1.jpg)  
+Figure 17: 2D t-SNE plots from the final hidden layer of a fully trained ResNet164 model on CIFAR10 and a $30 \%$ subset selected (black) with ResNet20 trained after a varying number of epochs. Rankings are calculated with forgetting events (top) and entropy (bottom). Notably, the ranking from forgetting events is much more stable because the model’s uncertainty is effectively averaged throughout training rather than a single snapshot at the end like entropy. For t-SNE plots of the entire training run, please see http://bit.ly/svp-cifar10-tsne-entropy and http: //bit.ly/svp-cifar10-tsne-forget for entropy and forgetting events respectively.