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+# IMAGENET-TRAINED CNNS ARE BIASED TOWARDS TEXTURE; INCREASING SHAPE BIAS IMPROVES ACCURACY AND ROBUSTNESS
+
+Robert Geirhos University of Tubingen & IMPRS-IS¨ robert.geirhos@bethgelab.org
+
+Patricia Rubisch University of Tubingen & U. of Edinburgh ¨ p.rubisch@sms.ed.ac.uk
+
+Claudio Michaelis University of Tubingen & IMPRS-IS¨ claudio.michaelis@bethgelab.org
+
+Matthias Bethge∗   
+University of Tubingen ¨   
+matthias.bethge@bethgelab.org
+
+# Felix A. Wichmann∗
+
+# Wieland Brendel∗
+
+University of Tubingen ¨ felix.wichmann@uni-tuebingen.de
+
+University of Tubingen ¨ wieland.brendel@bethgelab.org
+
+# ABSTRACT
+
+Convolutional Neural Networks (CNNs) are commonly thought to recognise objects by learning increasingly complex representations of object shapes. Some recent studies suggest a more important role of image textures. We here put these conflicting hypotheses to a quantitative test by evaluating CNNs and human observers on images with a texture-shape cue conflict. We show that ImageNettrained CNNs are strongly biased towards recognising textures rather than shapes, which is in stark contrast to human behavioural evidence and reveals fundamentally different classification strategies. We then demonstrate that the same standard architecture (ResNet-50) that learns a texture-based representation on ImageNet is able to learn a shape-based representation instead when trained on ‘StylizedImageNet’, a stylized version of ImageNet. This provides a much better fit for human behavioural performance in our well-controlled psychophysical lab setting (nine experiments totalling 48,560 psychophysical trials across 97 observers) and comes with a number of unexpected emergent benefits such as improved object detection performance and previously unseen robustness towards a wide range of image distortions, highlighting advantages of a shape-based representation.
+
+![](images/274db1c31568c3f0dede84860fbaaa0ada5982fae2f455bd5ff43c538ba99f38.jpg)  
+Figure 1: Classification of a standard ResNet-50 of (a) a texture image (elephant skin: only texture cues); (b) a normal image of a cat (with both shape and texture cues), and (c) an image with a texture-shape cue conflict, generated by style transfer between the first two images.
+
+# 1 INTRODUCTION
+
+How are Convolutional Neural Networks (CNNs) able to reach impressive performance on complex perceptual tasks such as object recognition (Krizhevsky et al., 2012) and semantic segmentation (Long et al., 2015)? One widely accepted intuition is that CNNs combine low-level features (e.g. edges) to increasingly complex shapes (such as wheels, car windows) until the object (e.g. car) can be readily classified. As Kriegeskorte (2015) puts it, “the network acquires complex knowledge about the kinds of shapes associated with each category. [...] High-level units appear to learn representations of shapes occurring in natural images” (p. 429). This notion also appears in other explanations, such as in LeCun et al. (2015): Intermediate CNN layers recognise “parts of familiar objects, and subsequent layers [...] detect objects as combinations of these parts” (p. 436). We term this explanation the shape hypothesis.
+
+This hypothesis is supported by a number of empirical findings. Visualisation techniques like Deconvolutional Networks (Zeiler & Fergus, 2014) often highlight object parts in high-level CNN features.1 Moreover, CNNs have been proposed as computational models of human shape perception by Kubilius et al. (2016), who conducted an impressive number of experiments comparing human and CNN shape representations and concluded that CNNs “implicitly learn representations of shape that reflect human shape perception” (p. 15). Ritter et al. (2017) discovered that CNNs develop a so-called “shape bias” just like children, i.e. that object shape is more important than colour for object classification (although see Hosseini et al. (2018) for contrary evidence). Furthermore, CNNs are currently the most predictive models for human ventral stream object recognition (e.g. Cadieu et al., 2014; Yamins et al., 2014); and it is well-known that object shape is the single most important cue for human object recognition (Landau et al., 1988), much more than other cues like size or texture (which may explain the ease at which humans recognise line drawings or millennia-old cave paintings).
+
+On the other hand, some rather disconnected findings point to an important role of object textures for CNN object recognition. CNNs can still classify texturised images perfectly well, even if the global shape structure is completely destroyed (Gatys et al., 2017; Brendel & Bethge, 2019). Conversely, standard CNNs are bad at recognising object sketches where object shapes are preserved yet all texture cues are missing (Ballester & de Araujo, 2016). Additionally, two studies suggest that ´ local information such as textures may actually be sufficient to “solve” ImageNet object recognition: Gatys et al. (2015) discovered that a linear classifier on top of a CNN’s texture representation (Gram matrix) achieves hardly any classification performance loss compared to original network performance. More recently, Brendel & Bethge (2019) demonstrated that CNNs with explicitly constrained receptive field sizes throughout all layers are able to reach surprisingly high accuracies on ImageNet, even though this effectively limits a model to recognising small local patches rather than integrating object parts for shape recognition. Taken together, it seems that local textures indeed provide sufficient information about object classes—ImageNet object recognition could, in principle, be achieved through texture recognition alone. In the light of these findings, we believe that it is time to consider a second explanation, which we term the texture hypothesis: in contrast to the common assumption, object textures are more important than global object shapes for CNN object recognition.
+
+Resolving these two contradictory hypotheses is important both for the deep learning community (to increase our understanding of neural network decisions) as well as for the human vision and neuroscience communities (where CNNs are being used as computational models of human object recognition and shape perception). In this work we aim to shed light on this debate with a number of carefully designed yet relatively straightforward experiments. Utilising style transfer (Gatys et al., 2016), we created images with a texture-shape cue conflict such as the cat shape with elephant texture depicted in Figure 1c. This enables us to quantify texture and shape biases in both humans and CNNs. To this end, we perform nine comprehensive and careful psychophysical experiments comparing humans against CNNs on exactly the same images, totalling 48,560 psychophysical trials across 97 observers. These experiments provide behavioural evidence in favour of the texture hypothesis: A cat with an elephant texture is an elephant to CNNs, and still a cat to humans. Beyond quantifying existing biases, we subsequently present results for our two other main contributions:
+
+![](images/6254a4609e9ab8f3ddf67a7773284041fdb48ec5e33b70152dc980e792a8141f.jpg)  
+Figure 2: Accuracies and example stimuli for five different experiments without cue conflict.
+
+changing biases, and discovering emergent benefits of changed biases. We show that the texture bias in standard CNNs can be overcome and changed towards a shape bias if trained on a suitable data set. Remarkably, networks with a higher shape bias are inherently more robust to many different image distortions (for some even reaching or surpassing human performance, despite never being trained on any of them) and reach higher performance on classification and object recognition tasks.
+
+# 2 METHODS
+
+In this section we outline the core elements of paradigm and procedure. Extensive details to facilitate replication are provided in the Appendix. Data, code and materials are available from this repository: https://github.com/rgeirhos/texture-vs-shape
+
+# 2.1 PSYCHOPHYSICAL EXPERIMENTS
+
+All psychophysical experiments were conducted in a well-controlled psychophysical lab setting and follow the paradigm of Geirhos et al. (2018), which allows for direct comparisons between human and CNN classification performance on exactly the same images. Briefly, in each trial participants were presented a fixation square for $3 0 0 ~ \mathrm { { m s } }$ , followed by a $3 0 0 ~ \mathrm { { m s } }$ presentation of the stimulus image. After the stimulus image we presented a full-contrast pink noise mask ( $1 / f$ spectral shape) for $2 0 0 ~ \mathrm { { m s } }$ to minimise feedback processing in the human visual system and to thereby make the comparison to feedforward CNNs as fair as possible. Subsequently, participants had to choose one of 16 entry-level categories by clicking on a response screen shown for $1 5 0 0 ~ \mathrm { { m s } }$ . On this screen, icons of all 16 categories were arranged in a $4 \times 4$ grid. Those categories were airplane, bear, bicycle, bird, boat, bottle, car, cat, chair, clock, dog, elephant, keyboard, knife, oven and truck. Those are the so-called “16-class-ImageNet” categories introduced in Geirhos et al. (2018).
+
+The same images were fed to four CNNs pre-trained on standard ImageNet, namely AlexNet (Krizhevsky et al., 2012), GoogLeNet (Szegedy et al., 2015), VGG-16 (Simonyan & Zisserman, 2015) and ResNet-50 (He et al., 2015). The 1,000 ImageNet class predictions were mapped to the 16 categories using the WordNet hierarchy (Miller, 1995)—e.g. ImageNet category tabby cat would be mapped to cat. In total, the results presented in this study are based on 48,560 psychophysical trials and 97 participants.
+
+# 2.2 DATA SETS (PSYCHOPHYSICS)
+
+In order to assess texture and shape biases, we conducted six major experiments along with three control experiments, which are described in the Appendix. The first five experiments (samples visualised in Figure 2) are simple object recognition tasks with the only difference being the image features available to the participant:
+
+Original 160 natural colour images of objects (10 per category) with white background.
+
+![](images/3a4704aa819bff765d1d49babe0991053d3ff3456cef2cefdffe1e6cd07823bb.jpg)  
+Figure 3: Visualisation of Stylized-ImageNet (SIN), created by applying AdaIN style transfer to ImageNet images. Left: randomly selected ImageNet image of class ring-tailed lemur. Right: ten examples of images with content/shape of left image and style/texture from different paintings. After applying AdaIN style transfer, local texture cues are no longer highly predictive of the target class, while the global shape tends to be retained. Note that within SIN, every source image is stylized only once.
+
+Greyscale Images from Original data set converted to greyscale using skimage.color.rgb2gray. For CNNs, greyscale images were stacked along the colour channel.
+
+Silhouette Images from Original data set converted to silhouette images showing an entirely black object on a white background (see Appendix A.6 for procedure).
+
+Edges Images from Original data set converted to an edge-based representation using Canny edge extractor implemented in MATLAB.
+
+Texture 48 natural colour images of textures (3 per category). Typically the textures consist of full-width patches of an animal (e.g. skin or fur) or, in particular for man-made objects, of images with many repetitions of the same objects (e.g. many bottles next to each other, see Figure 7 in the Appendix).
+
+It is important to note that we only selected object and texture images that were correctly classified by all four networks. This was made to ensure that our results in the sixth experiment on cue conflicts, which is most decisive in terms of the shape vs texture hypothesis, are fully interpretable. In the cue conflict experiment we present images with contradictory features (see Figure 1) but still ask the participant to assign a single class. Note that the instructions to human observers were entirely neutral w.r.t. shape or texture (“click on the object category that you see in the presented image; guess if unsure. There is no right or wrong answer, we are interested in your subjective impression”).
+
+Cue conflict Images generated using iterative style transfer (Gatys et al., 2016) between an image of the Texture data set (as style) and an image from the Original data set (as content). We generated a total of 1280 cue conflict images (80 per category), which allows for presentation to human observers within a single experimental session.
+
+We define “silhouette” as the bounding contour of an object in 2D (i.e., the outline of object segmentation). When mentioning “object shape”, we use a definition that is broader than just the silhouette of an object: we refer to the set of contours that describe the 3D form of an object, i.e. including those contours that are not part of the silhouette. Following Gatys et al. (2017), we define “texture” as an image (region) with spatially stationary statistics. Note that on a very local level, textures (according to this definition) can have non-stationary elements (such as a local shape): e.g. a single bottle clearly has non-stationary statistics, but many bottles next to each other are perceived as a texture: “things” become “stuff” (Gatys et al., 2017, p. 178). For an example of a “bottle texture” see Figure 7.
+
+# 2.3 STYLIZED-IMAGENET
+
+Starting from ImageNet we constructed a new data set (termed Stylized-ImageNet or SIN) by stripping every single image of its original texture and replacing it with the style of a randomly selected painting through AdaIN style transfer (Huang & Belongie, 2017) (see examples in Figure 3) with a stylization coefficient of $\alpha = 1 . 0$ . We used Kaggle’s Painter by Numbers data set2 as a style source due to its large style variety and size (79,434 paintings). We used AdaIN fast style transfer rather than iterative stylization (e.g. Gatys et al., 2016) for two reasons: Firstly, to ensure that training on SIN and testing on cue conflict stimuli is done using different stylization techniques, such that the results do not rely on a single stylization method. Secondly, to enable stylizing entire ImageNet, which would take prohibitively long with an iterative approach. We provide code to create Stylized-ImageNet here:
+
+https://github.com/rgeirhos/Stylized-ImageNet
+
+# 3 RESULTS
+
+# 3.1 TEXTURE VS SHAPE BIAS IN HUMANS AND IMAGENET-TRAINED CNNS
+
+Almost all object and texture images (Original and Texture data set) were recognised correctly by both CNNs and humans (Figure 2). Greyscale versions of the objects, which still contain both shape and texture, were recognised equally well. When object outlines were filled in with black colour to generate a silhouette, CNN recognition accuracies were much lower than human accuracies. This was even more pronounced for edge stimuli, indicating that human observers cope much better with images that have little to no texture information. One confound in these experiments is that CNNs tend not to cope well with domain shifts, i.e. the large change in image statistics from natural images (on which the networks have been trained) to sketches (which the networks have never seen before).
+
+We thus devised a cue conflict experiment that is based on images with a natural statistic but contradicting texture and shape evidence (see Methods). Participants and CNNs have to classify the images based on the features (shape or texture) that they most rely on. The results of this experiment are visualised in Figure 4. Human observers show a striking bias towards responding with the shape category $( 9 5 . 9 \%$ of correct decisions).3 This pattern is reversed for CNNs, which show a clear bias towards responding with the texture category (VGG-16: $1 7 . 2 \%$ shape vs. $8 2 . 8 \%$ texture; GoogLeNet: $3 1 . 2 \%$ vs. $6 8 . 8 \%$ ; AlexNet: $4 2 . 9 \%$ vs. $5 7 . 1 \%$ ; ResNet-50: $2 2 . 1 \%$ vs. $7 7 . 9 \%$ ).
+
+# 3.2 OVERCOMING THE TEXTURE BIAS OF CNNS
+
+The psychophysical experiments suggest that ImageNet-trained CNNs, but not humans, exhibit a strong texture bias. One reason might be the training task itself: from Brendel & Bethge (2019) we know that ImageNet can be solved to high accuracy using only local information. In other words, it might simply suffice to integrate evidence from many local texture features rather than going through the process of integrating and classifying global shapes. In order to test this hypothesis we train a ResNet-50 on our Stylized-ImageNet (SIN) data set in which we replaced the object-related local texture information with the uninformative style of randomly selected artistic paintings.
+
+A standard ResNet-50 trained and evaluated on Stylized-ImageNet (SIN) achieves $7 9 . 0 \%$ top-5 accuracy (see Table 1). In comparison, the same architecture trained and evaluated on ImageNet (IN) achieves $9 2 . 9 \%$ top-5 accuracy. This performance difference indicates that SIN is a much harder task than IN since textures are no longer predictive, but instead a nuisance factor (as desired). Intriguingly, ImageNet features generalise poorly to SIN (only $1 6 . 4 \%$ top-5 accuracy); yet features learned on SIN generalise very well to ImageNet $8 2 . 6 \%$ top-5 accuracy without any fine-tuning).
+
+In order to test wheter local texture features are still sufficient to “solve” SIN we evaluate the performance of so-called BagNets. Introduced recently by Brendel & Bethge (2019), BagNets have a ResNet-50 architecture but their maximum receptive field size is limited to $9 \times 9$ , $1 7 \times 1 7$ or $3 3 \times 3 3$
+
+Figure 4: Classification results for human observers (red circles) and ImageNet-trained networks AlexNet (purple diamonds), VGG16 (blue triangles), GoogLeNet (turquoise circles) and ResNet-50 (grey squares). Shape vs. texture biases for stimuli with cue conflict (sorted by human shape bias). Within the responses that corresponded to either the correct texture or correct shape category, the fractions of texture and shape decisions are depicted in the main plot (averages visualised by vertical lines). On the right side, small barplots display the proportion of correct decisions (either texture or shape correctly recognised) as a fraction of all trials. Similar results for ResNet-152, DenseNet-121 and Squeezenet1 1 are reported in the Appendix, Figure 13.
+
+![](images/bb6f35cf3a4cbc1a9c53ba9010ca564e44a8186cac95ef8f692785ca74974bf0.jpg)
+
+pixels. This precludes BagNets from learning or using any long-range spatial relationships for classification. While these restricted networks can reach high accuracies on ImageNet, they are unable to achieve the same on SIN, showing dramatically reduced performance with smaller receptive field sizes (such as $1 0 . 0 \%$ top-5 accuracy on SIN compared to $7 0 . 0 \%$ on ImageNet for a BagNet with receptive field size of $9 \times 9$ pixels). This is a clear indication that the SIN data set we propose does actually remove local texture cues, forcing a network to integrate long-range spatial information.
+
+Most importantly, the SIN-trained ResNet-50 shows a much stronger shape bias in our cue conflict experiment (Figure 5), which increases from $22 \%$ for a IN-trained model to $81 \%$ . In many categories the shape bias is almost as strong as for humans.
+
+# 3.3 ROBUSTNESS AND ACCURACY OF SHAPE-BASED REPRESENTATIONS
+
+Does the increased shape bias, and thus the shifted representations, also affect the performance or robustness of CNNs? In addition to the IN- and SIN-trained ResNet-50 architecture we here additionally analyse two joint training schemes:
+
+• Training jointly on SIN and IN. • Training jointly on SIN and IN with fine-tuning on IN. We refer to this model as Shape-ResNet.   
+
+<table><tr><td>architecture</td><td>IN→IN</td><td>IN→SIN</td><td>SIN→SIN</td><td>SIN→IN</td></tr><tr><td>ResNet-50</td><td>92.9</td><td>16.4</td><td>79.0</td><td>82.6</td></tr><tr><td>BagNet-33 (mod.ResNet-50)</td><td>86.4</td><td>4.2</td><td>48.9</td><td>53.0</td></tr><tr><td>BagNet-17 (mod.ResNet-50)</td><td>80.3</td><td>2.5</td><td>29.3</td><td>32.6</td></tr><tr><td>BagNet-9 (mod. ResNet-50)</td><td>70.0</td><td>1.4</td><td>10.0</td><td>10.9</td></tr></table>
+
+Table 1: Stylized-ImageNet cannot be solved with texture features alone. Accuracy comparison (in percent; top-5 on validation data set) of a standard ResNet-50 with Bag of Feature networks (BagNets) with restricted receptive field sizes of $3 3 \times 3 3$ , $1 7 \times 1 7$ and $9 \times 9$ pixels. Arrows indicate: train data test data, e.g. $\mathrm { I N } {  } \mathrm { S I N }$ means training on ImageNet and testing on Stylized-ImageNet.
+
+![](images/e82cbe88bcdab73f5866af2d8478832c0844a5f451be64f969b7a18115eb4e18.jpg)  
+Figure 5: Shape vs. texture biases for stimuli with a texture-shape cue conflict after training ResNet50 on Stylized-ImageNet (orange squares) and on ImageNet (grey squares). Plotting conventions and human data (red circles) for comparison are identical to Figure 4. Similar results for other networks are reported in the Appendix, Figure 11.   
+Fraction of 'texture' decisions
+
+Table 2: Accuracy comparison on the ImageNet (IN) validation data set as well as object detection performance (mAP50) on PASCAL VOC 2007 and MS COCO. All models have an identical ResNet-50 architecture. Method details reported in the Appendix, where we also report similar results for ResNet-152 (Table 4).   
+
+<table><tr><td>name</td><td>training</td><td>fine-tuning</td><td>top-1 IN accuracy (%)</td><td>top-5 IN accuracy (%)</td><td>Pascal VOC mAP50 (%)</td><td>MS COCO mAP50 (%)</td></tr><tr><td rowspan="3">vanilla ResNet</td><td>IN</td><td>=</td><td>76.13</td><td>92.86</td><td>70.7</td><td>52.3</td></tr><tr><td>SIN</td><td>=</td><td>60.18</td><td>82.62</td><td>70.6</td><td>51.9</td></tr><tr><td>SIN+IN</td><td>1</td><td>74.59</td><td>92.14</td><td>74.0</td><td>53.8</td></tr><tr><td>Shape-ResNet</td><td>SIN+IN</td><td>IN</td><td>76.72</td><td>93.28</td><td>75.1</td><td>55.2</td></tr></table>
+
+We then compared these models with a vanilla ResNet-50 on three experiments: (1) classification performance on IN, (2) transfer to Pascal VOC 2007 and (3) robustness against image perturbations.
+
+Classification performance Shape-ResNet surpasses the vanilla ResNet in terms of top-1 and top5 ImageNet validation accuracy as reported in Table 2. This indicates that SIN may be a useful data augmentation on ImageNet that can improve model performance without any architectural changes.
+
+Transfer learning We tested the representations of each model as backbone features for Faster RCNN (Ren et al., 2017) on Pascal VOC 2007 and MS COCO. Incorporating SIN in the training data substantially improves object detection performance from 70.7 to $7 5 . 1 \mathrm { m A P 5 0 }$ (52.3 to 55.2 mAP50 on MS COCO) as shown in Table 2. This is in line with the intuition that for object detection, a shape-based representation is more beneficial than a texture-based representation, since the ground truth rectangles encompassing an object are by design aligned with global object shape.
+
+Robustness against distortions We systematically tested how model accuracies degrade if images are distorted by uniform or phase noise, contrast changes, high- and low-pass filtering or eidolon perturbations.4 The results of this comparison, including human data for reference, are visualised in Figure 6. While lacking a few percent accuracy on undistorted images, the SIN-trained network outperforms the IN-trained CNN on almost all image manipulations. (Low-pass filtering / blurring is the only distortion type on which SIN-trained networks are more susceptible, which might be due to the over-representation of high frequency signals in SIN through paintings and the reliance on sharp edges.) The SIN-trained ResNet-50 approaches human-level distortion robustness—despite never seeing any of the distortions during training.
+
+![](images/6598670bd3c67af075d961671bb2678957f23bd422acd3ddcd50ba41b899c61c.jpg)  
+Figure 6: Classification accuracy on parametrically distorted images. ResNet-50 trained on StylizedImageNet (SIN) is more robust towards distortions than the same network trained on ImageNet (IN).
+
+Furthermore, we provide robustness results for our models tested on ImageNet-C, a comprehensive benchmark of 15 different image corruptions (Hendrycks & Dietterich, 2019), in Table 5 of the Appendix. Training jointly on SIN and IN leads to strong improvements for 13 corruption types (Gaussian, Shot and Impulse noise; Defocus, Glas and Motion blur; Snow, Frost and Fog weather types; Contrast, Elastic, Pixelate and JPEG digital corruptions). This substantially reduces overall corruption error from 76.7 for a vanilla ResNet-50 to 69.3. Again, none of these corruption types were explicitly part of the training data, reinforcing that incorporating SIN in the training regime improves model robustness in a very general way.
+
+# 4 DISCUSSION
+
+As noted in the Introduction, there seems to be a large discrepancy between the common assumption that CNNs use increasingly complex shape features to recognise objects and recent empirical findings which suggest a crucial role of object textures instead. In order to explicitly probe this question, we utilised style transfer (Gatys et al., 2016) to generate images with conflicting shape and texture information. On the basis of extensive experiments on both CNNs and human observers in a controlled psychophysical lab setting, we provide evidence that unlike humans, ImageNet-trained CNNs tend to classify objects according to local textures instead of global object shapes. In combination with previous work which showed that changing other major object dimensions such as colour (Geirhos et al., 2018) and object size relative to the context (Eckstein et al., 2017) do not have a strong detrimental impact on CNN recognition performance, this highlights the special role that local cues such as textures seem to play in CNN object recognition.
+
+Intriguingly, this offers an explanation for a number of rather disconnected findings: CNNs match texture appearance for humans (Wallis et al., 2017), and their predictive power for neural responses along the human ventral stream appears to be largely due to human-like texture representations, but not human-like contour representations (Laskar et al., 2018; Long & Konkle, 2018). Furthermore, texture-based generative modelling approaches such as style transfer (Gatys et al., 2016), single image super-resolution (Gondal et al., 2018) as well as static and dynamic texture synthesis (Gatys et al., 2015; Funke et al., 2017) all produce excellent results using standard CNNs, while CNNbased shape transfer seems to be very difficult (Gokaslan et al., 2018). CNNs can still recognise images with scrambled shapes (Gatys et al., 2017; Brendel & Bethge, 2019), but they have much more difficulties recognising objects with missing texture information (Ballester & de Araujo, 2016; ´ Yu et al., 2017). Our hypothesis might also explain why an image segmentation model trained on a database of synthetic texture images transfers to natural images and videos (Ustyuzhaninov et al.,
+
+2018). Beyond that, our results show marked behavioural differences between ImageNet-trained CNNs and human observers. While both human and machine vision systems achieve similarly high accuracies on standard images (Geirhos et al., 2018), our findings suggest that the underlying classification strategies might actually be very different. This is problematic, since CNNs are being used as computational models for human object recognition (e.g. Cadieu et al., 2014; Yamins et al., 2014).
+
+In order to reduce the texture bias of CNNs we introduced Stylized-ImageNet (SIN), a data set that removes local cues through style transfer and thereby forces networks to go beyond texture recognition. Using this data set, we demonstrated that a ResNet-50 architecture can indeed learn to recognise objects based on object shape, revealing that the texture bias in current CNNs is not by design but induced by ImageNet training data. This indicates that standard ImageNet-trained models may be taking a “shortcut” by focusing on local textures, which could be seen as a version of Occam’s razor: If textures are sufficient, why should a CNN learn much else? While texture classification may be easier than shape recognition, we found that shape-based features trained on SIN generalise well to natural images.
+
+Our results indicate that a more shape-based representation can be beneficial for recognition tasks that rely on pre-trained ImageNet CNNs. Furthermore, while ImageNet-trained CNNs generalise poorly towards a wide range of image distortions (e.g. Dodge & Karam, 2017; Geirhos et al., 2017; 2018), our ResNet-50 trained on Stylized-ImageNet often reaches or even surpasses human-level robustness (without ever being trained on the specific image degradations). This is exciting because Geirhos et al. (2018) showed that networks trained on specific distortions in general do not acquire robustness against other unseen image manipulations. This emergent behaviour highlights the usefulness of a shape-based representation: While local textures are easily distorted by all sorts of noise (including those in the real world, such as rain and snow), the object shape remains relatively stable. Furthermore, this finding offers a compellingly simple explanation for the incredible robustness of humans when coping with distortions: a shape-based representation.
+
+# 5 CONCLUSION
+
+In summary, we provided evidence that machine recognition today overly relies on object textures rather than global object shapes as commonly assumed. We demonstrated the advantages of a shapebased representation for robust inference (using our Stylized-ImageNet data set5 to induce such a representation in neural networks). We envision our findings as well as our openly available model weights, code and behavioural data set (49K trials across 97 observers)6 to achieve three goals: Firstly, an improved understanding of CNN representations and biases. Secondly, a step towards more plausible models of human visual object recognition. Thirdly, a useful starting point for future undertakings where domain knowledge suggests that a shape-based representation may be more beneficial than a texture-based one.
+
+# ACKNOWLEDGMENTS
+
+This work has been funded, in part, by the German Research Foundation (DFG; Sachbeihilfe Wi 2103/4-1 and SFB 1233 on “Robust Vision”). The authors thank the International Max Planck Research School for Intelligent Systems (IMPRS-IS) for supporting R.G. and C.M.; M.B. acknowledges support by the Centre for Integrative Neuroscience Tubingen (EXC 307) and by the Intelli- ¨ gence Advanced Research Projects Activity (IARPA) via Department of Interior/Interior Business Center (DoI/IBC) contract number D16PC00003.
+
+We would like to thank Dan Hendrycks for providing the results of Table 5 (corruption robustness of our models on ImageNet-C). Furthermore, we would like to express our gratitude towards Alexander Ecker, Leon Gatys, Tina Gauger, Silke Gramer, Heike Konig, Jonas Rauber, Steffen Schneider, ¨ Heiko Schutt, Tom Wallis and Uli Wannek for support and/or useful discussions. ¨
+
+# REFERENCES
+
+Pedro Ballester and Ricardo Matsumura de Araujo. On the performance of GoogLeNet and AlexNet ´ applied to sketches. In AAAI, pp. 1124–1128, 2016.
+
+Wieland Brendel and Matthias Bethge. Approximating CNNs with bag-of-local-features models works surprisingly well on ImageNet. In International Conference on Learning Representations, 2019.
+
+Charles F Cadieu, H Hong, D L K Yamins, N Pinto, D Ardila, E A Solomon, N J Majaj, and J J DiCarlo. Deep neural networks rival the representation of primate IT cortex for core visual object recognition. PLoS Computational Biology, 10(12), 2014.
+
+Samuel Dodge and Lina Karam. A study and comparison of human and deep learning recognition performance under visual distortions. arXiv preprint arXiv:1705.02498, 2017.
+
+Miguel P Eckstein, Kathryn Koehler, Lauren E Welbourne, and Emre Akbas. Humans, but not deep neural networks, often miss giant targets in scenes. Current Biology, 27(18):2827–2832, 2017.
+
+Christina M Funke, Leon A Gatys, Alexander S Ecker, and Matthias Bethge. Synthesising dynamic textures using convolutional neural networks. arXiv preprint arXiv:1702.07006, 2017.
+
+Leon A Gatys, Alexander S Ecker, and Matthias Bethge. Texture synthesis using convolutional neural networks. In Advances in Neural Information Processing Systems, pp. 262–270, 2015.
+
+Leon A Gatys, Alexander S Ecker, and Matthias Bethge. Image style transfer using convolutional neural networks. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 2414–2423, 2016.
+
+Leon A Gatys, Alexander S Ecker, and Matthias Bethge. Texture and art with deep neural networks. Current Opinion in Neurobiology, 46:178–186, 2017.
+
+Robert Geirhos, David HJ Janssen, Heiko H Schutt, Jonas Rauber, Matthias Bethge, and Felix A ¨ Wichmann. Comparing deep neural networks against humans: object recognition when the signal gets weaker. arXiv preprint arXiv:1706.06969, 2017.
+
+Robert Geirhos, Carlos M. Medina Temme, Jonas Rauber, Heiko H Schutt, Matthias Bethge, ¨ and Felix A Wichmann. Generalisation in humans and deep neural networks. arXiv preprint arXiv:1808.08750, 2018.
+
+Aaron Gokaslan, Vivek Ramanujan, Daniel Ritchie, Kwang In Kim, and James Tompkin. Improving shape deformation in unsupervised image-to-image translation. arXiv preprint arXiv:1808.04325, 2018.
+
+Muhammad W Gondal, Bernhard Scholkopf, and Michael Hirsch. The unreasonable effectiveness ¨ of texture transfer for single image super-resolution. arXiv preprint arXiv:1808.00043, 2018.
+
+Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recognition. arXiv preprint arXiv:1512.03385, 2015.
+
+Dan Hendrycks and Thomas Dietterich. Benchmarking neural network robustness to common corruptions and perturbations. In International Conference on Learning Representations, 2019.
+
+Hossein Hosseini, Baicen Xiao, Mayoore Jaiswal, and Radha Poovendran. Assessing shape bias property of Convolutional Neural Networks. arXiv preprint arXiv:1803.07739, 2018.
+
+Xun Huang and Serge J Belongie. Arbitrary style transfer in real-time with adaptive instance normalization. In ICCV, pp. 1510–1519, 2017.
+
+Yangqing Jia, Evan Shelhamer, Jeff Donahue, Sergey Karayev, Jonathan Long, Ross Girshick, Sergio Guadarrama, and Trevor Darrell. Caffe: Convolutional architecture for fast feature embedding. In Proceedings of the 22nd ACM International Conference on Multimedia, pp. 675–678. ACM, 2014.
+
+Ivan Krasin, Tom Duerig, Neil Alldrin, Vittorio Ferrari, Sami Abu-El-Haija, Alina Kuznetsova, Hassan Rom, Jasper Uijlings, Stefan Popov, Andreas Veit, Serge Belongie, Victor Gomes, Abhinav Gupta, Chen Sun, Gal Chechik, David Cai, Zheyun Feng, Dhyanesh Narayanan, and Kevin Murphy. OpenImages: A public dataset for large-scale multi-label and multi-class image classification. Dataset available from https://github.com/openimages, 2017.
+
+N. Kriegeskorte. Deep neural networks: A new framework for modeling biological vision and brain information processing. Annual Review of Vision Science, 1(15):417–446, 2015.
+
+A. Krizhevsky, I. Sutskever, and G. E. Hinton. ImageNet classification with deep convolutional neural networks. In Advances in Neural Information Processing Systems, pp. 1097–1105, 2012.
+
+Jonas Kubilius, Stefania Bracci, and Hans P Op de Beeck. Deep neural networks as a computational model for human shape sensitivity. PLoS Computational Biology, 12(4):e1004896, 2016.
+
+Barbara Landau, Linda B Smith, and Susan S Jones. The importance of shape in early lexical learning. Cognitive Development, 3(3):299–321, 1988.
+
+Md Nasir Uddin Laskar, Luis G Sanchez Giraldo, and Odelia Schwartz. Correspondence of deep neural networks and the brain for visual textures. arXiv preprint arXiv:1806.02888, 2018.
+
+Y. LeCun, Y. Bengio, and G. Hinton. Deep learning. Nature, 521(7553):436–444, 2015.
+
+Bria Long and Talia Konkle. The role of textural statistics vs. outer contours in deep CNN and neural responses to objects. http://konklab.fas.harvard.edu/ ConferenceProceedings/Long_2018_CCN.pdf, 2018.
+
+Jonathan Long, Evan Shelhamer, and Trevor Darrell. Fully convolutional networks for semantic segmentation. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 3431–3440, 2015.
+
+George A Miller. WordNet: a lexical database for English. Communications of the ACM, 38(11): 39–41, 1995.
+
+Adam Paszke, Sam Gross, Soumith Chintala, Gregory Chanan, Edward Yang, Zachary DeVito, Zeming Lin, Alban Desmaison, Luca Antiga, and Adam Lerer. Automatic differentiation in PyTorch, 2017.
+
+Shaoqing Ren, Kaiming He, Ross Girshick, and Jian Sun. Faster R-CNN: towards real-time object detection with region proposal networks. IEEE Transactions on Pattern Analysis & Machine Intelligence, pp. 1137–1149, 2017.
+
+Samuel Ritter, David GT Barrett, Adam Santoro, and Matt M Botvinick. Cognitive psychology for deep neural networks: A shape bias case study. arXiv preprint arXiv:1706.08606, 2017.
+
+Karen Simonyan and Andrew Zisserman. Very deep convolutional networks for large-scale image recognition. arXiv preprint arXiv:1409.1556, 2015.
+
+Christian Szegedy, Wei Liu, Yangqing Jia, Pierre Sermanet, Scott Reed, Dragomir Anguelov, Dumitru Erhan, Vincent Vanhoucke, and Andrew Rabinovich. Going deeper with convolutions. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 1–9, 2015.
+
+Ivan Ustyuzhaninov, Claudio Michaelis, Wieland Brendel, and Matthias Bethge. One-shot texture segmentation. arXiv preprint arXiv:1807.02654, 2018.
+
+Thomas SA Wallis, Christina M Funke, Alexander S Ecker, Leon A Gatys, Felix A Wichmann, and Matthias Bethge. A parametric texture model based on deep convolutional features closely matches texture appearance for humans. Journal of Vision, 17(12):5–5, 2017.
+
+Daniel LK Yamins, Ha Hong, Charles F Cadieu, Ethan A Solomon, Darren Seibert, and James J DiCarlo. Performance-optimized hierarchical models predict neural responses in higher visual cortex. Proceedings of the National Academy of Sciences, 111(23):8619–8624, 2014.
+
+Qian Yu, Yongxin Yang, Feng Liu, Yi-Zhe Song, Tao Xiang, and Timothy M Hospedales. Sketcha-net: A deep neural network that beats humans. International Journal of Computer Vision, 122 (3):411–425, 2017.
+
+Matthew D Zeiler and Rob Fergus. Visualizing and understanding convolutional networks. In European Conference on Computer Vision, pp. 818–833. Springer, 2014.
+
+# A APPENDIX
+
+# A.1 REPRODUCIBILITY & ACCESS TO CODE / MODELS / DATA
+
+In this Appendix, we report experimental details for human and CNN experiments. All trained model weights reported in this paper as well as our human behavioural data set (48,560 psychophysical trials across 97 observers) are openly available from this repository:
+
+https://github.com/rgeirhos/texture-vs-shape
+
+# A.2 PROCEDURE
+
+We followed the paradigm of Geirhos et al. (2018) for maximal comparability. A trial consisted of $3 0 0 ~ \mathrm { { m s } }$ presentation of a fixation square and a $2 0 0 ~ \mathrm { { m s } }$ presentation of the stimulus image, which was followed by a full-contrast pink noise mask $1 / f$ spectral shape) of the same size lasting for 200 ms. Participants had to choose one of 16 entry-level categories by clicking on a response screen shown for $1 5 0 0 ~ \mathrm { { m s } }$ . On this screen, icons of all 16 categories were arranged in a $4 \times 4$ grid. The experiments were not self-paced and therefore one trial always lasted $2 2 0 0 ~ \mathrm { { m s } }$ $3 0 0 \mathrm { m s } + 2 0 0 \mathrm { m s } +$ $2 0 0 ~ \mathrm { m s } + 1 5 0 0 ~ \mathrm { m s } = 2 2 0 0 ~ \mathrm { m s }$ . The necessary time to complete an experiment with 1280 stimuli was 47 minutes, for 160 stimuli six minutes, and for 48 stimuli two minutes. In the experiments with 1280 trials, observers were given the possibility of taking a brief break after every block of 256 trials (five blocks in total).
+
+As preparation, participants were shown the response screen prior to an experiment and were asked to name all 16 categories in order to get an overview over the possible stimuli categories and to make sure that all categories were clear from the beginning. They were instructed to click on the category they believed was presented. Responses through clicking on a response screen could be changed within the $1 5 0 0 ~ \mathrm { { m s } }$ response interval, only the last entered response was counted as the answer. Prior to the real experiment a practice session was performed for the participants to get used to the time course of the experiment and the position of category items on the response screen. This screen was shown for an additional $3 0 0 ~ \mathrm { { m s } }$ in order to provide feedback and indicate whether the entered answer was incorrect. In that case, a short low beep sound occurred and the correct category was highlighted by setting its background to white. The practice session consisted of 320 trials. After 160 trials the participants had the chance to take a short break. In the break, their performance of the first block was shown on the screen along the percentage of trials where no answer was entered. After the practice blocks, observers were shown an example image of the manipulation (not used in the experiment) to minimise surprise. Images used in the practice session were natural images from 16-class-ImageNet (Geirhos et al., 2018), hence there was no overlap with images or manipulations used in the experiments.
+
+# A.3 APPARATUS
+
+Observers were shown the $2 2 4 \times 2 2 4$ pixels stimuli in a dark cabin on a $2 2 '$ , $1 2 0 \mathrm { H z }$ VIEWPixx LCD monitor (VPixx Technologies, Saint-Bruno, Canada). The screen of size $4 8 4 \times 3 0 2 \mathrm { m m }$ corresponds to $1 9 2 0 \times 1 2 0 0$ pixels, although stimuli were only presented foveally at the center of the screen $3 \times 3$ degrees of visual angle at a viewing distance of $1 0 7 \ \mathrm { c m }$ ) while the background was set to a grey value of 0.7614 in the $[ 0 , 1 ]$ range, the average greyscale value of all stimuli used in the original experiment. Participants used a chin rest to keep their head position static during an experiment. Stimulus presentation was conducted with the Psychophysics Toolbox (version 3.0.12) in MATLAB (Release 2016a, The MathWorks, Inc., Natick, Massachusetts, United States) using a 12-core desktop computer (AMD HD7970 graphics card “Tahiti” by AMD, Sunnyvale, California, United States) running Kubuntu 14.04 LTS. Participants clicked on a response screen, showing an iconic representation of all of the 16 object categories as reported in Geirhos et al. (2018), with a normal computer mouse.
+
+Table 3: Characteristics of human participants (p.) across experiments. The symbol ‘#’ refers to “number of”; ‘rt’ stands for “median reaction time (ms)” in an experiment.   
+
+<table><tr><td>experiment</td><td>instruction</td><td>#p.</td><td>#</td><td>#</td><td>age range</td><td>mean age</td><td># stimuli</td><td>rt</td></tr><tr><td>original</td><td>neutral</td><td>5</td><td>5</td><td>0</td><td>21-27</td><td>24.2</td><td>160</td><td>772</td></tr><tr><td>greyscale</td><td>neutral</td><td>5</td><td>4</td><td>1</td><td>20-26</td><td>23.4</td><td>160</td><td>811</td></tr><tr><td> texture</td><td>neutral</td><td>5</td><td>2</td><td>3</td><td>23-36</td><td>29.0</td><td>48</td><td>769</td></tr><tr><td>silhouette</td><td>neutral</td><td>10</td><td>9</td><td>1</td><td>21-37</td><td>24.1</td><td>160</td><td>861</td></tr><tr><td>edge</td><td>neutral</td><td>10</td><td>6</td><td>4</td><td>18-30</td><td>23.0</td><td>160</td><td>791</td></tr><tr><td>cue conflict</td><td>neutral</td><td>10</td><td>7</td><td>3</td><td>20-29</td><td>23.0</td><td>1280</td><td>828</td></tr><tr><td>cue conflict control</td><td>texture</td><td>10</td><td>5</td><td>5</td><td>23-32</td><td>26.6</td><td>1280</td><td>942</td></tr><tr><td>cue conflict control</td><td>shape</td><td>10</td><td>9</td><td>1</td><td>18-25</td><td>21.8</td><td>1280</td><td>827</td></tr><tr><td>filled silhouette</td><td>neutral</td><td>32</td><td>22</td><td>10</td><td>18-30</td><td>22.3</td><td>160</td><td>881</td></tr><tr><td>overall</td><td></td><td>97</td><td>69</td><td>28</td><td>18-37</td><td>23.5</td><td>48,560 trials</td><td>857</td></tr></table>
+
+# A.4 PARTICIPANTS
+
+In total, 97 human observers participated in the study. For a detailed overview about how they were distributed across experiments see Table 3. No observer participated in more than one experiment, and all participants reported normal or corrected-to-normal vision. Observers participating in experiments with a cue conflict manipulation were paid $\notin 1 0$ per hour or gained course credit. Observers measured in all other experiments (with a clear ground truth category) were able to earn an additional bonus up to $\notin 5$ or equivalent further course credit based on their performance. This motivation scheme was applied to ensure reliable answer rates, and explained to observers in advance. Participant bonus, in these cases, was calculated as follows: The base level with a bonus of $\notin 0$ was set to $50 \%$ accuracy. For every additional $5 \%$ of accuracy, participants gained $_ { 1 } \notin 0 . 5 0$ bonus. This means that with a performance above $9 5 \%$ , an observer was able to gain the full bonus of $\notin 5$ or equivalent course credit. Overall, we took the following steps to prevent low quality human data: 1., using a controlled lab environment instead of an online crowdsourcing platform; 2. the payment motivation scheme as explained above; 3. displaying observer performance on the screen at regular intervals during the practice session; and 4. splitting longer experiments into five blocks, where participants could take a break in between blocks.
+
+# A.5 CNN MODELS & TRAINING DETAILS
+
+ResNet-50 We used a standard ResNet-50 architecture from PyTorch (Paszke et al., 2017), the torchvision.models.resnet50 implementation. For the comparison against BagNets reported in Table 1, results for IN training correspond to a ResNet-50 pre-trained on ImageNet without any modifications (model weights from torchvision.models). Reported results for SIN training correspond to the same architecture trained on SIN for 60 epochs with Stochastic Gradient Descent (torch.optim.SGD) using a momentum term of 0.9, weight decay (1e-4) and a learning rate of 0.1 which was multiplied by a factor of 0.1 after 20 and 40 epochs of training. We used a batch size of 256. This SIN-trained model is the same model that is reported in Figures 5 and 6 as well as in Table 2. In the latter, this corresponds to the second row (training performed on SIN, no fine-tuning on ImageNet). For the model reported in the third row, training was jointly performed on SIN and on IN. This means that both training data sets were treated as one big data set (exactly twice the size of the IN training data set), on which training was performed for 45 epochs with identical hyperparameters as described above, except that the initial learning rate of 0.1 was multiplied by 0.1 after 15 and 30 epochs. The weights of this model were then used to initialise the model reported in the fourth row of Table 2, which was fine-tuned for 60 epochs on ImageNet (identical hyperparameters except that the initial learning rate of 0.01 was multiplied by 0.1 after 30 epochs). We compared training models from scratch versus starting from an ImageNet-pretrained model. Empirically, using features pre-trained on ImageNet led to better results across experiments, which is why we used ImageNet pre-training throughout experiments and models (for both ResNet-50 and restricted ResNet-50 models).
+
+BagNets Model weights (pre-trained on ImageNet) and architectures for BagNets (results reported in Table 1) were kindly provided by Brendel & Bethge (2019). For SIN training, identical settings as for the SIN-trained ResNet-50 were used to ensure comparability (training for 60 epochs with SGD and identical hyperparameters as reported above).
+
+Faster R-CNN We used the Faster R-CNN implementation from https://github.com/ jwyang/faster-rcnn.pytorch (commit 21f28986) with all hyperparameters kept at default. The only changes we made to the model is replacing the encoder with ResNet-50 (respectively ResNet-152 for the results in Table 4) and applying custom input whitening. For Pascal VOC 2007 we trained the model for 7 epochs with a batch size of 1, a learning rate of 0.001 and a learning rate decay step after epoch 5. Images were resized to have a short edge of 600 pixels. For MS COCO we trained the same model on the 2017 train/val split for training and testing respectively. We trained for 6 epochs with a batch size of 16 on 8 GPUs employing a learning rate of 0.02 and a decay step after 4 epochs. Images were resized to have a short edge of 800 pixels.
+
+Pre-trained AlexNet, GoogLeNet, VGG-16 We used AlexNet (Krizhevsky et al., 2012), GoogLeNet (Szegedy et al., 2015) and VGG-16 (Simonyan & Zisserman, 2015) for the evaluation reported in Figure 4. Evaluation was performed using Caffe (Jia et al., 2014). Network weights (training on ImageNet) were obtained from https://github.com/BVLC/caffe/ wiki/Model-Zoo (AlexNet & GoogLeNet) and http://www.robots.ox.ac.uk/ (VGG16).
+
+ResNet-101 pre-trained on Open Images V2 For our comparison of biases in ImageNet vs. OpenImages (Figure 13 right) the ResNet-101 pretrained on Open Images V2 (Krasin et al., 2017) was used. It was obtained from https://github.com/openimages/dataset/blob/ master/READMEV2.md along with the inference code provided by the authors. In order to map predictions to the 16 classes, we used the parameters to $p _ { - } k = 1 0 0 0 0 0$ and score thresho $\ ' d = 0 . 0$ to obtain as all predictions, and then mapped the responses to our 16 classes using the provided label map. 15 out of our 16 classes are classes in Open Images as well; the remaining class keyboard was mapped to Open Images class computer keyboard (in this case, Open Images makes a finer distinction to separate musical keyboards from computer keyboards).
+
+ResNet-101, ResNet-152, DenseNet-121, SqueezeNet1 1 For the comparison to other models pre-trained on ImageNet (Figure 13 left), we evaluated the pre-trained networks provided by torchvision.models.
+
+Training AlexNet, VGG-16 on SIN For the evaluation of model biases after training on SIN (Figure 11), we obtained the model architectures from torchvision.models and trained the networks under identical circumstances as ResNet-50. This includes identical hyperparameter settings, except for the learning rate. The learning rate for AlexNet was set to 0.001 and for VGG-16 to 0.01 initially; both learning rates were multiplied by 0.1 after 20 and 40 epochs of training (60 epochs in total).
+
+# A.6 IMAGE MANIPULATIONS AND IMAGE DATABASE
+
+In total, we conducted nine different experiments. Here is an overview of the images and / or image manipulations for all of them. All images were saved in the png format and had a size of $2 2 4 \times 2 2 4$ pixels. Original, texture and cue conflict images are visualised in Figure 7.
+
+Original experiment This experiment consisted of 160 coloured images, 10 per category. All of them had a single, unmanipulated object (belonging to one category) in front of a white background. This white background was especially important since these stimuli were being used as content images for style transfer, and we thus made sure that the background was neutral to produce better style transfer results. The images for this experiment as well as for the texture experiment described below were carefully selected using Google advanced image search with the criteria “labelled for noncommercial reuse with modification (free to use, share and modify)” and the search term “<entity $>$ white background” (original) or “<entity $>$ texture” (texture). In some cases where this did not lead to sufficient results, we used images from the ImageNet validation data set which were manually modified to have a white background if necessary. We made sure that both the images from this experiment as well as the texture images were all correctly recognised by all four pre-trained CNNs (if an image was not correctly recognised, we replaced it by another one). This was used to ensure that our results for cue conflict experiments are fully interpretable: if, e.g., a texture image was not correctly recognised by CNNs, there would be no point in using it as a texture (style) source for style transfer.
+
+Greyscale experiment This experiment used the same images as the original experiment with the difference that they were converted to greyscale using skimage.color.rgb2gray. For CNNs, greyscale images were stacked three times along the colour channel.
+
+Silhouette experiment The images from the original experiment were transformed into silhouette images showing an entirely black object on a white background. We used the following transformation procedure: First, images were converted to bmp using command line utility (convert). They were then converted to svg using potrace, and then to png using convert again. Since an entirely automatic binarization pipeline is not feasible (it takes domain knowledge to understand that a car wheel should, but a doughnut should not be filled with black colour), we then manually checked every single image and adapted the silhouette using GIMP if necessary.
+
+Edge experiment The stimuli shown in this condition were generated by applying the “Canny” edge extractor implemented in MATLAB (Release 2016a, The MathWorks, Inc., Natick, Massachusetts, United States) to the images used in the original experiment. No further manipulations were performed on this data set. This line of code was used to detect edges and generate the stimuli used in this experiment:
+
+imwrite(1-edge(imgaussfilt(rgb2gray(imread(filename)), 2), ’Canny’), targetFilename);
+
+Texture experiment Images were selected using the procedure outlined above for the original experiment. Some objects have a fairly stationary texture (e.g. animals), which makes it easy to find texture images for them. For the more difficult case (e.g. man-made objects), we made use of the fact that every object can become a texture if it is used not in isolation, but rather in a clutter of many objects of the same kind (e.g. Gatys et al., 2017). That is, for a bottle texture we used images with many bottles next to each other (as visualised in Figure 7).
+
+Cue conflict experiment This experiment used images with a texture-shape cue conflict. They were generated using iterative style transfer (Gatys et al., 2016) between a texture image (from the texture experiment described above) and a content image (from the original experiment) each. While 48 texture images and 160 content images would allow for a total of $4 8 \times 1 6 0 = 7 6 8 0$ cue conflict images (480 per category), we used a balanced subset of 1280 images instead (80 per category), which allows for presentation to human observers within a single experimental session. The procedure for selecting the style and content images was done as follows. For all possible $1 6 \times 1 6$ combinations of style and texture categories, exactly five cue conflict images were generated by randomly sampling style and content images from their respective categories. Sampling was performed without replacement for as long as possible, and then without replacement for the remaining images. The same stimuli acquired with this method were used for the cue conflict control experiments, where participants saw exactly these images but with different instructions biased towards shape and towards texture (results described later). For our analysis of texture vs. shape biases (Figure 4), we excluded trials for which no cue conflict was present (i.e., those trials where a bicycle content image was fused with a bicycle texture image, hence no texture-shape cue conflict present).
+
+Filled silhouette experiment Style transfer is not the only possibility to generate a texture-shape cue conflict, and we here aimed at testing one other method to generate such stimuli: cropping texture images with a shape mask, such that the silhouette of an object and its texture constitute a cue conflict (visualised in Figure 7). Stimuli were generated by using the silhouette images from the silhouette experiment as a mask for texture images. If the silhouette image at a certain location has a black pixel, the texture was used at this location, and for white pixels the resulting target image pixel was white. In order to have a larger variety of textures than the 48 textures used in the texture experiment, the texture database was augmented by rotating all textures with ten different previously chosen angles uniformly distributed between 0 and 360 degrees, resulting in a texture database of 480 images. Results for this control experiment, not part of the main paper, are reported later. We ensured that no silhouette was seen more than once per observer.
+
+![](images/dbf98203708333e23a83fd1381e1055d5b691cce2a92eead6ffcf8b006ac104f.jpg)  
+Figure 7: Visualisation of stimuli in data sets. Top two rows: content and texture images. Bottom rows: cue conflict stimuli generated from the texture and content images above (silhouettes filled with rotated textures; style transfer stimuli).
+
+![](images/cb3e32fb3d32cab8f283bb80c8481f025513c639d21e02b9bea31c51a219a28a.jpg)  
+Figure 8: Visualisation of image distortions. One exemplary image (class bird, original image in colour at the top left) is manipulated as follows. From left to right: additive uniform noise, low contrast, high-pass filtering, low-pass filtering. In the row below, a greyscale version for comparison; the other manipulations from left to right are: Eidolon manipulations I, II and III as well as phase noise. Figure adapted from Geirhos et al. (2018) with the authors’ permission.
+
+Robustness experiment (distorted images) For this experiment, human accuracies for reference were provided by Geirhos et al. (2018). Human ‘error bars’ indicate the full range of results for human observers. CNNs were then evaluated on different image manipulations applied to natural images as outlined in the paper. For maximal comparability, we also used the same images. For a description of the parametric distortion we kindly refer the reader to Geirhos et al. (2018). In Figure 8, we plot one example image across manipulations.
+
+# A.7 STYLIZED-IMAGENET (SIN)
+
+We used AdaIN style transfer (Huang & Belongie, 2017) to generate Stylized-ImageNet. More specifically, the AdaIN implementation from https://github.com/naoto0804/ pytorch-AdaIN (commit 31e769c159d4c8639019f7db7e035a7f938a6a46) was employed to stylize the entire ImageNet training and validation data sets. Style transfer was performed once per ImageNet image. As a style source, we used images from Kaggle’s Painter by Numbers data set (https://www.kaggle.com/c/painter-by-numbers/, accessed on March 1, 2018). Style selection was performed randomly with replacement. Every ImageNet image was stylized once and only once. Paintings from the Kaggle data set were used if at least $2 2 4 \times 2 2 4$ pixels in size; the largest possible square crop was then downsampled to this size prior to using it as a style image. All accuracies are reported on the respective validation data sets. Code to generate StylizedImageNet from ImageNet (and the Kaggle paintings) is available on github in this repository:
+
+https://github.com/rgeirhos/Stylized-ImageNet
+
+# A.8 RESULTS: CUE CONFLICT CONTROL EXPERIMENTS (DIFFERENT INSTRUCTIONS)
+
+We investigated the effect of different instructions to human observers. The results presented in the main paper for cue conflict stimuli correspond all to a neutral instruction, not biased w.r.t. texture or shape. In two separate experiments, participants were explicitly instructed to ignore the textures and click on the shape category of cue conflict stimuli, and vice versa. The results, presented in
+
+Table 4: Accuracy and object detection performance for ResNet-152. Accuracy comparison on the ImageNet (IN) validation data set as well as object detection performance (mAP50) on PASCAL VOC 2007. All models have an identical ResNet-152 architecture.   
+
+<table><tr><td>training</td><td>fine-tuning</td><td>top-1 IN accuracy (%)</td><td>top-5 IN accuracy (%)</td><td>Pascal VOC mAP50 (%)</td></tr><tr><td>IN (vanilla ResNet-152)</td><td></td><td>78.31</td><td>94.05</td><td>76.9</td></tr><tr><td>SIN</td><td>=</td><td>65.26</td><td>86.31</td><td>75.0</td></tr><tr><td>SIN+IN</td><td>=</td><td>77.62</td><td>93.59</td><td>77.3</td></tr><tr><td>SIN+IN</td><td>IN</td><td>78.87</td><td>94.41</td><td>78.3</td></tr></table>
+
+<table><tr><td></td><td></td><td></td><td colspan="3">Noise</td><td colspan="4">Blur</td></tr><tr><td>training</td><td>ft</td><td>mCE</td><td>Gaussian</td><td>Shot</td><td>Impulse</td><td>Defocus</td><td>Glas</td><td>Motion</td><td>Zoom</td></tr><tr><td>IN (vanilla ResNet-50)</td><td>1</td><td>76.7</td><td>79.8</td><td>81.6</td><td>82.6</td><td>74.7</td><td>88.6</td><td>78.0</td><td>79.9</td></tr><tr><td>SIN</td><td>1</td><td>77.3</td><td>71.2</td><td>73.3</td><td>72.1</td><td>88.8</td><td>85.0</td><td>79.7</td><td>90.9</td></tr><tr><td>SIN+IN</td><td>-</td><td>69.3</td><td>66.2</td><td>66.8</td><td>68.1</td><td>69.6</td><td>81.9</td><td>69.4</td><td>80.5</td></tr><tr><td>SIN+IN</td><td>IN</td><td>73.8</td><td>75.9</td><td>77.0</td><td>77.5</td><td>71.7</td><td>86.0</td><td>74.0</td><td>79.7</td></tr><tr><td></td><td colspan="7">Weather</td><td colspan="2">Digital</td></tr><tr><td>training</td><td>ft</td><td>Snow</td><td>Frost</td><td>Fog</td><td>Brightness</td><td>Contrast</td><td>Elastic</td><td>Pixelate</td><td>JPEG</td></tr><tr><td>IN (vanilla ResNet-50)</td><td>-</td><td>77.8</td><td>74.8</td><td>66.1</td><td>56.6</td><td>71.4</td><td>84.8</td><td>76.9</td><td>76.8</td></tr><tr><td>SIN</td><td>-</td><td>71.8</td><td>74.4</td><td>66.0</td><td>79.0</td><td>63.6</td><td>81.1</td><td>72.9</td><td>89.3</td></tr><tr><td>SIN+IN</td><td>-</td><td>68.0</td><td>70.6</td><td>64.7</td><td>57.8</td><td>66.4</td><td>78.2</td><td>61.9</td><td>69.7</td></tr><tr><td>SIN+IN</td><td>IN</td><td>74.5</td><td>72.3</td><td>66.2</td><td>55.7</td><td>67.6</td><td>80.8</td><td>75.0</td><td>73.2</td></tr></table>
+
+Table 5: Corruption error (lower=better) on ImageNet-C (Hendrycks & Dietterich, 2019), consisting of different types of noise, blur, weather and digital corruptions. Abbreviations: $\mathbf { m } { \mathrm { C E } } = $ mean Corruption Error (average of the 15 individual corruption error values); SIN $=$ Stylized-ImageNet; $\mathbf { W } =$ ImageNet; ft $=$ fine-tuning. Results kindly provided by Dan Hendrycks.
+
+![](images/934d8430609950153e9a0f756aa1038848f3bbe32296bf4467fa817a92c78480.jpg)  
+Figure 9: Accuracies and example stimuli for five different experiments without cue conflict, comparing training on ImageNet (IN) to training on Stylized-ImageNet (SIN).
+
+![](images/358219a6106cb787f12e04f33546683271c75c0954bdb3a8b6dca93dc69a0936.jpg)  
+Figure 10: Classification results for human observers (red circles) and ImageNet-trained networks AlexNet (purple diamonds), VGG-16 (blue triangles), GoogLeNet (turquoise circles) and ResNet50 (grey squares) on stimuli with a texture-shape cue conflict generated with style transfer, and biased rather than neutral instructions to human observers. Plotting conventions and CNN data as in Figure 4.
+
+Figure 10, indicate that for a shape bias instruction, human data are almost exactly the same as for the neutral instruction reported earlier (indicating that human observers are indeed using shapes per default); and if they are instructed to ignore the shapes and click on the texture category, they still show a substantial shape bias (indicating that even if they seek to ignore shapes, they find it extremely difficult to do so).
+
+# A.9 RESULTS: FILLED SILHOUETTE EXPERIMENT
+
+This experiment was conducted as a control experiment to make sure that the strong differences between humans and CNNs when presented with cue conflict images are not merely an artefact of the particular setup that we employed. Stimuli are visualised in Figure 7; results in Figure 12. In a nutshell, we also find a shape bias in humans when stimuli are not generated via style transfer but instead through cropping texture images with a shape mask, such that the silhouette of an object and its texture constitute a cue conflict. CNNs have a less pronounced texture bias in these experiments;
+
+![](images/e910766aa5fc362ada4d24b7fb77b5246b064cdb0e35cf5179afe0e580712988.jpg)  
+Figure 11: Texture vs shape biases on of AlexNet and VGG-16 after training on Stylized-ImageNet. Plotting conventions as in Figures 4 and 5. Plot shows biases for AlexNet (purple diamonds), VGG16 (blue triangles) and human observers (red circles) for comparison. For GoogLeNet, no data is available since network training was performed in PyTorch and torchvision.models unfortunately does not provide a GoogLeNet (inception v1) architecture.
+
+ResNet-50 trained on SIN still responds with the shape category more than ResNet-50 trained on IN. Overall, these results are much more difficult to interpret since the texture-silhouette cue conflict stimuli, visualised in Figure 7, do not have a clear-cut texture-shape distinction like the cue conflict stimuli generated via style transfer. Still, they are largely in accord with the style transfer results presented in the main paper.
+
+# A.10 IMAGE RIGHTS & ATTRIBUTION
+
+The images presented in Figure 7 were collected from different origins. We here indicate their URL, creator and license terms (if applicable). Some of the images presented in Figure 7 also appear in Figures 1, 2 and 9; the terms below apply accordingly. Top row, cat image: $\operatorname { h t t p s : / / p i x a b a y . c o m / p - 9 6 4 3 4 3 / }$ , released under the CC0 creative commons license as indicated on the website. The CC0 creative commons license is accessible from https://creativecommons.org/publicdomain/zero/1.0/legalcode. Car image: https://pixabay. $\mathtt { c o m / p - 1 9 3 0 2 3 7 } /$ , released under the CC0 creative commons license as indicated on the website. Bear image: ImageNet image n02132136 871.JPEG, manually modified to have a white background. Second row, elephant texture: cropped from https://www.flickr.com/photos/flowcomm/5089601226, released under the CC BY 2.0 license by user flowcomm as indicated on the website. The license is accessible from https://creativecommons.org/licenses/by/2.0/legalcode. Clock texture: cropped from https://commons.wikimedia.org/wiki/File: HK_Sheung_Wan_%E4%B8%AD%E6%BA%90%E4%B8%AD%E5%BF%83_Midland_Plaza shop_Japan_Home_City_clocks_displayed_for_sale_April-2011.jpg, released under the Creative Commons Attribution-Share Alike 3.0 Unported, 2.5 Generic, 2.0 Generic and 1.0 Generic licenses by user Ho Mei Danniel as indicated on the website. The CC Attribution-Share Alike 3.0 license is accessible from https://creativecommons. org/licenses/by-sa/3.0/legalcode. Bottle texture: cropped from https: //commons.wikimedia.org/wiki/File:Liquor_bottles.jpg, released under the CC BY 2.0 license by user scottfeldstein as indicated on the website. The CC BY 2.0 license is accessible from https://creativecommons.org/licenses/by/2.0/legalcode.
+
+![](images/634798b0b4e7c758d950f3641996ecd7ffc46e7eeca4baaeef443418704546f4.jpg)  
+Figure 12: Classification results for human observers and CNNs on stimuli with a texture-silhouette cue conflict (filled silhouette experiment). Plotting conventions as in Figures 4 and 5. Left: Human observers (red circles) and ImageNet-trained networks AlexNet (purple diamonds), VGG-16 (blue triangles), GoogLeNet (turquoise circles) and ResNet-50 (grey squares). Right: Human observers (red circles, data identical to the left) and ResNet-50 trained on ImageNet (grey squares) vs. ResNet-50 trained on Stylized-ImageNet (orange squares).
+
+![](images/6a61a6c8d52abd8fda91b7671bbaaf91f7dc7d3fcbb52cef500cc8d241c64882.jpg)  
+Figure 13: The texture bias on cue conflict stimuli is not specific to ImageNet-trained networks (left) and also occurs in very deep, wide and compressed networks (right).
+
+Left: The texture bias is not specific to ImageNet-trained networks. Comparison of texture-shape biases on cue conflict stimuli generated with style transfer for ResNet-101 trained on ImageNet (grey squares) and ResNet-101 trained on the Open Images Dataset V2 (green squares) along with human data for comparison (red circles). Both networks have a qualitatively similar texture bias. We use a ResNet-101 architecture here since Open Images has released a pre-trained ResNet-101.
+
+Right: The texture bias also appears in a very deep network (ResNet-152, grey squares), a very wide one (DenseNet-121, purple trianlges), and a very compact one (SqueezeNet1 1, brown diamonds). Human data for comparison (red circles). All networks are pre-trained on ImageNet.

parse/train/Q32U7dzWXpc/Q32U7dzWXpc.md

@@ -0,0 +1,307 @@
+# A Minimalist Approach to Offline Reinforcement Learning
+
+Scott Fujimoto1,2 Shixiang Shane Gu2 1Mila, McGill University 2Google Research, Brain Team scott.fujimoto@mail.mcgill.ca
+
+# Abstract
+
+Offline reinforcement learning (RL) defines the task of learning from a fixed batch of data. Due to errors in value estimation from out-of-distribution actions, most offline RL algorithms take the approach of constraining or regularizing the policy with the actions contained in the dataset. Built on pre-existing RL algorithms, modifications to make an RL algorithm work offline comes at the cost of additional complexity. Offline RL algorithms introduce new hyperparameters and often leverage secondary components such as generative models, while adjusting the underlying RL algorithm. In this paper we aim to make a deep RL algorithm work while making minimal changes. We find that we can match the performance of state-of-the-art offline RL algorithms by simply adding a behavior cloning term to the policy update of an online RL algorithm and normalizing the data. The resulting algorithm is a simple to implement and tune baseline, while more than halving the overall run time by removing the additional computational overheads of previous methods.
+
+# 1 Introduction
+
+Traditionally, reinforcement learning (RL) is thought of as a paradigm for online learning, where the interaction between the RL agent and its environment is of fundamental concern for how the agent learns. In offline RL (historically known as batch RL), the agent learns from a fixed-sized dataset, collected by some arbitrary and possibly unknown process [Lange et al., 2012]. Eliminating the need to interact with the environment is noteworthy as data collection can often be expensive, risky, or otherwise challenging, particularly in real-world applications. Consequently, offline RL enables the use of previously logged data or leveraging an expert, such as a human operator, without any of the risk associated with an untrained RL agent.
+
+Unfortunately, the main benefit of offline RL, the lack of environment interaction, is also what makes it a challenging task. While most off-policy RL algorithms are applicable in the offline setting, they tend to under-perform due to “extrapolation error”: an error in policy evaluation, where agents tend to poorly estimate the value of state-action pairs not contained in the dataset. This in turn affects policy improvement, where agents learn to prefer out-of-distribution actions whose value has been overestimated, resulting in poor performance [Fujimoto et al., 2019b]. The solution class for this problem revolves around the idea that the learned policy should be kept close to the data-generating process (or behavior policy), and has been given a variety of names (such as batchconstrained [Fujimoto et al., 2019b], KL-control [Jaques et al., 2019], behavior-regularized [Wu et al., 2019], or policy constraint [Levine et al., 2020]) depending on how this “closeness” is chosen to be implemented.
+
+While there are many proposed approaches to offline RL, we remark that few are truly “simple”, and even the algorithms which claim to work with minor additions to an underlying online RL algorithm make a significant number of implementation-level adjustments. In other cases, there are unmentioned hyperparameters, or secondary components, such as generative models, which make offline RL algorithms difficult to reproduce, and even more challenging to tune. Additionally, such mixture of details slow down the run times of the algorithms, and make causal attributions of performance gains and transfers of techniques across algorithms difficult, as in the case for many online RL algorithms [Henderson et al., 2017, Tucker et al., 2018, Engstrom et al., 2020, Andrychowicz et al., 2021, Furuta et al., 2021]. This motivates the need for more minimalist approaches in offline RL.
+
+In this paper, we ask: can we make a deep RL algorithm work offline with minimal changes? We find that we can match the performance of state-of-the-art offline RL algorithms with a single adjustment to the policy update step of the TD3 algorithm [Fujimoto et al., 2018]. TD3’s policy $\pi$ is updated with the deterministic policy gradient [Silver et al., 2014]:
+
+$$
+\pi = \underset { \pi } { \mathrm { a r g m a x } } \mathbb { E } _ { ( s , a ) \sim \mathcal { D } } [ Q ( s , \pi ( s ) ) ] .
+$$
+
+Our proposed change, $\mathrm { T D } 3 { + } \mathrm { B C }$ , is to simply add a behavior cloning term to regularize the policy:
+
+$$
+\pi = \underset { \pi } { \mathrm { a r g m a x } } \mathbb { E } _ { ( s , a ) \sim \mathcal { D } } \left[ \lambda Q ( s , \pi ( s ) ) - ( \pi ( s ) - a ) ^ { 2 } \right] ,
+$$
+
+with a single hyperparameter $\lambda$ to control the strength of the regularizer. This modification can be made by adjusting only a single line of code. Additionally, we remark that normalizing the states over the dataset, such that they have mean 0 and standard deviation 1, improves the stability of the learned policy. Importantly, these are the only changes made to the underlying deep RL algorithm. To accommodate reproduciblity, all of our code is open-sourced1.
+
+We evaluate our minimal changes to the TD3 algorithm on the D4RL benchmark of continuous control tasks [Fu et al., 2020]. We find that our algorithm compares favorably against many offline RL algorithms, while being significantly easier to implement and more than halving the required computation cost. The surprising effectiveness of our minimalist approach suggests that in the context of offline RL, simpler approaches have been left underexplored in favor of more elaborate algorithmic contributions.
+
+# 2 Related Work
+
+Although to the best of our knowledge, we are the first to use TD3 with behavior cloning (BC) for the purpose of offline RL, we remark that combining RL with BC, and other imitation learning approaches, has been previously considered by many authors.
+
+$\mathbf { R L } + \mathbf { B C }$ . With the aim of accelerating reinforcement learning from examples (known as learning from demonstrations [Atkeson and Schaal, 1997]), BC has been used as a regularization for policy optimization with DDPG [Lillicrap et al., 2015, Nair et al., 2018, Goecks et al., 2020] and the natural policy gradient [Kakade, 2001, Rajeswaran et al., 2017], but with additional sophistication through modified replay buffers and pre-training. The most similar work to our own is a $\mathrm { S A C + B C }$ baseline [Haarnoja et al., 2018] from Nair et al. [2020] and an unpublished course project [Booher] combining PPO [Schulman et al., 2017] with BC.
+
+RL $^ +$ Imitation. Other than directly using BC with RL, imitation learning has been combined with RL in a variety of manners, such as mixed with adversarial methods [Zhu et al., 2018, Kang et al., 2018], used for pre-training [Pfeiffer et al., 2018], modifying the replay buffer [Vecerík et al., 2017, ˇ Gulcehre et al., 2020], adjusting the value function [Kim et al., 2013, Hester et al., 2017], or reward shaping [Judah et al., 2014, Wu et al., 2021]. In all cases, these methods use demonstrations as a method for overcoming challenges in exploration or improving the learning speed of the RL agent.
+
+Offline RL. As aforementioned, offline RL methods generally rely on some approach for “staying close” to the data. This may be implemented using an estimate of the behavior policy and then defining an explicit policy parameterization [Fujimoto et al., 2019b, Ghasemipour et al., 2020] or by using divergence regularization [Jaques et al., 2019, Kumar et al., 2019, Wu et al., 2019, Siegel et al., 2020, Guo et al., 2021, Kostrikov et al., 2021]. Other approaches use a weighted version of BC to favor high advantage actions [Wang et al., 2018, Peng et al., 2019, Siegel et al., 2020, Wang et al.,
+
+2020, Nair et al., 2020] or perform BC over an explicit subset of the data [Chen et al., 2020]. Some methods have modified the set of valid actions based on counts [Laroche et al., 2019] or the learned behavior policy [Fujimoto et al., 2019a]. Another direction is to implement divergence regularization as a form of pessimism into the value estimate [Nachum et al., 2019, Kumar et al., 2020, Buckman et al., 2020].
+
+Meta Analyses of RL Algorithms. There are a substantial amount of meta analysis works on online RL algorithms. While some focus on inadequacies in the experimental protocols [Henderson et al., 2017, Osband et al., 2019], others study the roles of subtle implementation details in algorithms [Tucker et al., 2018, Engstrom et al., 2020, Andrychowicz et al., 2021, Furuta et al., 2021]. For example, Tucker et al. [2018], Engstrom et al. [2020] identified that superior performances of certain algorithms were more dependent on, or even accidentally due to, minor implementation rather than algorithmic differences. Furuta et al. [2021] study two broad families of off-policy algorithms, which most offline algorithms are based on, and find that a few subtle implementation details are strongly co-adapted and critical to specific algorithms, making attributions of performance gains difficult. Recent offline research also follows a similar trend, where a number of implementation modifications are necessary for high algorithmic performances (see Table 1). In contrast, we derive our algorithm by modifying the existing TD3 with only a few lines of codes. Our results suggest the community could also learn from careful explorations of simpler alternatives, besides emphasizing algorithmic novelties and complexities.
+
+# 3 Background
+
+RL. Reinforcement learning (RL) is a framework aimed to deal with tasks of sequential nature. Typically, the problem is defined by a Markov decision process (MDP) $( S , { \mathcal { A } } , { \mathcal { R } } , p , \gamma )$ , with state space $s$ , action space $\mathcal { A }$ , scalar reward function $\mathcal { R }$ , transition dynamics $p$ , and discount factor $\gamma$ [Sutton and Barto, 1998]. The behavior of an RL agent is determined by a policy $\pi$ which maps states to actions (deterministic policy), or states to a probability distribution over actions The objective of an RL agent is to maximize the expected discounted return $\mathbb { E } _ { \pi } [ \sum _ { t = 0 } ^ { \infty } \bar { \gamma } ^ { t } r _ { t + 1 } \bar { ] } .$ which is the expected cumulative sum of rewards when following the policy in the MDP, where the importance of the horizon is determined by the discount factor. We measure this objective by a value function, which measures the expected discounted return after taking the action $a$ in state $s$ : $\begin{array} { r } { Q ^ { \pi } ( s , a ) = \mathbb { E } _ { \pi } \left[ \sum _ { t = 0 } ^ { \infty } \gamma ^ { t } r _ { t + 1 } | s _ { 0 } = s , \dot { a } _ { 0 } = a \right] . } \end{array}$ .
+
+BC. Another approach for training policies is through imitation of an expert or behavior policy. Behavior cloning (BC) is an approach for imitation learning [Pomerleau, 1991], where the policy is trained with supervised learning to directly imitate the actions of a provided dataset. Unlike RL, this process is highly dependent on the performance of the data-collecting process.
+
+Offline RL. Offline RL breaks the assumption that the agent can interact with the environment. Instead, the agent is provided a fixed dataset which has been collected by some unknown datagenerating process (such as a collection of behavior policies). This setting may be considered more challenging as the agent loses the opportunity to explore the MDP according to its current beliefs, and instead from infer good behavior from only the provided data.
+
+One challenge for offline RL is the problem of extrapolation error [Fujimoto et al., 2019b], which is generalization error in the approximate value function, induced by selecting actions not contained in the dataset. Simply put, it is difficult to evaluate the expected value of a policy which is sufficiently different from the behavior policy. Consequently, algorithms have taken the approach of constraining or regularizing the policy to stay near to the actions in the dataset [Levine et al., 2020].
+
+# 4 Challenges in Offline RL
+
+In this section, we identify key open challenges in offline RL through analyzing and evaluating prior algorithms. We believe these challenges highlight the importance of minimalist approaches, where performance can be easily attributed to algorithmic contributions, rather than entangled with the specifics of implementation.
+
+Implementation and Tuning Complexities. RL algorithms are notoriously difficult to implement and tune [Henderson et al., 2017, Engstrom et al., 2020, Furuta et al., 2021], where minor code-level optimizations and hyperparameters can have non-trivial impact of performance and stability. This problem may be additionally amplified in the context of offline RL, where evaluating changes to implementation and hyperparameters is counter-intuitive to the nature of offline RL, which explicitly aims to eliminate environment interactions [Paine et al., 2020, Yang et al., 2020].
+
+<table><tr><td></td><td>CQL [Kumar et al., 2020]</td><td>Fisher-BRC [Kostrikov et al.,2021]</td><td>TD3+BC (Ours)</td></tr><tr><td>Algorithmic Adjustments</td><td>Add regularizer to critic† Approximate logsumexp with sampling‡</td><td>Train a generative modelt‡ Replace critic with offset function Gradient penalty on offset function†</td><td>Add a BC term+</td></tr><tr><td>Implementation Adjustments</td><td>Architecture†‡ Actor learning rate† Pre-training actor Remove SAC entropy term Max over sampled actionst</td><td>Architecture†‡ Reward bonus† Remove SAC entropy term</td><td>Normalize states</td></tr></table>
+
+Table 1: Implementation changes offline RL algorithms make to the underlying base RL algorithm. † corresponds to details that add additional hyperparameter(s), and ‡ corresponds to ones that add a computational cost.
+
+![](images/5b288cacfc289e3f9648574303a9b842ef1c5faa8fdaf11c9a0059088dead6a5.jpg)  
+Figure 1: Percent difference of performance of offline RL algorithms and their simplified versions which remove implementation adjustments to their underlying algorithm. $\mathbf { H } \mathbf { C } =$ HalfCheetah, Hop $=$ Hopper, $\mathbf { W } =$ Walker, $\mathbf { r } =$ random, $\mathbf { m } =$ medium, $\mathbf { m r } =$ medium-replay, me $=$ medium-expert, ${ \mathfrak { e } } =$ expert. Huge drops in performances show that the implementation complexities are crucial for achieving the best results in these prior algorithms.
+
+Most offline RL algorithms are built explicitly on top of an existing off-policy deep RL algorithm, such as TD3 [Fujimoto et al., 2018] or SAC [Haarnoja et al., 2018], but then further modify the underlying algorithm with “non-algorithmic” implementation changes, such as modifications to network architecture, learning rates, or pre-training the actor network. We remark that a desirable property of an offline RL algorithm would be to minimally modify the underlying algorithm, so as to reduce the space of possible adjustments required to achieve a strong performance.
+
+In Table 1 we examine the particular modifications made by two recent offline RL algorithms, CQL [Kumar et al., 2020] and Fisher-BRC [Kostrikov et al., 2021]. On top of algorithmic changes, CQL also adds a pre-training phase where the actor is only trained with imitation learning and selects the max action over a sampled set of actions from the policy during evaluation. Fisher-BRC adds a constant reward bonus to every transition. Both methods modify SAC by removing the entropy term in the target update and modify the default network architecture. These changes add supplementary hyperparameters which may need to be tuned or increase computational costs.
+
+In the online setting, these changes are relatively inconsequential and could be validated with some simple experimentation. However, in the offline setting, where we cannot interact with the environment, making additional adjustments to the underlying algorithm should be considered as more costly as validating their effectiveness is no longer a trivial additional step. This is also problematic because unlike the algorithmic changes proposed by these papers, these implementation details are not well justified, meaning there is much less intuition as to when to include these details, or how to adjust them with minimal experimentation. In the case of the D4RL benchmark on MuJoCo tasks [Todorov et al., 2012, Fu et al., 2020], we have a strong prior that our base deep RL algorithm performs well, as SAC/TD3 are considered state-of-the-art (or nearly) in these domains. If additional changes are necessary, then it suggests the algorithmic contributions alone are insufficient.
+
+![](images/49e35581bc108e701bb737cd283a99ee49ef68eddb42fdfbb560bd49f5647002.jpg)  
+Figure 2: Percent difference of the worst episode during the 10 evaluation episodes at the last evaluation. This measures the deviations in performance at single point in time. $\mathrm { H C } =$ HalfCheetah, Hop $=$ Hopper, $\mathbf { W } =$ Walker, $\mathbf { r } =$ random, $\mathbf { m } =$ medium, $\mathbf { m r } =$ medium-replay, me $=$ medium-expert, ${ \bf e } =$ expert. While online algorithms (TD3) typically have small episode variances per trained policy (as they should at convergence), all offline algorithms have surprisingly high episodic variances for trained policies.
+
+![](images/58530fed78a56afc2645b7777d9cf9e5929c1e774e6d4e92fd14f879f6f2ea1c.jpg)  
+Figure 3: Percent difference of the worst evaluation during the last 10 evaluations. This measures the deviations in performance over a period of time. $\mathrm { H C } =$ HalfCheetah, Hop $=$ Hopper, $\mathbf { W } =$ Walker, $\mathbf { r } =$ random, $\mathbf { m } =$ medium, $\mathbf { m r } =$ medium-replay, me $=$ medium-expert, ${ \bf e } =$ expert. Similarly to the result in Figure 2, all offline-trained policies have significant variances near the final stage of training that are absent in the online setting.
+
+In Figure 1 we examine the percent difference in performance when removing the implementation changes in CQL and Fisher-BRC. There is a significant drop in performance in many of the tasks. This is not necessarily a death knell to these algorithms, as it is certainly possible these changes could be kept without tuning when attempting new datasets and domains. However, since neither paper make mention of a training/validation split, we can only assume these changes were made with their evaluation datasets in mind (D4RL, in this instance), and remark there is insufficient evidence that these changes may be universal. Ultimately, we make this point not to suggest a fundamental flaw with pre-existing algorithms, but to suggest that there should be a preference for making minimal adjustments to the underlying RL algorithm, to reduce the need for hyperparameter tuning.
+
+Extra Computation Requirement. A secondary motivating factor for minimalism is avoiding the additional computational costs associated with modifying the underlying algorithm (in particular architecture) and more complex algorithmic ideas. In Table 3 (contained later in Section 6), we examine the run time of offline RL algorithms, as well as the change in cost over the underlying algorithm, and find their is a significant computational cost associated with these modifications. On top of the architecture changes, for CQL this is largely due to the costs of logsumexp over multiple sampled actions, and for Fisher-BRC, the costs associated with training the independent generative model. Since an objective of offline RL is to take advantage of existing, potentially large, datasets, there should be a preference for scalable and efficient solutions. Of course, run time should not come at the cost of performance, but as we will later demonstrate, there exists a simple, and computationally-free, approach for offline RL which matches the performance of current state-of-the-art algorithms.
+
+Instability of Trained Policies. In analyzing the final trained policies of prior offline algorithms, we learned of a tangential, and open, challenge in the form of instability. In online RL, if the current policy is unsatisfactory, we can use checkpoints of previous iterations of the policy, or to simply continue training. However, in offline RL, the evaluation should only occur once by definition, greatly increasing the importance of the single policy at evaluation time. We highlight two versions of instability in offline RL. Figure 2 shows that in contrast to the online-trained policy, which converges to a robust low-variance policy, the offline-trained policy exhibits huge variances in performance during a single evaluation. Therefore, even if the average performance is reasonable, the agent may still perform poorly on some episodes. Figure 3 shows instability over the set of evaluations, which means the performance of the agent may be dependent on the specific stopping point chosen for evaluation. This questions the empirical effectiveness of offline RL for safety-critical real-world use cases [Mandel et al., 2014, Gottesman et al., 2018, Gauci et al., 2018, Jaques et al., 2019, Matsushima et al., 2020] as well as the current trend of reporting only the mean-value of the final policy in offline benchmarking [Fu et al., 2020].
+
+Such variances are not likely caused by high policy entropies (e.g. $\mathrm { T D } 3 { + } \mathrm { B C }$ trains a deterministic policy), but rather our hypothesis is that such a problem is due to distributional shifts issues and poor generalizations across unobserved states caused by offline nature of training [Ross et al., 2011], where the optimized policy is never allowed to execute in the environment, similarly as in BC. This trait of offline RL algorithms appears to be consistent across all offline algorithms we evaluated, even for our minimalistic $\mathrm { T D } 3 { + } \mathrm { B C }$ that is only a few lines change from TD3. While we could not solve this challenge sufficiently within the scope of this work, the fact that this is reproducible even in the minimalistic variant proves that this a fundamental problem shared by all offline training settings, and is a critical problem for the community to study in the future.
+
+# 5 A Minimalist Offline RL Algorithm
+
+A key problem in offline RL, extrapolation error, can be summarized as the inability to properly evaluate out-of-distribution actions. Consequently, there has been a variety of different approaches to limiting, or regularizing, action selection such that the learned policy is easier to evaluate with the given dataset. We remark that while minimizing say, KL divergence, is a both logical and valid approach for reducing extrapolation error, there is no fundamental argument why minimizing one divergence or distance metric should be better than another. Thus, rather than derive an entirely new approach, we focus on simplicity, and present an offline RL algorithm which requires minimal modifications to a pre-existing deep RL algorithm. As discussed in Section 4 a minimalist approach has a variety of benefits, such as reducing the number of hyperparameters to tune, increasing scalability by reducing computational costs, and providing an avenue for analyzing problems by disentangling algorithmic contributions from implementation details.
+
+We now describe such an approach to offline RL. Our algorithm builds on top of TD3 [Fujimoto et al., 2018], making only two straightforward changes. Firstly, we add a behavior cloning regularization term to the standard policy update step of TD3, to push the policy towards favoring actions contained in the dataset $\mathcal { D }$ :
+
+$$
+\pi = \underset { \pi } { \operatorname { a r g m a x } } \mathbb { E } _ { s \sim \mathcal { D } } [ Q ( s , \pi ( s ) ) ]  \pi = \underset { \pi } { \operatorname { a r g m a x } } \mathbb { E } _ { ( s , a ) \sim \mathcal { D } } [ \lambda Q ( s , \pi ( s ) ) - ( \pi ( s ) - a ) ^ { 2 } ] .
+$$
+
+Secondly, we normalize the features of every state in the provided dataset. Let $s _ { i }$ be the ith feature of the state $s$ , let $\mu _ { i } \ \sigma _ { i }$ be the mean and standard deviation, respectively, of the ith feature across the dataset:
+
+$$
+s _ { i } = \frac { s _ { i } - \mu _ { i } } { \sigma _ { i } + \epsilon } ,
+$$
+
+where $\epsilon$ is a small normalization constant (we use $1 0 ^ { - 3 }$ ). While we remark this is a commonly used implementation detail in many deep RL algorithms [Raffin et al., 2019], we highlight it as (1) we want complete transparency about all implementation changes and (2) normalizing provides a non-trivial performance benefit in offline RL, where it is particularly well-suited as the dataset remains fixed.
+
+While the choice of $\lambda$ in Equation (3) is ultimately just a hyperparameter, we observe that the balance between RL (in maximizing $Q$ ) and imitation (in minimizing the BC term), is highly susceptible to the scale of $Q$ . If we assume an action range of $[ - 1 , 1 ]$ , the BC term is at most 4, however the range of $Q$ will be a function of the scale of the reward. Consequently, we can add a normalization term into $\lambda$ . Given the dataset of $N$ transitions $( s _ { i } , a _ { i } )$ , we define the scalar $\lambda$ as:
+
+$$
+\lambda = { \frac { \alpha } { { \frac { 1 } { N } } \sum _ { ( s _ { i } , a _ { i } ) } | Q ( s _ { i } , a _ { i } ) | } } .
+$$
+
+This is simply a normalization term based on the average absolute value of $Q$ . In practice, we estimate this mean term over mini-batches, rather than the entire dataset. Although this term includes $Q$ , it is
+
+Table 2: Average normalized score over the final 10 evaluations and 5 seeds. The highest performing scores are highlighted. CQL and Fisher-BRC are re-run using author-provided implementations to ensure an identical evaluation process, while BRAC and AWAC use previously reported results. $\pm$ captures the standard deviation over seeds. $\mathrm { T D } 3 { + } \mathrm { B C }$ achieves effectively the same performances as the state-of-the-art Fisher-BRC, despite being much simpler to implement and tune and more than halving the computation cost.   
+
+<table><tr><td></td><td></td><td>BC</td><td>BRAC-p</td><td>AWAC</td><td>CQL</td><td>Fisher-BRC</td><td>TD3+BC</td></tr><tr><td rowspan="3">aopaer</td><td>HalfCheetah</td><td>2.0 ±0.1</td><td>23.5</td><td>2.2</td><td>21.7 ±0.9</td><td>32.2 ±2.2</td><td>10.2 ±1.3</td></tr><tr><td>Hopper</td><td>9.5 ±0.1</td><td>11.1</td><td>9.6</td><td>10.7 ±0.1</td><td>11.4 ±0.2</td><td>11.0 ±0.1</td></tr><tr><td>Walker2d</td><td>1.2 ±0.2</td><td>0.8</td><td>5.1</td><td>2.7 ±1.2</td><td>0.6 ±0.6</td><td>1.4 ±1.6</td></tr><tr><td rowspan="3">airea</td><td>HalfCheetah</td><td>36.6 ±0.6</td><td>44.0</td><td>37.4</td><td>37.2 ±0.3</td><td>41.3 ±0.5</td><td>42.8 ±0.3</td></tr><tr><td>Hopper</td><td>30.0 ±0.5</td><td>31.2</td><td>72.0</td><td>44.2 ±10.8</td><td>99.4 ±0.4</td><td>99.5 ±1.0</td></tr><tr><td>Walker2d</td><td>11.4 ±6.3</td><td>72.7</td><td>30.1</td><td>57.5 ±8.3</td><td>79.5 ±1.0</td><td>79.7 ±1.8</td></tr><tr><td rowspan="3">wnipen rrer</td><td>HalfCheetah</td><td>34.7 ±1.8</td><td>45.6</td><td></td><td>41.9 ±1.1</td><td>43.3 ±0.9</td><td>43.3 ±0.5</td></tr><tr><td>Hopper</td><td>19.7 ±5.9</td><td>0.7</td><td></td><td>28.6 ±0.9</td><td>35.6 ±2.5</td><td>31.4 ±3.0</td></tr><tr><td>Walker2d</td><td>8.3 ±1.5</td><td>-0.3</td><td>1</td><td>15.8 ±2.6</td><td>42.6 ±7.0</td><td>25.2 ±5.1</td></tr><tr><td rowspan="3">wnipen adx</td><td>HalfCheetah</td><td>67.6±13.2</td><td>43.8</td><td>36.8</td><td>27.1 ±3.9</td><td>96.1 ±9.5</td><td>97.9 ±4.4</td></tr><tr><td>Hopper</td><td>89.6 ±27.6</td><td>1.1</td><td>80.9</td><td>111.4 ±1.2</td><td>90.6 ±43.3</td><td>112.2 ±0.2</td></tr><tr><td>Walker2d</td><td>12.0 ±5.8</td><td>-0.3</td><td>42.7</td><td>68.1 ±13.1</td><td>103.6 ±4.6</td><td>101.1 ±9.3</td></tr><tr><td rowspan="3">Jadxg</td><td>HalfCheetah</td><td>105.2 ±1.7</td><td>3.8</td><td>78.5</td><td>82.4 ±7.4</td><td>106.8 ±3.0</td><td>105.7 ±1.9</td></tr><tr><td>Hopper</td><td>111.5 ±1.3</td><td>6.6</td><td>85.2</td><td>111.2 ±2.1</td><td>112.3 ±0.2</td><td>112.2 ±0.2</td></tr><tr><td>Walker2d</td><td>56.0 ±24.9</td><td>-0.2</td><td>57.0</td><td>103.8 ±7.6</td><td>79.9 ±32.4</td><td>105.7 ±2.7</td></tr><tr><td></td><td>Total</td><td>595.3 ±91.5</td><td>284.1</td><td>1</td><td>764.3 ±61.5</td><td>974.6 ±108.3</td><td>979.3 ±33.4</td></tr></table>
+
+not differentiated over, and is simply used to scale the loss. This formulation has the added benefit of normalizing the learning rate across tasks, as the gradient $\nabla _ { a } Q ( s , a )$ will also be dependent on the scale of $Q$ . We use $\alpha = 2 . 5$ in our experiments.
+
+This completes the description of $\mathrm { T D } 3 { + } \mathrm { B C }$ . The Equations (3), (4), and (5) summarizes the entirety of our changes to TD3, and can be implemented by modifying only a handful of lines in most codebases.
+
+# 6 Experiments
+
+We evaluate our proposed approach on the D4RL benchmark of OpenAI gym MuJoCo tasks [Todorov et al., 2012, Brockman et al., 2016, Fu et al., 2020], which encompasses a variety of dataset settings and domains. Our offline RL baselines include two state-of-the-art algorithms, CQL [Kumar et al., 2020] and Fisher-BRC [Kostrikov et al., 2021], as well as BRAC [Wu et al., 2019] and AWAC [Nair et al., 2020] due to their algorithmic simplicity.
+
+To ensure a fair and identical experimental evaluation across algorithms, we re-run the state-of-theart algorithms CQL and Fisher-BRC using the author-provided implementations23. We train each algorithm for 1 million time steps and evaluate every 5000 time steps. Each evaluation consists of 10 episodes. Results for BRAC are obtained from the D4RL benchmark and from the CQL paper, while the AWAC results are obtained directly from the paper. BC results were obtained using our own implementation.
+
+D4RL. We report the final performance results in Table 2 and display the learning curves in Figure 4. Although our method is very simplistic in nature, it surpasses, or matches, the performance of the current state-of-the-art offline RL algorithms in most tasks. Only Fisher-BRC exhibits a comparable performance4. Examining the learning curves, we can see that our approach achieves a similar learning speed and stability, without requiring any pre-training phase.
+
+![](images/f3e0dfc3ac09294df518cab6aebee696472ea86ab296c286486976678110dd2c.jpg)  
+Figure 4: Learning curves comparing the performance of $\mathrm { T D } 3 { + } \mathrm { B C }$ against offline RL baselines in the D4RL datasets. Curves are averaged over 5 seeds, with the shaded area representing the standard deviation across seeds. $\mathrm { T D } 3 { + } \mathrm { B C }$ exhibits a similar learning speed and final performance as the state-of-the-art Fisher-BRC, without the need of pre-training a generative model.
+
+![](images/52515df029da56c675bd8c803ede1e109752ec343df71bd4dd005bd7fc5f84cc.jpg)
+
+Run time. We evaluate run time of training each of the offline RL algorithms for 1 million time steps, using the author-provoided implementations. Additionally, for fair comparison, we re-implement Fisher-BRC, allowing each method to be compared in the same framework (PyTorch [Paszke et al., 2019]). The results are reported in Table 3. Unsurprisingly, we find our approach compares favorably against previous methods in terms of wall-clock training time, effectively adding no cost to the underlying TD3 algorithm. All run time experiments were run with a single GeForce GTX 1080 GPU and an Intel Core i7-6700K CPU at 4.00GHz.
+
+Ablation. In Figure 5, we perform an ablation study over the components in our method. As noted in previous work [Fujimoto et al., 2019b], without behavior cloning regularization, the RL algorithm alone is insufficient to achieve a high performance (except on some of the random data sets). We also note that our algorithm never underperforms vanilla behavior cloning, even on the expert tasks. Predictably, the removal of state normalization has the least significant impact, but it still provides some benefit across a range of tasks while being a minor adjustment. In Figure 6, we evaluate the sensitivity of the algorithm to the hyperparameter α, where the weighting λ = P α(s,a) |Q(s,a)| on the value function is determined by $\alpha$ . On many tasks, our approach is robust to this weighting factor, but note the performance on a subset of tasks begins to decrease as $\alpha$ begins to more heavily favor imitation $( \alpha = 1$ ) or RL ( $\alpha = 4$ ).
+
+![](images/c3a3615df3f3991fa97861f847077b6e877772a07fe271f60ab186a38e136a87.jpg)  
+Figure 5: Percent difference of the performance of an ablation of our proposed approach, compared to the full algorithm. $\mathrm { T D } 3 + \lambda + \mathrm { B C } + \mathrm { N o r m }$ refers to the complete algorithm, where Norm refers to the state feature normalization. HC $=$ HalfCheetah, Hop $=$ Hopper, $\mathbf { W } =$ Walker, $\mathbf { r } =$ random, $\mathbf { m } =$ medium, $\mathbf { m r } =$ medium-replay, me $=$ medium-expert, ${ \mathfrak { e } } =$ expert. As expected, both BC and TD3 are necessary components to achieve a strong performance. While removing state normalization is not devastating to the performance of the algorithm, we remark it provides a boost in performance across many tasks, while being a straightforward addition.
+
+![](images/787e6c0b5ac86415e401a568dd6112a37c03182cace1d00fe8177e8bdf1c4671.jpg)  
+Figure 6: Percent difference of the performance of an ablation over $\alpha$ , compared to the full algorithm. Recall the form of the sole hyperparameter $\begin{array} { r } { \lambda = \frac { \alpha } { \sum \vert Q ( s , a ) \vert } } \end{array}$ , where $\lambda$ weights the $Q$ function during the policy update. $\alpha = 2 . 5$ is used by default. $\mathrm { H C } =$ HalfCheetah, $\mathrm { H o p } = \mathrm { H o p p e r }$ , ${ \bf W } =$ Walker, $\mathbf { r } =$ random, $\textrm { m } =$ medium, $\mathbf { m r } =$ medium-replay, me $=$ medium-expert, ${ \bf e } =$ expert. While there is effectively no performance difference between $\alpha = 2$ and $\alpha = 3$ , we remark that performance begins to degrade on select tasks as the algorithm begins to approach more RL $\alpha = 4$ ) or imitation $( \alpha = 1$ ).
+
+# 7 Conclusion
+
+Most recent advances in offline RL center around the idea of regularizing policy actions to be close to the support within batch data, and yet many state-of-the-art algorithms have significant complexities and additional modifications beyond base algorithms that lead to not only much slower run time, but also intractable attributions for sources of performance gains. Instead of complexity we optimize for simplicity, and introduce a minimalistic algorithm that achieves a state-of-the-art performance but is only a few lines of changes from the base TD3 algorithm, uses less than half of the computation time of competing algorithms, and has only one additional hyperparameter.
+
+Additionally, we highlight existing open challenges in offline RL research, including not only the extra implementation, computation, and hyperparameter-tuning complexities that we successfully address in this work, but also call attention to the neglected problem of high episodic variance in offline-trained policies compared to online-trained (see Figures 2 and 3) that we as the community should address in future works and benchmarking. Finally, we believe the sheer simplicity of our approach highlights a possible overemphasis on algorithmic complexity made by the community, and we hope to inspire future work to revisit simpler alternatives which may have been overlooked.
+
+# References
+
+Marcin Andrychowicz, Anton Raichuk, Piotr Stanczyk, Manu Orsini, Sertan Girgin, Raphaël Marinier, ´ Leonard Hussenot, Matthieu Geist, Olivier Pietquin, Marcin Michalski, Sylvain Gelly, and Olivier Bachem. What matters for on-policy deep actor-critic methods? a large-scale study. In International Conference on Learning Representations, 2021.
+
+Christopher G Atkeson and Stefan Schaal. Robot learning from demonstration. In Proceedings of the Fourteenth International Conference on Machine Learning, pages 12–20, 1997.
+
+Jonathan Booher. $\mathrm { B c + r l }$ : Imitation learning from non-optimal demonstrations. URL https://web. stanford.edu/\~jaustinb/papers/CS234.pdf.
+
+Greg Brockman, Vicki Cheung, Ludwig Pettersson, Jonas Schneider, John Schulman, Jie Tang, and Wojciech Zaremba. Openai gym, 2016.
+
+Jacob Buckman, Carles Gelada, and Marc G Bellemare. The importance of pessimism in fixed-dataset policy optimization. arXiv preprint arXiv:2009.06799, 2020.
+
+Xinyue Chen, Zijian Zhou, Zheng Wang, Che Wang, Yanqiu Wu, and Keith Ross. Bail: Bestaction imitation learning for batch deep reinforcement learning. Advances in Neural Information Processing Systems, 33, 2020.
+
+Logan Engstrom, Andrew Ilyas, Shibani Santurkar, Dimitris Tsipras, Firdaus Janoos, Larry Rudolph, and Aleksander Madry. Implementation matters in deep rl: A case study on ppo and trpo. In International Conference on Learning Representations, 2020.
+
+Justin Fu, Aviral Kumar, Ofir Nachum, George Tucker, and Sergey Levine. D4rl: Datasets for deep data-driven reinforcement learning. 2020.
+
+Scott Fujimoto, Herke van Hoof, and David Meger. Addressing function approximation error in actorcritic methods. In International Conference on Machine Learning, volume 80, pages 1587–1596. PMLR, 2018.
+
+Scott Fujimoto, Edoardo Conti, Mohammad Ghavamzadeh, and Joelle Pineau. Benchmarking batch deep reinforcement learning algorithms. arXiv preprint arXiv:1910.01708, 2019a.
+
+Scott Fujimoto, David Meger, and Doina Precup. Off-policy deep reinforcement learning without exploration. In International Conference on Machine Learning, pages 2052–2062, 2019b.
+
+Hiroki Furuta, Tadashi Kozuno, Tatsuya Matsushima, Yutaka Matsuo, and Shixiang Shane Gu. Identifying co-adaptation of algorithmic and implementational innovations in deep reinforcement learning: A taxonomy and case study of inference-based algorithms. arXiv preprint arXiv:2103.17258, 2021.
+
+Jason Gauci, Edoardo Conti, Yitao Liang, Kittipat Virochsiri, Yuchen He, Zachary Kaden, Vivek Narayanan, Xiaohui Ye, Zhengxing Chen, and Scott Fujimoto. Horizon: Facebook’s open source applied reinforcement learning platform. arXiv preprint arXiv:1811.00260, 2018.
+
+Seyed Kamyar Seyed Ghasemipour, Dale Schuurmans, and Shixiang Shane Gu. Emaq: Expected-max q-learning operator for simple yet effective offline and online rl. arXiv preprint arXiv:2007.11091, 2020.
+
+Vinicius G Goecks, Gregory M Gremillion, Vernon J Lawhern, John Valasek, and Nicholas R Waytowich. Integrating behavior cloning and reinforcement learning for improved performance in dense and sparse reward environments. In Proceedings of the 19th International Conference on Autonomous Agents and MultiAgent Systems, pages 465–473, 2020.
+
+Omer Gottesman, Fredrik Johansson, Joshua Meier, Jack Dent, Donghun Lee, Srivatsan Srinivasan, Linying Zhang, Yi Ding, David Wihl, Xuefeng Peng, et al. Evaluating reinforcement learning algorithms in observational health settings. arXiv preprint arXiv:1805.12298, 2018.
+
+Caglar Gulcehre, Tom Le Paine, Bobak Shahriari, Misha Denil, Matt Hoffman, Hubert Soyer, Richard Tanburn, Steven Kapturowski, Neil Rabinowitz, Duncan Williams, Gabriel Barth-Maron, Ziyu Wang, Nando de Freitas, and Worlds Team. Making efficient use of demonstrations to solve hard exploration problems. In International Conference on Learning Representations, 2020.
+
+Yijie Guo, Shengyu Feng, Nicolas Le Roux, Ed Chi, Honglak Lee, and Minmin Chen. Batch reinforcement learning through continuation method. In International Conference on Learning Representations, 2021.
+
+Tuomas Haarnoja, Aurick Zhou, Pieter Abbeel, and Sergey Levine. Soft actor-critic: Off-policy maximum entropy deep reinforcement learning with a stochastic actor. In International Conference on Machine Learning, volume 80, pages 1861–1870. PMLR, 2018.
+
+Peter Henderson, Riashat Islam, Philip Bachman, Joelle Pineau, Doina Precup, and David Meger. Deep reinforcement learning that matters. In AAAI Conference on Artificial Intelligence, 2017.
+
+Todd Hester, Matej Vecerik, Olivier Pietquin, Marc Lanctot, Tom Schaul, Bilal Piot, Dan Horgan, John Quan, Andrew Sendonaris, Gabriel Dulac-Arnold, et al. Deep q-learning from demonstrations. arXiv preprint arXiv:1704.03732, 2017.
+
+Natasha Jaques, Asma Ghandeharioun, Judy Hanwen Shen, Craig Ferguson, Agata Lapedriza, Noah Jones, Shixiang Gu, and Rosalind Picard. Way off-policy batch deep reinforcement learning of implicit human preferences in dialog. arXiv preprint arXiv:1907.00456, 2019.
+
+Kshitij Judah, Alan Fern, Prasad Tadepalli, and Robby Goetschalckx. Imitation learning with demonstrations and shaping rewards. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 28, 2014.
+
+Sham Kakade. A natural policy gradient. In Proceedings of the 14th International Conference on Neural Information Processing Systems: Natural and Synthetic, pages 1531–1538, 2001.
+
+Bingyi Kang, Zequn Jie, and Jiashi Feng. Policy optimization with demonstrations. In International Conference on Machine Learning, pages 2469–2478. PMLR, 2018.
+
+Beomjoon Kim, Amir-massoud Farahmand, Joelle Pineau, and Doina Precup. Learning from limited demonstrations. In Advances in Neural Information Processing Systems, pages 2859–2867, 2013.
+
+Ilya Kostrikov, Jonathan Tompson, Rob Fergus, and Ofir Nachum. Offline reinforcement learning with fisher divergence critic regularization. arXiv preprint arXiv:2103.08050, 2021.
+
+Aviral Kumar, Justin Fu, Matthew Soh, George Tucker, and Sergey Levine. Stabilizing off-policy q-learning via bootstrapping error reduction. In Advances in Neural Information Processing Systems, pages 11784–11794, 2019.
+
+Aviral Kumar, Aurick Zhou, George Tucker, and Sergey Levine. Conservative q-learning for offline reinforcement learning. arXiv preprint arXiv:2006.04779, 2020.
+
+Sascha Lange, Thomas Gabel, and Martin Riedmiller. Batch reinforcement learning. In Reinforcement learning, pages 45–73. Springer, 2012.
+
+Romain Laroche, Paul Trichelair, and Remi Tachet Des Combes. Safe policy improvement with baseline bootstrapping. In International Conference on Machine Learning, pages 3652–3661. PMLR, 2019.
+
+Sergey Levine, Aviral Kumar, George Tucker, and Justin Fu. Offline reinforcement learning: Tutorial, review, and perspectives on open problems. arXiv preprint arXiv:2005.01643, 2020.
+
+Timothy P Lillicrap, Jonathan J Hunt, Alexander Pritzel, Nicolas Heess, Tom Erez, Yuval Tassa, David Silver, and Daan Wierstra. Continuous control with deep reinforcement learning. arXiv preprint arXiv:1509.02971, 2015.
+
+Travis Mandel, Yun-En Liu, Sergey Levine, Emma Brunskill, and Zoran Popovic. Offline policy evaluation across representations with applications to educational games. In International Conference on Autonomous Agents and Multiagent Systems, 2014.
+
+Tatsuya Matsushima, Hiroki Furuta, Yutaka Matsuo, Ofir Nachum, and Shixiang Gu. Deploymentefficient reinforcement learning via model-based offline optimization. arXiv preprint arXiv:2006.03647, 2020.
+
+Ofir Nachum, Bo Dai, Ilya Kostrikov, Yinlam Chow, Lihong Li, and Dale Schuurmans. Algaedice: Policy gradient from arbitrary experience. arXiv preprint arXiv:1912.02074, 2019.
+
+Ashvin Nair, Bob McGrew, Marcin Andrychowicz, Wojciech Zaremba, and Pieter Abbeel. Overcoming exploration in reinforcement learning with demonstrations. In 2018 IEEE International Conference on Robotics and Automation (ICRA), pages 6292–6299. IEEE, 2018.
+
+Ashvin Nair, Murtaza Dalal, Abhishek Gupta, and Sergey Levine. Accelerating online reinforcement learning with offline datasets. arXiv preprint arXiv:2006.09359, 2020.
+
+Ian Osband, Yotam Doron, Matteo Hessel, John Aslanides, Eren Sezener, Andre Saraiva, Katrina McKinney, Tor Lattimore, Csaba Szepesvari, Satinder Singh, et al. Behaviour suite for reinforcement learning. arXiv preprint arXiv:1908.03568, 2019.
+
+Tom Le Paine, Cosmin Paduraru, Andrea Michi, Caglar Gulcehre, Konrad Zolna, Alexander Novikov, Ziyu Wang, and Nando de Freitas. Hyperparameter selection for offline reinforcement learning. arXiv preprint arXiv:2007.09055, 2020.
+
+Adam Paszke, Sam Gross, Francisco Massa, Adam Lerer, James Bradbury, Gregory Chanan, Trevor Killeen, Zeming Lin, Natalia Gimelshein, Luca Antiga, et al. Pytorch: An imperative style, high-performance deep learning library. In Advances in Neural Information Processing Systems, pages 8024–8035, 2019.
+
+Xue Bin Peng, Aviral Kumar, Grace Zhang, and Sergey Levine. Advantage-weighted regression: Simple and scalable off-policy reinforcement learning. arXiv preprint arXiv:1910.00177, 2019.
+
+Mark Pfeiffer, Samarth Shukla, Matteo Turchetta, Cesar Cadena, Andreas Krause, Roland Siegwart, and Juan Nieto. Reinforced imitation: Sample efficient deep reinforcement learning for mapless navigation by leveraging prior demonstrations. IEEE Robotics and Automation Letters, 3(4): 4423–4430, 2018.
+
+Dean A Pomerleau. Efficient training of artificial neural networks for autonomous navigation. Neural computation, 3(1):88–97, 1991.
+
+Antonin Raffin, Ashley Hill, Maximilian Ernestus, Adam Gleave, Anssi Kanervisto, and Noah Dormann. Stable baselines3. https://github.com/DLR-RM/stable-baselines3, 2019.
+
+Aravind Rajeswaran, Vikash Kumar, Abhishek Gupta, Giulia Vezzani, John Schulman, Emanuel Todorov, and Sergey Levine. Learning complex dexterous manipulation with deep reinforcement learning and demonstrations. arXiv preprint arXiv:1709.10087, 2017.
+
+Stéphane Ross, Geoffrey Gordon, and Drew Bagnell. A reduction of imitation learning and structured prediction to no-regret online learning. In Proceedings of the fourteenth international conference on artificial intelligence and statistics, pages 627–635. JMLR Workshop and Conference Proceedings, 2011.
+
+John Schulman, Filip Wolski, Prafulla Dhariwal, Alec Radford, and Oleg Klimov. Proximal policy optimization algorithms. arXiv preprint arXiv:1707.06347, 2017.
+
+Noah Siegel, Jost Tobias Springenberg, Felix Berkenkamp, Abbas Abdolmaleki, Michael Neunert, Thomas Lampe, Roland Hafner, Nicolas Heess, and Martin Riedmiller. Keep doing what worked: Behavior modelling priors for offline reinforcement learning. In International Conference on Learning Representations, 2020.
+
+David Silver, Guy Lever, Nicolas Heess, Thomas Degris, Daan Wierstra, and Martin Riedmiller. Deterministic policy gradient algorithms. In International Conference on Machine Learning, pages 387–395, 2014.
+
+Richard S Sutton and Andrew G Barto. Reinforcement learning: An introduction, volume 1. MIT press Cambridge, 1998.
+
+Emanuel Todorov, Tom Erez, and Yuval Tassa. Mujoco: A physics engine for model-based control. In IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pages 5026–5033. IEEE, 2012.
+
+George Tucker, Surya Bhupatiraju, Shixiang Gu, Richard Turner, Zoubin Ghahramani, and Sergey Levine. The mirage of action-dependent baselines in reinforcement learning. In International Conference on Machine Learning, 2018.
+
+Matej Vecerík, Todd Hester, Jonathan Scholz, Fumin Wang, Olivier Pietquin, Bilal Piot, Nicolas Heess, ˇ Thomas Rothörl, Thomas Lampe, and Martin Riedmiller. Leveraging demonstrations for deep reinforcement learning on robotics problems with sparse rewards. arXiv preprint arXiv:1707.08817, 2017.
+
+Qing Wang, Jiechao Xiong, Lei Han, Peng Sun, Han Liu, and Tong Zhang. Exponentially weighted imitation learning for batched historical data. In Proceedings of the 32nd International Conference on Neural Information Processing Systems, pages 6291–6300, 2018.
+
+Ziyu Wang, Alexander Novikov, Konrad Zolna, Josh S Merel, Jost Tobias Springenberg, Scott E Reed, Bobak Shahriari, Noah Siegel, Caglar Gulcehre, Nicolas Heess, et al. Critic regularized regression. Advances in Neural Information Processing Systems, 33, 2020.
+
+Yifan Wu, George Tucker, and Ofir Nachum. Behavior regularized offline reinforcement learning. arXiv preprint arXiv:1911.11361, 2019.
+
+Yuchen Wu, Melissa Mozifian, and Florian Shkurti. Shaping rewards for reinforcement learning with imperfect demonstrations using generative models. In 2021 IEEE International Conference on Robotics and Automation (ICRA), pages 6628–6634. IEEE, 2021.
+
+Mengjiao Yang, Bo Dai, Ofir Nachum, George Tucker, and Dale Schuurmans. Offline policy selection under uncertainty. arXiv preprint arXiv:2012.06919, 2020.
+
+Yuke Zhu, Ziyu Wang, Josh Merel, Andrei Rusu, Tom Erez, Serkan Cabi, Saran Tunyasuvunakool, János Kramár, Raia Hadsell, Nando de Freitas, et al. Reinforcement and imitation learning for diverse visuomotor skills. arXiv preprint arXiv:1802.09564, 2018.
+
+# Checklist
+
+1. For all authors...
+
+(a) Do the main claims made in the abstract and introduction accurately reflect the paper’s contributions and scope? [Yes]   
+(b) Did you describe the limitations of your work? [Yes] See the discussion on instability in Section 4.   
+(c) Did you discuss any potential negative societal impacts of your work? [Yes] In the supplementary material.   
+(d) Have you read the ethics review guidelines and ensured that your paper conforms to them? [Yes]
+
+2. If you are including theoretical results...
+
+(a) Did you state the full set of assumptions of all theoretical results? [N/A] (b) Did you include complete proofs of all theoretical results? [N/A]
+
+3. If you ran experiments...
+
+(a) Did you include the code, data, and instructions needed to reproduce the main experimental results (either in the supplemental material or as a URL)? [Yes] Included with the supplementary material.   
+(b) Did you specify all the training details (e.g., data splits, hyperparameters, how they were chosen)? [Yes] In the supplementary material.   
+(c) Did you report error bars (e.g., with respect to the random seed after running experiments multiple times)? [Yes] See Figure 4.   
+(d) Did you include the total amount of compute and the type of resources used (e.g., type of GPUs, internal cluster, or cloud provider)? [No] Partially. Run time experiments include compute description in Section 5.
+
+4. If you are using existing assets (e.g., code, data, models) or curating/releasing new assets...
+
+(a) If your work uses existing assets, did you cite the creators? [Yes]   
+(b) Did you mention the license of the assets? [Yes] In the supplementary material.   
+(c) Did you include any new assets either in the supplemental material or as a URL? [N/A]   
+(d) Did you discuss whether and how consent was obtained from people whose data you’re using/curating? [N/A]   
+(e) Did you discuss whether the data you are using/curating contains personally identifiable information or offensive content? [N/A]
+
+5. If you used crowdsourcing or conducted research with human subjects...
+
+(a) Did you include the full text of instructions given to participants and screenshots, if applicable? [N/A]   
+(b) Did you describe any potential participant risks, with links to Institutional Review Board (IRB) approvals, if applicable? [N/A]   
+(c) Did you include the estimated hourly wage paid to participants and the total amount spent on participant compensation? [N/A]

parse/train/Q32U7dzWXpc/Q32U7dzWXpc_content_list.json

@@ -0,0 +1,1632 @@
+[
+    {
+        "type": "text",
+        "text": "A Minimalist Approach to Offline Reinforcement Learning ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Scott Fujimoto1,2 Shixiang Shane Gu2 1Mila, McGill University 2Google Research, Brain Team scott.fujimoto@mail.mcgill.ca ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Abstract ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Offline reinforcement learning (RL) defines the task of learning from a fixed batch of data. Due to errors in value estimation from out-of-distribution actions, most offline RL algorithms take the approach of constraining or regularizing the policy with the actions contained in the dataset. Built on pre-existing RL algorithms, modifications to make an RL algorithm work offline comes at the cost of additional complexity. Offline RL algorithms introduce new hyperparameters and often leverage secondary components such as generative models, while adjusting the underlying RL algorithm. In this paper we aim to make a deep RL algorithm work while making minimal changes. We find that we can match the performance of state-of-the-art offline RL algorithms by simply adding a behavior cloning term to the policy update of an online RL algorithm and normalizing the data. The resulting algorithm is a simple to implement and tune baseline, while more than halving the overall run time by removing the additional computational overheads of previous methods. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "1 Introduction ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Traditionally, reinforcement learning (RL) is thought of as a paradigm for online learning, where the interaction between the RL agent and its environment is of fundamental concern for how the agent learns. In offline RL (historically known as batch RL), the agent learns from a fixed-sized dataset, collected by some arbitrary and possibly unknown process [Lange et al., 2012]. Eliminating the need to interact with the environment is noteworthy as data collection can often be expensive, risky, or otherwise challenging, particularly in real-world applications. Consequently, offline RL enables the use of previously logged data or leveraging an expert, such as a human operator, without any of the risk associated with an untrained RL agent. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Unfortunately, the main benefit of offline RL, the lack of environment interaction, is also what makes it a challenging task. While most off-policy RL algorithms are applicable in the offline setting, they tend to under-perform due to “extrapolation error”: an error in policy evaluation, where agents tend to poorly estimate the value of state-action pairs not contained in the dataset. This in turn affects policy improvement, where agents learn to prefer out-of-distribution actions whose value has been overestimated, resulting in poor performance [Fujimoto et al., 2019b]. The solution class for this problem revolves around the idea that the learned policy should be kept close to the data-generating process (or behavior policy), and has been given a variety of names (such as batchconstrained [Fujimoto et al., 2019b], KL-control [Jaques et al., 2019], behavior-regularized [Wu et al., 2019], or policy constraint [Levine et al., 2020]) depending on how this “closeness” is chosen to be implemented. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "While there are many proposed approaches to offline RL, we remark that few are truly “simple”, and even the algorithms which claim to work with minor additions to an underlying online RL algorithm make a significant number of implementation-level adjustments. In other cases, there are unmentioned hyperparameters, or secondary components, such as generative models, which make offline RL algorithms difficult to reproduce, and even more challenging to tune. Additionally, such mixture of details slow down the run times of the algorithms, and make causal attributions of performance gains and transfers of techniques across algorithms difficult, as in the case for many online RL algorithms [Henderson et al., 2017, Tucker et al., 2018, Engstrom et al., 2020, Andrychowicz et al., 2021, Furuta et al., 2021]. This motivates the need for more minimalist approaches in offline RL. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In this paper, we ask: can we make a deep RL algorithm work offline with minimal changes? We find that we can match the performance of state-of-the-art offline RL algorithms with a single adjustment to the policy update step of the TD3 algorithm [Fujimoto et al., 2018]. TD3’s policy $\\pi$ is updated with the deterministic policy gradient [Silver et al., 2014]: ",
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+        "page_idx": 1
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+    {
+        "type": "equation",
+        "img_path": "images/d25d933166cbced66aa6585c69168282fc9ed2c132b45b8b155d8df452490d6a.jpg",
+        "text": "$$\n\\pi = \\underset { \\pi } { \\mathrm { a r g m a x } } \\mathbb { E } _ { ( s , a ) \\sim \\mathcal { D } } [ Q ( s , \\pi ( s ) ) ] .\n$$",
+        "text_format": "latex",
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+    },
+    {
+        "type": "text",
+        "text": "Our proposed change, $\\mathrm { T D } 3 { + } \\mathrm { B C }$ , is to simply add a behavior cloning term to regularize the policy: ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "equation",
+        "img_path": "images/f4991ffb110398cb95f544d2fc3b5035f36394f6f6b3880540ba303ec696cfed.jpg",
+        "text": "$$\n\\pi = \\underset { \\pi } { \\mathrm { a r g m a x } } \\mathbb { E } _ { ( s , a ) \\sim \\mathcal { D } } \\left[ \\lambda Q ( s , \\pi ( s ) ) - ( \\pi ( s ) - a ) ^ { 2 } \\right] ,\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "with a single hyperparameter $\\lambda$ to control the strength of the regularizer. This modification can be made by adjusting only a single line of code. Additionally, we remark that normalizing the states over the dataset, such that they have mean 0 and standard deviation 1, improves the stability of the learned policy. Importantly, these are the only changes made to the underlying deep RL algorithm. To accommodate reproduciblity, all of our code is open-sourced1. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We evaluate our minimal changes to the TD3 algorithm on the D4RL benchmark of continuous control tasks [Fu et al., 2020]. We find that our algorithm compares favorably against many offline RL algorithms, while being significantly easier to implement and more than halving the required computation cost. The surprising effectiveness of our minimalist approach suggests that in the context of offline RL, simpler approaches have been left underexplored in favor of more elaborate algorithmic contributions. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "2 Related Work ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Although to the best of our knowledge, we are the first to use TD3 with behavior cloning (BC) for the purpose of offline RL, we remark that combining RL with BC, and other imitation learning approaches, has been previously considered by many authors. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "$\\mathbf { R L } + \\mathbf { B C }$ . With the aim of accelerating reinforcement learning from examples (known as learning from demonstrations [Atkeson and Schaal, 1997]), BC has been used as a regularization for policy optimization with DDPG [Lillicrap et al., 2015, Nair et al., 2018, Goecks et al., 2020] and the natural policy gradient [Kakade, 2001, Rajeswaran et al., 2017], but with additional sophistication through modified replay buffers and pre-training. The most similar work to our own is a $\\mathrm { S A C + B C }$ baseline [Haarnoja et al., 2018] from Nair et al. [2020] and an unpublished course project [Booher] combining PPO [Schulman et al., 2017] with BC. ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "RL $^ +$ Imitation. Other than directly using BC with RL, imitation learning has been combined with RL in a variety of manners, such as mixed with adversarial methods [Zhu et al., 2018, Kang et al., 2018], used for pre-training [Pfeiffer et al., 2018], modifying the replay buffer [Vecerík et al., 2017, ˇ Gulcehre et al., 2020], adjusting the value function [Kim et al., 2013, Hester et al., 2017], or reward shaping [Judah et al., 2014, Wu et al., 2021]. In all cases, these methods use demonstrations as a method for overcoming challenges in exploration or improving the learning speed of the RL agent. ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Offline RL. As aforementioned, offline RL methods generally rely on some approach for “staying close” to the data. This may be implemented using an estimate of the behavior policy and then defining an explicit policy parameterization [Fujimoto et al., 2019b, Ghasemipour et al., 2020] or by using divergence regularization [Jaques et al., 2019, Kumar et al., 2019, Wu et al., 2019, Siegel et al., 2020, Guo et al., 2021, Kostrikov et al., 2021]. Other approaches use a weighted version of BC to favor high advantage actions [Wang et al., 2018, Peng et al., 2019, Siegel et al., 2020, Wang et al., ",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2020, Nair et al., 2020] or perform BC over an explicit subset of the data [Chen et al., 2020]. Some methods have modified the set of valid actions based on counts [Laroche et al., 2019] or the learned behavior policy [Fujimoto et al., 2019a]. Another direction is to implement divergence regularization as a form of pessimism into the value estimate [Nachum et al., 2019, Kumar et al., 2020, Buckman et al., 2020]. ",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Meta Analyses of RL Algorithms. There are a substantial amount of meta analysis works on online RL algorithms. While some focus on inadequacies in the experimental protocols [Henderson et al., 2017, Osband et al., 2019], others study the roles of subtle implementation details in algorithms [Tucker et al., 2018, Engstrom et al., 2020, Andrychowicz et al., 2021, Furuta et al., 2021]. For example, Tucker et al. [2018], Engstrom et al. [2020] identified that superior performances of certain algorithms were more dependent on, or even accidentally due to, minor implementation rather than algorithmic differences. Furuta et al. [2021] study two broad families of off-policy algorithms, which most offline algorithms are based on, and find that a few subtle implementation details are strongly co-adapted and critical to specific algorithms, making attributions of performance gains difficult. Recent offline research also follows a similar trend, where a number of implementation modifications are necessary for high algorithmic performances (see Table 1). In contrast, we derive our algorithm by modifying the existing TD3 with only a few lines of codes. Our results suggest the community could also learn from careful explorations of simpler alternatives, besides emphasizing algorithmic novelties and complexities. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3 Background ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "RL. Reinforcement learning (RL) is a framework aimed to deal with tasks of sequential nature. Typically, the problem is defined by a Markov decision process (MDP) $( S , { \\mathcal { A } } , { \\mathcal { R } } , p , \\gamma )$ , with state space $s$ , action space $\\mathcal { A }$ , scalar reward function $\\mathcal { R }$ , transition dynamics $p$ , and discount factor $\\gamma$ [Sutton and Barto, 1998]. The behavior of an RL agent is determined by a policy $\\pi$ which maps states to actions (deterministic policy), or states to a probability distribution over actions The objective of an RL agent is to maximize the expected discounted return $\\mathbb { E } _ { \\pi } [ \\sum _ { t = 0 } ^ { \\infty } \\bar { \\gamma } ^ { t } r _ { t + 1 } \\bar { ] } .$ which is the expected cumulative sum of rewards when following the policy in the MDP, where the importance of the horizon is determined by the discount factor. We measure this objective by a value function, which measures the expected discounted return after taking the action $a$ in state $s$ : $\\begin{array} { r } { Q ^ { \\pi } ( s , a ) = \\mathbb { E } _ { \\pi } \\left[ \\sum _ { t = 0 } ^ { \\infty } \\gamma ^ { t } r _ { t + 1 } | s _ { 0 } = s , \\dot { a } _ { 0 } = a \\right] . } \\end{array}$ . ",
+        "bbox": [
+            173,
+            414,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "BC. Another approach for training policies is through imitation of an expert or behavior policy. Behavior cloning (BC) is an approach for imitation learning [Pomerleau, 1991], where the policy is trained with supervised learning to directly imitate the actions of a provided dataset. Unlike RL, this process is highly dependent on the performance of the data-collecting process. ",
+        "bbox": [
+            174,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Offline RL. Offline RL breaks the assumption that the agent can interact with the environment. Instead, the agent is provided a fixed dataset which has been collected by some unknown datagenerating process (such as a collection of behavior policies). This setting may be considered more challenging as the agent loses the opportunity to explore the MDP according to its current beliefs, and instead from infer good behavior from only the provided data. ",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "One challenge for offline RL is the problem of extrapolation error [Fujimoto et al., 2019b], which is generalization error in the approximate value function, induced by selecting actions not contained in the dataset. Simply put, it is difficult to evaluate the expected value of a policy which is sufficiently different from the behavior policy. Consequently, algorithms have taken the approach of constraining or regularizing the policy to stay near to the actions in the dataset [Levine et al., 2020]. ",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "4 Challenges in Offline RL ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            787,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In this section, we identify key open challenges in offline RL through analyzing and evaluating prior algorithms. We believe these challenges highlight the importance of minimalist approaches, where performance can be easily attributed to algorithmic contributions, rather than entangled with the specifics of implementation. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Implementation and Tuning Complexities. RL algorithms are notoriously difficult to implement and tune [Henderson et al., 2017, Engstrom et al., 2020, Furuta et al., 2021], where minor code-level optimizations and hyperparameters can have non-trivial impact of performance and stability. This problem may be additionally amplified in the context of offline RL, where evaluating changes to implementation and hyperparameters is counter-intuitive to the nature of offline RL, which explicitly aims to eliminate environment interactions [Paine et al., 2020, Yang et al., 2020]. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "table",
+        "img_path": "images/29ec8410421bf5f2de7d087855959ba475eac919e637b157fed3ce8726042100.jpg",
+        "table_caption": [],
+        "table_footnote": [
+            "Table 1: Implementation changes offline RL algorithms make to the underlying base RL algorithm. † corresponds to details that add additional hyperparameter(s), and ‡ corresponds to ones that add a computational cost. "
+        ],
+        "table_body": "<table><tr><td></td><td>CQL [Kumar et al., 2020]</td><td>Fisher-BRC [Kostrikov et al.,2021]</td><td>TD3+BC (Ours)</td></tr><tr><td>Algorithmic Adjustments</td><td>Add regularizer to critic† Approximate logsumexp with sampling‡</td><td>Train a generative modelt‡ Replace critic with offset function Gradient penalty on offset function†</td><td>Add a BC term+</td></tr><tr><td>Implementation Adjustments</td><td>Architecture†‡ Actor learning rate† Pre-training actor Remove SAC entropy term Max over sampled actionst</td><td>Architecture†‡ Reward bonus† Remove SAC entropy term</td><td>Normalize states</td></tr></table>",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/5b288cacfc289e3f9648574303a9b842ef1c5faa8fdaf11c9a0059088dead6a5.jpg",
+        "image_caption": [
+            "Figure 1: Percent difference of performance of offline RL algorithms and their simplified versions which remove implementation adjustments to their underlying algorithm. $\\mathbf { H } \\mathbf { C } =$ HalfCheetah, Hop $=$ Hopper, $\\mathbf { W } =$ Walker, $\\mathbf { r } =$ random, $\\mathbf { m } =$ medium, $\\mathbf { m r } =$ medium-replay, me $=$ medium-expert, ${ \\mathfrak { e } } =$ expert. Huge drops in performances show that the implementation complexities are crucial for achieving the best results in these prior algorithms. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Most offline RL algorithms are built explicitly on top of an existing off-policy deep RL algorithm, such as TD3 [Fujimoto et al., 2018] or SAC [Haarnoja et al., 2018], but then further modify the underlying algorithm with “non-algorithmic” implementation changes, such as modifications to network architecture, learning rates, or pre-training the actor network. We remark that a desirable property of an offline RL algorithm would be to minimally modify the underlying algorithm, so as to reduce the space of possible adjustments required to achieve a strong performance. ",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In Table 1 we examine the particular modifications made by two recent offline RL algorithms, CQL [Kumar et al., 2020] and Fisher-BRC [Kostrikov et al., 2021]. On top of algorithmic changes, CQL also adds a pre-training phase where the actor is only trained with imitation learning and selects the max action over a sampled set of actions from the policy during evaluation. Fisher-BRC adds a constant reward bonus to every transition. Both methods modify SAC by removing the entropy term in the target update and modify the default network architecture. These changes add supplementary hyperparameters which may need to be tuned or increase computational costs. ",
+        "bbox": [
+            174,
+            670,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In the online setting, these changes are relatively inconsequential and could be validated with some simple experimentation. However, in the offline setting, where we cannot interact with the environment, making additional adjustments to the underlying algorithm should be considered as more costly as validating their effectiveness is no longer a trivial additional step. This is also problematic because unlike the algorithmic changes proposed by these papers, these implementation details are not well justified, meaning there is much less intuition as to when to include these details, or how to adjust them with minimal experimentation. In the case of the D4RL benchmark on MuJoCo tasks [Todorov et al., 2012, Fu et al., 2020], we have a strong prior that our base deep RL algorithm performs well, as SAC/TD3 are considered state-of-the-art (or nearly) in these domains. If additional changes are necessary, then it suggests the algorithmic contributions alone are insufficient. ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/49e35581bc108e701bb737cd283a99ee49ef68eddb42fdfbb560bd49f5647002.jpg",
+        "image_caption": [
+            "Figure 2: Percent difference of the worst episode during the 10 evaluation episodes at the last evaluation. This measures the deviations in performance at single point in time. $\\mathrm { H C } =$ HalfCheetah, Hop $=$ Hopper, $\\mathbf { W } =$ Walker, $\\mathbf { r } =$ random, $\\mathbf { m } =$ medium, $\\mathbf { m r } =$ medium-replay, me $=$ medium-expert, ${ \\bf e } =$ expert. While online algorithms (TD3) typically have small episode variances per trained policy (as they should at convergence), all offline algorithms have surprisingly high episodic variances for trained policies. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "img_path": "images/58530fed78a56afc2645b7777d9cf9e5929c1e774e6d4e92fd14f879f6f2ea1c.jpg",
+        "image_caption": [
+            "Figure 3: Percent difference of the worst evaluation during the last 10 evaluations. This measures the deviations in performance over a period of time. $\\mathrm { H C } =$ HalfCheetah, Hop $=$ Hopper, $\\mathbf { W } =$ Walker, $\\mathbf { r } =$ random, $\\mathbf { m } =$ medium, $\\mathbf { m r } =$ medium-replay, me $=$ medium-expert, ${ \\bf e } =$ expert. Similarly to the result in Figure 2, all offline-trained policies have significant variances near the final stage of training that are absent in the online setting. "
+        ],
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+        "type": "text",
+        "text": "In Figure 1 we examine the percent difference in performance when removing the implementation changes in CQL and Fisher-BRC. There is a significant drop in performance in many of the tasks. This is not necessarily a death knell to these algorithms, as it is certainly possible these changes could be kept without tuning when attempting new datasets and domains. However, since neither paper make mention of a training/validation split, we can only assume these changes were made with their evaluation datasets in mind (D4RL, in this instance), and remark there is insufficient evidence that these changes may be universal. Ultimately, we make this point not to suggest a fundamental flaw with pre-existing algorithms, but to suggest that there should be a preference for making minimal adjustments to the underlying RL algorithm, to reduce the need for hyperparameter tuning. ",
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+        "type": "text",
+        "text": "Extra Computation Requirement. A secondary motivating factor for minimalism is avoiding the additional computational costs associated with modifying the underlying algorithm (in particular architecture) and more complex algorithmic ideas. In Table 3 (contained later in Section 6), we examine the run time of offline RL algorithms, as well as the change in cost over the underlying algorithm, and find their is a significant computational cost associated with these modifications. On top of the architecture changes, for CQL this is largely due to the costs of logsumexp over multiple sampled actions, and for Fisher-BRC, the costs associated with training the independent generative model. Since an objective of offline RL is to take advantage of existing, potentially large, datasets, there should be a preference for scalable and efficient solutions. Of course, run time should not come at the cost of performance, but as we will later demonstrate, there exists a simple, and computationally-free, approach for offline RL which matches the performance of current state-of-the-art algorithms. ",
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+    {
+        "type": "text",
+        "text": "Instability of Trained Policies. In analyzing the final trained policies of prior offline algorithms, we learned of a tangential, and open, challenge in the form of instability. In online RL, if the current policy is unsatisfactory, we can use checkpoints of previous iterations of the policy, or to simply continue training. However, in offline RL, the evaluation should only occur once by definition, greatly increasing the importance of the single policy at evaluation time. We highlight two versions of instability in offline RL. Figure 2 shows that in contrast to the online-trained policy, which converges to a robust low-variance policy, the offline-trained policy exhibits huge variances in performance during a single evaluation. Therefore, even if the average performance is reasonable, the agent may still perform poorly on some episodes. Figure 3 shows instability over the set of evaluations, which means the performance of the agent may be dependent on the specific stopping point chosen for evaluation. This questions the empirical effectiveness of offline RL for safety-critical real-world use cases [Mandel et al., 2014, Gottesman et al., 2018, Gauci et al., 2018, Jaques et al., 2019, Matsushima et al., 2020] as well as the current trend of reporting only the mean-value of the final policy in offline benchmarking [Fu et al., 2020]. ",
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+        "type": "text",
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+        "type": "text",
+        "text": "Such variances are not likely caused by high policy entropies (e.g. $\\mathrm { T D } 3 { + } \\mathrm { B C }$ trains a deterministic policy), but rather our hypothesis is that such a problem is due to distributional shifts issues and poor generalizations across unobserved states caused by offline nature of training [Ross et al., 2011], where the optimized policy is never allowed to execute in the environment, similarly as in BC. This trait of offline RL algorithms appears to be consistent across all offline algorithms we evaluated, even for our minimalistic $\\mathrm { T D } 3 { + } \\mathrm { B C }$ that is only a few lines change from TD3. While we could not solve this challenge sufficiently within the scope of this work, the fact that this is reproducible even in the minimalistic variant proves that this a fundamental problem shared by all offline training settings, and is a critical problem for the community to study in the future. ",
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+    {
+        "type": "text",
+        "text": "5 A Minimalist Offline RL Algorithm ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "A key problem in offline RL, extrapolation error, can be summarized as the inability to properly evaluate out-of-distribution actions. Consequently, there has been a variety of different approaches to limiting, or regularizing, action selection such that the learned policy is easier to evaluate with the given dataset. We remark that while minimizing say, KL divergence, is a both logical and valid approach for reducing extrapolation error, there is no fundamental argument why minimizing one divergence or distance metric should be better than another. Thus, rather than derive an entirely new approach, we focus on simplicity, and present an offline RL algorithm which requires minimal modifications to a pre-existing deep RL algorithm. As discussed in Section 4 a minimalist approach has a variety of benefits, such as reducing the number of hyperparameters to tune, increasing scalability by reducing computational costs, and providing an avenue for analyzing problems by disentangling algorithmic contributions from implementation details. ",
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+        "text": "We now describe such an approach to offline RL. Our algorithm builds on top of TD3 [Fujimoto et al., 2018], making only two straightforward changes. Firstly, we add a behavior cloning regularization term to the standard policy update step of TD3, to push the policy towards favoring actions contained in the dataset $\\mathcal { D }$ : ",
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+        "type": "equation",
+        "img_path": "images/b6dbd6ccfe05a67b85c8e85c37d6bc9fd65f6df3bc8cb1262a0f6df36c4236bd.jpg",
+        "text": "$$\n\\pi = \\underset { \\pi } { \\operatorname { a r g m a x } } \\mathbb { E } _ { s \\sim \\mathcal { D } } [ Q ( s , \\pi ( s ) ) ]  \\pi = \\underset { \\pi } { \\operatorname { a r g m a x } } \\mathbb { E } _ { ( s , a ) \\sim \\mathcal { D } } [ \\lambda Q ( s , \\pi ( s ) ) - ( \\pi ( s ) - a ) ^ { 2 } ] .\n$$",
+        "text_format": "latex",
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+        "type": "text",
+        "text": "Secondly, we normalize the features of every state in the provided dataset. Let $s _ { i }$ be the ith feature of the state $s$ , let $\\mu _ { i } \\ \\sigma _ { i }$ be the mean and standard deviation, respectively, of the ith feature across the dataset: ",
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+    {
+        "type": "equation",
+        "img_path": "images/01b079136607e36fba05c3b2e7d1903c4947fba4b1e9c4ce9de844ccbde6dc1a.jpg",
+        "text": "$$\ns _ { i } = \\frac { s _ { i } - \\mu _ { i } } { \\sigma _ { i } + \\epsilon } ,\n$$",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "where $\\epsilon$ is a small normalization constant (we use $1 0 ^ { - 3 }$ ). While we remark this is a commonly used implementation detail in many deep RL algorithms [Raffin et al., 2019], we highlight it as (1) we want complete transparency about all implementation changes and (2) normalizing provides a non-trivial performance benefit in offline RL, where it is particularly well-suited as the dataset remains fixed. ",
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+        "text": "While the choice of $\\lambda$ in Equation (3) is ultimately just a hyperparameter, we observe that the balance between RL (in maximizing $Q$ ) and imitation (in minimizing the BC term), is highly susceptible to the scale of $Q$ . If we assume an action range of $[ - 1 , 1 ]$ , the BC term is at most 4, however the range of $Q$ will be a function of the scale of the reward. Consequently, we can add a normalization term into $\\lambda$ . Given the dataset of $N$ transitions $( s _ { i } , a _ { i } )$ , we define the scalar $\\lambda$ as: ",
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+    {
+        "type": "equation",
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+        "text": "$$\n\\lambda = { \\frac { \\alpha } { { \\frac { 1 } { N } } \\sum _ { ( s _ { i } , a _ { i } ) } | Q ( s _ { i } , a _ { i } ) | } } .\n$$",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "This is simply a normalization term based on the average absolute value of $Q$ . In practice, we estimate this mean term over mini-batches, rather than the entire dataset. Although this term includes $Q$ , it is ",
+        "bbox": [
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+    {
+        "type": "table",
+        "img_path": "images/2c90edf32b3661ec004dabb8f0e42e9d632574a72824eab2e720a43a63755c8e.jpg",
+        "table_caption": [
+            "Table 2: Average normalized score over the final 10 evaluations and 5 seeds. The highest performing scores are highlighted. CQL and Fisher-BRC are re-run using author-provided implementations to ensure an identical evaluation process, while BRAC and AWAC use previously reported results. $\\pm$ captures the standard deviation over seeds. $\\mathrm { T D } 3 { + } \\mathrm { B C }$ achieves effectively the same performances as the state-of-the-art Fisher-BRC, despite being much simpler to implement and tune and more than halving the computation cost. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td></td><td>BC</td><td>BRAC-p</td><td>AWAC</td><td>CQL</td><td>Fisher-BRC</td><td>TD3+BC</td></tr><tr><td rowspan=\"3\">aopaer</td><td>HalfCheetah</td><td>2.0 ±0.1</td><td>23.5</td><td>2.2</td><td>21.7 ±0.9</td><td>32.2 ±2.2</td><td>10.2 ±1.3</td></tr><tr><td>Hopper</td><td>9.5 ±0.1</td><td>11.1</td><td>9.6</td><td>10.7 ±0.1</td><td>11.4 ±0.2</td><td>11.0 ±0.1</td></tr><tr><td>Walker2d</td><td>1.2 ±0.2</td><td>0.8</td><td>5.1</td><td>2.7 ±1.2</td><td>0.6 ±0.6</td><td>1.4 ±1.6</td></tr><tr><td rowspan=\"3\">airea</td><td>HalfCheetah</td><td>36.6 ±0.6</td><td>44.0</td><td>37.4</td><td>37.2 ±0.3</td><td>41.3 ±0.5</td><td>42.8 ±0.3</td></tr><tr><td>Hopper</td><td>30.0 ±0.5</td><td>31.2</td><td>72.0</td><td>44.2 ±10.8</td><td>99.4 ±0.4</td><td>99.5 ±1.0</td></tr><tr><td>Walker2d</td><td>11.4 ±6.3</td><td>72.7</td><td>30.1</td><td>57.5 ±8.3</td><td>79.5 ±1.0</td><td>79.7 ±1.8</td></tr><tr><td rowspan=\"3\">wnipen rrer</td><td>HalfCheetah</td><td>34.7 ±1.8</td><td>45.6</td><td></td><td>41.9 ±1.1</td><td>43.3 ±0.9</td><td>43.3 ±0.5</td></tr><tr><td>Hopper</td><td>19.7 ±5.9</td><td>0.7</td><td></td><td>28.6 ±0.9</td><td>35.6 ±2.5</td><td>31.4 ±3.0</td></tr><tr><td>Walker2d</td><td>8.3 ±1.5</td><td>-0.3</td><td>1</td><td>15.8 ±2.6</td><td>42.6 ±7.0</td><td>25.2 ±5.1</td></tr><tr><td rowspan=\"3\">wnipen adx</td><td>HalfCheetah</td><td>67.6±13.2</td><td>43.8</td><td>36.8</td><td>27.1 ±3.9</td><td>96.1 ±9.5</td><td>97.9 ±4.4</td></tr><tr><td>Hopper</td><td>89.6 ±27.6</td><td>1.1</td><td>80.9</td><td>111.4 ±1.2</td><td>90.6 ±43.3</td><td>112.2 ±0.2</td></tr><tr><td>Walker2d</td><td>12.0 ±5.8</td><td>-0.3</td><td>42.7</td><td>68.1 ±13.1</td><td>103.6 ±4.6</td><td>101.1 ±9.3</td></tr><tr><td rowspan=\"3\">Jadxg</td><td>HalfCheetah</td><td>105.2 ±1.7</td><td>3.8</td><td>78.5</td><td>82.4 ±7.4</td><td>106.8 ±3.0</td><td>105.7 ±1.9</td></tr><tr><td>Hopper</td><td>111.5 ±1.3</td><td>6.6</td><td>85.2</td><td>111.2 ±2.1</td><td>112.3 ±0.2</td><td>112.2 ±0.2</td></tr><tr><td>Walker2d</td><td>56.0 ±24.9</td><td>-0.2</td><td>57.0</td><td>103.8 ±7.6</td><td>79.9 ±32.4</td><td>105.7 ±2.7</td></tr><tr><td></td><td>Total</td><td>595.3 ±91.5</td><td>284.1</td><td>1</td><td>764.3 ±61.5</td><td>974.6 ±108.3</td><td>979.3 ±33.4</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "not differentiated over, and is simply used to scale the loss. This formulation has the added benefit of normalizing the learning rate across tasks, as the gradient $\\nabla _ { a } Q ( s , a )$ will also be dependent on the scale of $Q$ . We use $\\alpha = 2 . 5$ in our experiments. ",
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+    {
+        "type": "text",
+        "text": "This completes the description of $\\mathrm { T D } 3 { + } \\mathrm { B C }$ . The Equations (3), (4), and (5) summarizes the entirety of our changes to TD3, and can be implemented by modifying only a handful of lines in most codebases. ",
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+    {
+        "type": "text",
+        "text": "6 Experiments ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We evaluate our proposed approach on the D4RL benchmark of OpenAI gym MuJoCo tasks [Todorov et al., 2012, Brockman et al., 2016, Fu et al., 2020], which encompasses a variety of dataset settings and domains. Our offline RL baselines include two state-of-the-art algorithms, CQL [Kumar et al., 2020] and Fisher-BRC [Kostrikov et al., 2021], as well as BRAC [Wu et al., 2019] and AWAC [Nair et al., 2020] due to their algorithmic simplicity. ",
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+    {
+        "type": "text",
+        "text": "To ensure a fair and identical experimental evaluation across algorithms, we re-run the state-of-theart algorithms CQL and Fisher-BRC using the author-provided implementations23. We train each algorithm for 1 million time steps and evaluate every 5000 time steps. Each evaluation consists of 10 episodes. Results for BRAC are obtained from the D4RL benchmark and from the CQL paper, while the AWAC results are obtained directly from the paper. BC results were obtained using our own implementation. ",
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+    {
+        "type": "text",
+        "text": "D4RL. We report the final performance results in Table 2 and display the learning curves in Figure 4. Although our method is very simplistic in nature, it surpasses, or matches, the performance of the current state-of-the-art offline RL algorithms in most tasks. Only Fisher-BRC exhibits a comparable performance4. Examining the learning curves, we can see that our approach achieves a similar learning speed and stability, without requiring any pre-training phase. ",
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+    {
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+        "img_path": "images/f3e0dfc3ac09294df518cab6aebee696472ea86ab296c286486976678110dd2c.jpg",
+        "image_caption": [
+            "Figure 4: Learning curves comparing the performance of $\\mathrm { T D } 3 { + } \\mathrm { B C }$ against offline RL baselines in the D4RL datasets. Curves are averaged over 5 seeds, with the shaded area representing the standard deviation across seeds. $\\mathrm { T D } 3 { + } \\mathrm { B C }$ exhibits a similar learning speed and final performance as the state-of-the-art Fisher-BRC, without the need of pre-training a generative model. "
+        ],
+        "image_footnote": [],
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+        "page_idx": 7
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+    {
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+    {
+        "type": "text",
+        "text": "",
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+    {
+        "type": "text",
+        "text": "Run time. We evaluate run time of training each of the offline RL algorithms for 1 million time steps, using the author-provoided implementations. Additionally, for fair comparison, we re-implement Fisher-BRC, allowing each method to be compared in the same framework (PyTorch [Paszke et al., 2019]). The results are reported in Table 3. Unsurprisingly, we find our approach compares favorably against previous methods in terms of wall-clock training time, effectively adding no cost to the underlying TD3 algorithm. All run time experiments were run with a single GeForce GTX 1080 GPU and an Intel Core i7-6700K CPU at 4.00GHz. ",
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+    {
+        "type": "text",
+        "text": "Ablation. In Figure 5, we perform an ablation study over the components in our method. As noted in previous work [Fujimoto et al., 2019b], without behavior cloning regularization, the RL algorithm alone is insufficient to achieve a high performance (except on some of the random data sets). We also note that our algorithm never underperforms vanilla behavior cloning, even on the expert tasks. Predictably, the removal of state normalization has the least significant impact, but it still provides some benefit across a range of tasks while being a minor adjustment. In Figure 6, we evaluate the sensitivity of the algorithm to the hyperparameter α, where the weighting λ = P α(s,a) |Q(s,a)| on the value function is determined by $\\alpha$ . On many tasks, our approach is robust to this weighting factor, but note the performance on a subset of tasks begins to decrease as $\\alpha$ begins to more heavily favor imitation $( \\alpha = 1$ ) or RL ( $\\alpha = 4$ ). ",
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+    },
+    {
+        "type": "image",
+        "img_path": "images/c3a3615df3f3991fa97861f847077b6e877772a07fe271f60ab186a38e136a87.jpg",
+        "image_caption": [
+            "Figure 5: Percent difference of the performance of an ablation of our proposed approach, compared to the full algorithm. $\\mathrm { T D } 3 + \\lambda + \\mathrm { B C } + \\mathrm { N o r m }$ refers to the complete algorithm, where Norm refers to the state feature normalization. HC $=$ HalfCheetah, Hop $=$ Hopper, $\\mathbf { W } =$ Walker, $\\mathbf { r } =$ random, $\\mathbf { m } =$ medium, $\\mathbf { m r } =$ medium-replay, me $=$ medium-expert, ${ \\mathfrak { e } } =$ expert. As expected, both BC and TD3 are necessary components to achieve a strong performance. While removing state normalization is not devastating to the performance of the algorithm, we remark it provides a boost in performance across many tasks, while being a straightforward addition. "
+        ],
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+    {
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+        "image_caption": [
+            "Figure 6: Percent difference of the performance of an ablation over $\\alpha$ , compared to the full algorithm. Recall the form of the sole hyperparameter $\\begin{array} { r } { \\lambda = \\frac { \\alpha } { \\sum \\vert Q ( s , a ) \\vert } } \\end{array}$ , where $\\lambda$ weights the $Q$ function during the policy update. $\\alpha = 2 . 5$ is used by default. $\\mathrm { H C } =$ HalfCheetah, $\\mathrm { H o p } = \\mathrm { H o p p e r }$ , ${ \\bf W } =$ Walker, $\\mathbf { r } =$ random, $\\textrm { m } =$ medium, $\\mathbf { m r } =$ medium-replay, me $=$ medium-expert, ${ \\bf e } =$ expert. While there is effectively no performance difference between $\\alpha = 2$ and $\\alpha = 3$ , we remark that performance begins to degrade on select tasks as the algorithm begins to approach more RL $\\alpha = 4$ ) or imitation $( \\alpha = 1$ ). "
+        ],
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+    {
+        "type": "text",
+        "text": "7 Conclusion ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Most recent advances in offline RL center around the idea of regularizing policy actions to be close to the support within batch data, and yet many state-of-the-art algorithms have significant complexities and additional modifications beyond base algorithms that lead to not only much slower run time, but also intractable attributions for sources of performance gains. Instead of complexity we optimize for simplicity, and introduce a minimalistic algorithm that achieves a state-of-the-art performance but is only a few lines of changes from the base TD3 algorithm, uses less than half of the computation time of competing algorithms, and has only one additional hyperparameter. ",
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+    {
+        "type": "text",
+        "text": "Additionally, we highlight existing open challenges in offline RL research, including not only the extra implementation, computation, and hyperparameter-tuning complexities that we successfully address in this work, but also call attention to the neglected problem of high episodic variance in offline-trained policies compared to online-trained (see Figures 2 and 3) that we as the community should address in future works and benchmarking. Finally, we believe the sheer simplicity of our approach highlights a possible overemphasis on algorithmic complexity made by the community, and we hope to inspire future work to revisit simpler alternatives which may have been overlooked. ",
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "References ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            89,
+            267,
+            106
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Marcin Andrychowicz, Anton Raichuk, Piotr Stanczyk, Manu Orsini, Sertan Girgin, Raphaël Marinier, ´ Leonard Hussenot, Matthieu Geist, Olivier Pietquin, Marcin Michalski, Sylvain Gelly, and Olivier Bachem. What matters for on-policy deep actor-critic methods? a large-scale study. In International Conference on Learning Representations, 2021. ",
+        "bbox": [
+            174,
+            114,
+            826,
+            170
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Christopher G Atkeson and Stefan Schaal. Robot learning from demonstration. In Proceedings of the Fourteenth International Conference on Machine Learning, pages 12–20, 1997. ",
+        "bbox": [
+            174,
+            181,
+            821,
+            210
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Jonathan Booher. $\\mathrm { B c + r l }$ : Imitation learning from non-optimal demonstrations. URL https://web. stanford.edu/\\~jaustinb/papers/CS234.pdf. ",
+        "bbox": [
+            173,
+            222,
+            823,
+            251
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Greg Brockman, Vicki Cheung, Ludwig Pettersson, Jonas Schneider, John Schulman, Jie Tang, and Wojciech Zaremba. Openai gym, 2016. ",
+        "bbox": [
+            173,
+            262,
+            825,
+            291
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Jacob Buckman, Carles Gelada, and Marc G Bellemare. The importance of pessimism in fixed-dataset policy optimization. arXiv preprint arXiv:2009.06799, 2020. ",
+        "bbox": [
+            169,
+            301,
+            825,
+            332
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Xinyue Chen, Zijian Zhou, Zheng Wang, Che Wang, Yanqiu Wu, and Keith Ross. Bail: Bestaction imitation learning for batch deep reinforcement learning. Advances in Neural Information Processing Systems, 33, 2020. ",
+        "bbox": [
+            173,
+            342,
+            825,
+            386
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Logan Engstrom, Andrew Ilyas, Shibani Santurkar, Dimitris Tsipras, Firdaus Janoos, Larry Rudolph, and Aleksander Madry. Implementation matters in deep rl: A case study on ppo and trpo. In International Conference on Learning Representations, 2020. ",
+        "bbox": [
+            173,
+            396,
+            826,
+            439
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Justin Fu, Aviral Kumar, Ofir Nachum, George Tucker, and Sergey Levine. D4rl: Datasets for deep data-driven reinforcement learning. 2020. ",
+        "bbox": [
+            171,
+            450,
+            823,
+            479
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Scott Fujimoto, Herke van Hoof, and David Meger. Addressing function approximation error in actorcritic methods. In International Conference on Machine Learning, volume 80, pages 1587–1596. PMLR, 2018. ",
+        "bbox": [
+            173,
+            491,
+            825,
+            532
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Scott Fujimoto, Edoardo Conti, Mohammad Ghavamzadeh, and Joelle Pineau. Benchmarking batch deep reinforcement learning algorithms. arXiv preprint arXiv:1910.01708, 2019a. ",
+        "bbox": [
+            173,
+            545,
+            823,
+            574
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Scott Fujimoto, David Meger, and Doina Precup. Off-policy deep reinforcement learning without exploration. In International Conference on Machine Learning, pages 2052–2062, 2019b. ",
+        "bbox": [
+            173,
+            584,
+            821,
+            614
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Hiroki Furuta, Tadashi Kozuno, Tatsuya Matsushima, Yutaka Matsuo, and Shixiang Shane Gu. Identifying co-adaptation of algorithmic and implementational innovations in deep reinforcement learning: A taxonomy and case study of inference-based algorithms. arXiv preprint arXiv:2103.17258, 2021. ",
+        "bbox": [
+            173,
+            626,
+            826,
+            681
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Jason Gauci, Edoardo Conti, Yitao Liang, Kittipat Virochsiri, Yuchen He, Zachary Kaden, Vivek Narayanan, Xiaohui Ye, Zhengxing Chen, and Scott Fujimoto. Horizon: Facebook’s open source applied reinforcement learning platform. arXiv preprint arXiv:1811.00260, 2018. ",
+        "bbox": [
+            174,
+            693,
+            823,
+            736
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Seyed Kamyar Seyed Ghasemipour, Dale Schuurmans, and Shixiang Shane Gu. Emaq: Expected-max q-learning operator for simple yet effective offline and online rl. arXiv preprint arXiv:2007.11091, 2020. ",
+        "bbox": [
+            173,
+            746,
+            826,
+            789
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Vinicius G Goecks, Gregory M Gremillion, Vernon J Lawhern, John Valasek, and Nicholas R Waytowich. Integrating behavior cloning and reinforcement learning for improved performance in dense and sparse reward environments. In Proceedings of the 19th International Conference on Autonomous Agents and MultiAgent Systems, pages 465–473, 2020. ",
+        "bbox": [
+            174,
+            801,
+            825,
+            858
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Omer Gottesman, Fredrik Johansson, Joshua Meier, Jack Dent, Donghun Lee, Srivatsan Srinivasan, Linying Zhang, Yi Ding, David Wihl, Xuefeng Peng, et al. Evaluating reinforcement learning algorithms in observational health settings. arXiv preprint arXiv:1805.12298, 2018. ",
+        "bbox": [
+            174,
+            869,
+            825,
+            911
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Caglar Gulcehre, Tom Le Paine, Bobak Shahriari, Misha Denil, Matt Hoffman, Hubert Soyer, Richard Tanburn, Steven Kapturowski, Neil Rabinowitz, Duncan Williams, Gabriel Barth-Maron, Ziyu Wang, Nando de Freitas, and Worlds Team. Making efficient use of demonstrations to solve hard exploration problems. In International Conference on Learning Representations, 2020. ",
+        "bbox": [
+            173,
+            90,
+            825,
+            147
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Yijie Guo, Shengyu Feng, Nicolas Le Roux, Ed Chi, Honglak Lee, and Minmin Chen. Batch reinforcement learning through continuation method. In International Conference on Learning Representations, 2021. ",
+        "bbox": [
+            176,
+            155,
+            821,
+            199
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Tuomas Haarnoja, Aurick Zhou, Pieter Abbeel, and Sergey Levine. Soft actor-critic: Off-policy maximum entropy deep reinforcement learning with a stochastic actor. In International Conference on Machine Learning, volume 80, pages 1861–1870. PMLR, 2018. ",
+        "bbox": [
+            174,
+            207,
+            826,
+            251
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Peter Henderson, Riashat Islam, Philip Bachman, Joelle Pineau, Doina Precup, and David Meger. Deep reinforcement learning that matters. In AAAI Conference on Artificial Intelligence, 2017. ",
+        "bbox": [
+            174,
+            258,
+            823,
+            287
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Todd Hester, Matej Vecerik, Olivier Pietquin, Marc Lanctot, Tom Schaul, Bilal Piot, Dan Horgan, John Quan, Andrew Sendonaris, Gabriel Dulac-Arnold, et al. Deep q-learning from demonstrations. arXiv preprint arXiv:1704.03732, 2017. ",
+        "bbox": [
+            174,
+            296,
+            826,
+            339
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Natasha Jaques, Asma Ghandeharioun, Judy Hanwen Shen, Craig Ferguson, Agata Lapedriza, Noah Jones, Shixiang Gu, and Rosalind Picard. Way off-policy batch deep reinforcement learning of implicit human preferences in dialog. arXiv preprint arXiv:1907.00456, 2019. ",
+        "bbox": [
+            174,
+            348,
+            826,
+            391
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Kshitij Judah, Alan Fern, Prasad Tadepalli, and Robby Goetschalckx. Imitation learning with demonstrations and shaping rewards. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 28, 2014. ",
+        "bbox": [
+            173,
+            398,
+            826,
+            441
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Sham Kakade. A natural policy gradient. In Proceedings of the 14th International Conference on Neural Information Processing Systems: Natural and Synthetic, pages 1531–1538, 2001. ",
+        "bbox": [
+            173,
+            450,
+            823,
+            481
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Bingyi Kang, Zequn Jie, and Jiashi Feng. Policy optimization with demonstrations. In International Conference on Machine Learning, pages 2469–2478. PMLR, 2018. ",
+        "bbox": [
+            171,
+            488,
+            823,
+            517
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Beomjoon Kim, Amir-massoud Farahmand, Joelle Pineau, and Doina Precup. Learning from limited demonstrations. In Advances in Neural Information Processing Systems, pages 2859–2867, 2013. ",
+        "bbox": [
+            173,
+            526,
+            825,
+            556
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Ilya Kostrikov, Jonathan Tompson, Rob Fergus, and Ofir Nachum. Offline reinforcement learning with fisher divergence critic regularization. arXiv preprint arXiv:2103.08050, 2021. ",
+        "bbox": [
+            169,
+            564,
+            823,
+            593
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Aviral Kumar, Justin Fu, Matthew Soh, George Tucker, and Sergey Levine. Stabilizing off-policy q-learning via bootstrapping error reduction. In Advances in Neural Information Processing Systems, pages 11784–11794, 2019. ",
+        "bbox": [
+            174,
+            601,
+            823,
+            643
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Aviral Kumar, Aurick Zhou, George Tucker, and Sergey Levine. Conservative q-learning for offline reinforcement learning. arXiv preprint arXiv:2006.04779, 2020. ",
+        "bbox": [
+            169,
+            652,
+            823,
+            683
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Sascha Lange, Thomas Gabel, and Martin Riedmiller. Batch reinforcement learning. In Reinforcement learning, pages 45–73. Springer, 2012. ",
+        "bbox": [
+            173,
+            690,
+            823,
+            719
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Romain Laroche, Paul Trichelair, and Remi Tachet Des Combes. Safe policy improvement with baseline bootstrapping. In International Conference on Machine Learning, pages 3652–3661. PMLR, 2019. ",
+        "bbox": [
+            174,
+            728,
+            825,
+            771
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Sergey Levine, Aviral Kumar, George Tucker, and Justin Fu. Offline reinforcement learning: Tutorial, review, and perspectives on open problems. arXiv preprint arXiv:2005.01643, 2020. ",
+        "bbox": [
+            169,
+            779,
+            825,
+            809
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Timothy P Lillicrap, Jonathan J Hunt, Alexander Pritzel, Nicolas Heess, Tom Erez, Yuval Tassa, David Silver, and Daan Wierstra. Continuous control with deep reinforcement learning. arXiv preprint arXiv:1509.02971, 2015. ",
+        "bbox": [
+            174,
+            818,
+            825,
+            861
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Travis Mandel, Yun-En Liu, Sergey Levine, Emma Brunskill, and Zoran Popovic. Offline policy evaluation across representations with applications to educational games. In International Conference on Autonomous Agents and Multiagent Systems, 2014. ",
+        "bbox": [
+            174,
+            868,
+            826,
+            911
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Tatsuya Matsushima, Hiroki Furuta, Yutaka Matsuo, Ofir Nachum, and Shixiang Gu. Deploymentefficient reinforcement learning via model-based offline optimization. arXiv preprint arXiv:2006.03647, 2020. ",
+        "bbox": [
+            173,
+            90,
+            823,
+            133
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Ofir Nachum, Bo Dai, Ilya Kostrikov, Yinlam Chow, Lihong Li, and Dale Schuurmans. Algaedice: Policy gradient from arbitrary experience. arXiv preprint arXiv:1912.02074, 2019. ",
+        "bbox": [
+            171,
+            141,
+            825,
+            171
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Ashvin Nair, Bob McGrew, Marcin Andrychowicz, Wojciech Zaremba, and Pieter Abbeel. Overcoming exploration in reinforcement learning with demonstrations. In 2018 IEEE International Conference on Robotics and Automation (ICRA), pages 6292–6299. IEEE, 2018. ",
+        "bbox": [
+            174,
+            179,
+            823,
+            222
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Ashvin Nair, Murtaza Dalal, Abhishek Gupta, and Sergey Levine. Accelerating online reinforcement learning with offline datasets. arXiv preprint arXiv:2006.09359, 2020. ",
+        "bbox": [
+            169,
+            229,
+            825,
+            260
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Ian Osband, Yotam Doron, Matteo Hessel, John Aslanides, Eren Sezener, Andre Saraiva, Katrina McKinney, Tor Lattimore, Csaba Szepesvari, Satinder Singh, et al. Behaviour suite for reinforcement learning. arXiv preprint arXiv:1908.03568, 2019. ",
+        "bbox": [
+            174,
+            267,
+            825,
+            310
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Tom Le Paine, Cosmin Paduraru, Andrea Michi, Caglar Gulcehre, Konrad Zolna, Alexander Novikov, Ziyu Wang, and Nando de Freitas. Hyperparameter selection for offline reinforcement learning. arXiv preprint arXiv:2007.09055, 2020. ",
+        "bbox": [
+            174,
+            319,
+            826,
+            362
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Adam Paszke, Sam Gross, Francisco Massa, Adam Lerer, James Bradbury, Gregory Chanan, Trevor Killeen, Zeming Lin, Natalia Gimelshein, Luca Antiga, et al. Pytorch: An imperative style, high-performance deep learning library. In Advances in Neural Information Processing Systems, pages 8024–8035, 2019. ",
+        "bbox": [
+            173,
+            371,
+            826,
+            426
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Xue Bin Peng, Aviral Kumar, Grace Zhang, and Sergey Levine. Advantage-weighted regression: Simple and scalable off-policy reinforcement learning. arXiv preprint arXiv:1910.00177, 2019. ",
+        "bbox": [
+            173,
+            435,
+            823,
+            464
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Mark Pfeiffer, Samarth Shukla, Matteo Turchetta, Cesar Cadena, Andreas Krause, Roland Siegwart, and Juan Nieto. Reinforced imitation: Sample efficient deep reinforcement learning for mapless navigation by leveraging prior demonstrations. IEEE Robotics and Automation Letters, 3(4): 4423–4430, 2018. ",
+        "bbox": [
+            173,
+            473,
+            826,
+            529
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Dean A Pomerleau. Efficient training of artificial neural networks for autonomous navigation. Neural computation, 3(1):88–97, 1991. ",
+        "bbox": [
+            173,
+            537,
+            825,
+            568
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Antonin Raffin, Ashley Hill, Maximilian Ernestus, Adam Gleave, Anssi Kanervisto, and Noah Dormann. Stable baselines3. https://github.com/DLR-RM/stable-baselines3, 2019. ",
+        "bbox": [
+            173,
+            575,
+            825,
+            604
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Aravind Rajeswaran, Vikash Kumar, Abhishek Gupta, Giulia Vezzani, John Schulman, Emanuel Todorov, and Sergey Levine. Learning complex dexterous manipulation with deep reinforcement learning and demonstrations. arXiv preprint arXiv:1709.10087, 2017. ",
+        "bbox": [
+            174,
+            612,
+            825,
+            656
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Stéphane Ross, Geoffrey Gordon, and Drew Bagnell. A reduction of imitation learning and structured prediction to no-regret online learning. In Proceedings of the fourteenth international conference on artificial intelligence and statistics, pages 627–635. JMLR Workshop and Conference Proceedings, 2011. ",
+        "bbox": [
+            174,
+            664,
+            826,
+            719
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "John Schulman, Filip Wolski, Prafulla Dhariwal, Alec Radford, and Oleg Klimov. Proximal policy optimization algorithms. arXiv preprint arXiv:1707.06347, 2017. ",
+        "bbox": [
+            169,
+            728,
+            825,
+            758
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Noah Siegel, Jost Tobias Springenberg, Felix Berkenkamp, Abbas Abdolmaleki, Michael Neunert, Thomas Lampe, Roland Hafner, Nicolas Heess, and Martin Riedmiller. Keep doing what worked: Behavior modelling priors for offline reinforcement learning. In International Conference on Learning Representations, 2020. ",
+        "bbox": [
+            174,
+            766,
+            826,
+            823
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "David Silver, Guy Lever, Nicolas Heess, Thomas Degris, Daan Wierstra, and Martin Riedmiller. Deterministic policy gradient algorithms. In International Conference on Machine Learning, pages 387–395, 2014. ",
+        "bbox": [
+            174,
+            832,
+            825,
+            875
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Richard S Sutton and Andrew G Barto. Reinforcement learning: An introduction, volume 1. MIT press Cambridge, 1998. ",
+        "bbox": [
+            173,
+            882,
+            820,
+            911
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Emanuel Todorov, Tom Erez, and Yuval Tassa. Mujoco: A physics engine for model-based control. In IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pages 5026–5033. IEEE, 2012. ",
+        "bbox": [
+            173,
+            90,
+            825,
+            132
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "George Tucker, Surya Bhupatiraju, Shixiang Gu, Richard Turner, Zoubin Ghahramani, and Sergey Levine. The mirage of action-dependent baselines in reinforcement learning. In International Conference on Machine Learning, 2018. ",
+        "bbox": [
+            176,
+            142,
+            823,
+            184
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Matej Vecerík, Todd Hester, Jonathan Scholz, Fumin Wang, Olivier Pietquin, Bilal Piot, Nicolas Heess, ˇ Thomas Rothörl, Thomas Lampe, and Martin Riedmiller. Leveraging demonstrations for deep reinforcement learning on robotics problems with sparse rewards. arXiv preprint arXiv:1707.08817, 2017. ",
+        "bbox": [
+            173,
+            194,
+            826,
+            250
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Qing Wang, Jiechao Xiong, Lei Han, Peng Sun, Han Liu, and Tong Zhang. Exponentially weighted imitation learning for batched historical data. In Proceedings of the 32nd International Conference on Neural Information Processing Systems, pages 6291–6300, 2018. ",
+        "bbox": [
+            174,
+            258,
+            826,
+            301
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Ziyu Wang, Alexander Novikov, Konrad Zolna, Josh S Merel, Jost Tobias Springenberg, Scott E Reed, Bobak Shahriari, Noah Siegel, Caglar Gulcehre, Nicolas Heess, et al. Critic regularized regression. Advances in Neural Information Processing Systems, 33, 2020. ",
+        "bbox": [
+            174,
+            309,
+            826,
+            353
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Yifan Wu, George Tucker, and Ofir Nachum. Behavior regularized offline reinforcement learning. arXiv preprint arXiv:1911.11361, 2019. ",
+        "bbox": [
+            174,
+            361,
+            825,
+            391
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Yuchen Wu, Melissa Mozifian, and Florian Shkurti. Shaping rewards for reinforcement learning with imperfect demonstrations using generative models. In 2021 IEEE International Conference on Robotics and Automation (ICRA), pages 6628–6634. IEEE, 2021. ",
+        "bbox": [
+            174,
+            398,
+            826,
+            443
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Mengjiao Yang, Bo Dai, Ofir Nachum, George Tucker, and Dale Schuurmans. Offline policy selection under uncertainty. arXiv preprint arXiv:2012.06919, 2020. ",
+        "bbox": [
+            171,
+            450,
+            825,
+            479
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Yuke Zhu, Ziyu Wang, Josh Merel, Andrei Rusu, Tom Erez, Serkan Cabi, Saran Tunyasuvunakool, János Kramár, Raia Hadsell, Nando de Freitas, et al. Reinforcement and imitation learning for diverse visuomotor skills. arXiv preprint arXiv:1802.09564, 2018. ",
+        "bbox": [
+            176,
+            488,
+            825,
+            531
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Checklist ",
+        "text_level": 1,
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+        "text": "(a) Do the main claims made in the abstract and introduction accurately reflect the paper’s contributions and scope? [Yes]   \n(b) Did you describe the limitations of your work? [Yes] See the discussion on instability in Section 4.   \n(c) Did you discuss any potential negative societal impacts of your work? [Yes] In the supplementary material.   \n(d) Have you read the ethics review guidelines and ensured that your paper conforms to them? [Yes] ",
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+        "text": "(a) Did you state the full set of assumptions of all theoretical results? [N/A] (b) Did you include complete proofs of all theoretical results? [N/A] ",
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parse/train/R-616EWWKF5/R-616EWWKF5_content_list.json

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+    {
+        "type": "text",
+        "text": "Do Vision Transformers See Like Convolutional Neural Networks? ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Maithra Raghu Google Research, Brain Team maithrar@gmail.com ",
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "Thomas Unterthiner Google Research, Brain Team unterthiner@google.com ",
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+    {
+        "type": "text",
+        "text": "Simon Kornblith Google Research, Brain Team kornblith@google.com ",
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+    {
+        "type": "text",
+        "text": "Chiyuan Zhang Google Research, Brain Team chiyuan@google.com ",
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+    },
+    {
+        "type": "text",
+        "text": "Alexey Dosovitskiy Google Research, Brain Team adosovitskiy@google.com ",
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+    {
+        "type": "text",
+        "text": "Abstract ",
+        "text_level": 1,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Convolutional neural networks (CNNs) have so far been the de-facto model for visual data. Recent work has shown that (Vision) Transformer models (ViT) can achieve comparable or even superior performance on image classification tasks. This raises a central question: how are Vision Transformers solving these tasks? Are they acting like convolutional networks, or learning entirely different visual representations? Analyzing the internal representation structure of ViTs and CNNs on image classification benchmarks, we find striking differences between the two architectures, such as ViT having more uniform representations across all layers. We explore how these differences arise, finding crucial roles played by self-attention, which enables early aggregation of global information, and ViT residual connections, which strongly propagate features from lower to higher layers. We study the ramifications for spatial localization, demonstrating ViTs successfully preserve input spatial information, with noticeable effects from different classification methods. Finally, we study the effect of (pretraining) dataset scale on intermediate features and transfer learning, and conclude with a discussion on connections to new architectures such as the MLP-Mixer. ",
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+    {
+        "type": "text",
+        "text": "1 Introduction ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Over the past several years, the successes of deep learning on visual tasks has critically relied on convolutional neural networks [20, 16]. This is largely due to the powerful inductive bias of spatial equivariance encoded by convolutional layers, which have been key to learning general purpose visual representations for easy transfer and strong performance. Remarkably however, recent work has demonstrated that Transformer neural networks are capable of equal or superior performance on image classification tasks at large scale [14]. These Vision Transformers (ViT) operate almost identically to Transformers used in language [13], using self-attention, rather than convolution, to aggregate information across locations. This is in contrast with a large body of prior work, which has focused on more explicitly incorporating image-specific inductive biases [30, 9, 4] ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "This breakthrough highlights a fundamental question: how are Vision Transformers solving these image based tasks? Do they act like convolutions, learning the same inductive biases from scratch? Or are they developing novel task representations? What is the role of scale in learning these representations? And are there ramifications for downstream tasks? In this paper, we study these questions, uncovering key representational differences between ViTs and CNNs, the ways in which these difference arise, and effects on classification and transfer learning. Specifically, our contributions are: ",
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+    {
+        "type": "text",
+        "text": "35th Conference on Neural Information Processing Systems (NeurIPS 2021). ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "• We investigate the internal representation structure of ViTs and CNNs, finding striking differences between the two models, such as ViT having more uniform representations, with greater similarity between lower and higher layers.   \n• Analyzing how local/global spatial information is utilised, we find ViT incorporates more global information than ResNet at lower layers, leading to quantitatively different features.   \n• Nevertheless, we find that incorporating local information at lower layers remains vital, with large-scale pre-training data helping early attention layers learn to do this   \n• We study the uniform internal structure of ViT, finding that skip connections in ViT are even more influential than in ResNets, having strong effects on performance and representation similarity.   \n• Motivated by potential future uses in object detection, we examine how well input spatial information is preserved, finding connections between spatial localization and methods of classification.   \n• We study the effects of dataset scale on transfer learning, with a linear probes study revealing its importance for high quality intermediate representations. ",
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+    {
+        "type": "text",
+        "text": "2 Related Work ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Developing non-convolutional neural networks to tackle computer vision tasks, particularly Transformer neural networks [44] has been an active area of research. Prior works have looked at local multiheaded self-attention, drawing from the structure of convolutional receptive fields [30, 36], directly combining CNNs with self-attention [4, 2, 46] or applying Transformers to smaller-size images [6, 9]. In comparison to these, the Vision Transformer [14] performs even less modification to the Transformer architecture, making it especially interesting to compare to CNNs. Since its development, there has also been very recent work analyzing aspects of ViT, particularly robustness [3, 31, 28] and effects of self-supervision [5, 7]. Other recent related work has looked at designing hybrid ViT-CNN models [49, 11], drawing on structural differences between the models. Comparison between Transformers and CNNs are also recently studied in the text domain [41]. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Our work focuses on the representational structure of ViTs. To study ViT representations, we draw on techniques from neural network representation similarity, which allow the quantitative comparisons of representations within and across neural networks [17, 34, 26, 19]. These techniques have been very successful in providing insights on properties of different vision architectures [29, 22, 18], representation structure in language models [48, 25, 47, 21], dynamics of training methods [33, 24] and domain specific model behavior [27, 35, 38]. We also apply linear probes in our study, which has been shown to be useful to analyze the learned representations in both vision [1] and text [8, 32, 45] models. ",
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+    {
+        "type": "text",
+        "text": "3 Background and Experimental Setup ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Our goal is to understand whether there are differences in the way ViTs represent and solve image tasks compared to CNNs. Based on the results of Dosovitskiy et al. [14], we take a representative set of CNN and ViT models — ResNet50x1, ResNet152x2, ViT-B/32, ViT-B/16, ViT-L/16 and ViT-H/14. Unless otherwise specified, models are trained on the JFT-300M dataset [40], although we also investigate models trained on the ImageNet ILSVRC 2012 dataset [12, 37] and standard transfer learning benchmarks [50, 14]. We use a variety of analysis methods to study the layer representations of these models, gaining many insights into how these models function. We provide further details of the experimental setting in Appendix A. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Representation Similarity and CKA (Centered Kernel Alignment): Analyzing (hidden) layer representations of neural networks is challenging because their features are distributed across a large number of neurons. This distributed aspect also makes it difficult to meaningfully compare representations across neural networks. Centered kernel alignment (CKA) [17, 10] addresses these challenges, enabling quantitative comparisons of representations within and across networks. Specifically, CKA takes as input $\\mathbf { X } \\in \\mathbb { R } ^ { m \\times p _ { 1 } }$ and $\\mathbf { Y } \\in \\mathbb { R } ^ { \\bar { m } \\times p _ { 2 } }$ which are representations (activation matrices), of two layers, with $p _ { 1 }$ and $p _ { 2 }$ neurons respectively, evaluated on the same $m$ examples. Letting $K = X X ^ { \\top }$ and $\\pmb { L } = \\pmb { Y } \\pmb { Y } ^ { \\top }$ denote the Gram matrices for the two layers (which measures the similarity of a pair of datapoints according to layer representations) CKA computes: ",
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+        "page_idx": 1
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+    {
+        "type": "equation",
+        "img_path": "images/ece24298fde019dc1a4a5669e643d97477ac0f369e9ff88e48ba6c20ad46631d.jpg",
+        "text": "$$\n\\operatorname { C K A } ( K , L ) = { \\frac { \\operatorname { H S I C } ( K , L ) } { \\sqrt { \\operatorname { H S I C } ( K , K ) \\operatorname { H S I C } ( L , L ) } } } ,\n$$",
+        "text_format": "latex",
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+    {
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+        "img_path": "images/6c5a9b6bab30d7d98cdfbdbc8c227090753b2fe9a3879c54d415bd98c335c458.jpg",
+        "image_caption": [
+            "Figure 1: Representation structure of ViTs and convolutional networks show significant differences, with ViTs having highly similar representations throughout the model, while the ResNet models show much lower similarity between lower and higher layers. We plot CKA similarities between all pairs of layers across different model architectures. The results are shown as a heatmap, with the x and y axes indexing the layers from input to output. We observe that ViTs have relatively uniform layer similarity structure, with a clear grid-like pattern and large similarity between lower and higher layers. By contrast, the ResNet models show clear stages in similarity structure, with smaller similarity scores between lower and higher layers. "
+        ],
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+    {
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+        "img_path": "images/8a4393cdf55bae8dbc53a5b8d7bc4fe6b0b545fc47427224ecdfabf1f9bbf2ea.jpg",
+        "image_caption": [
+            "Figure 2: Cross model CKA heatmap between ViT and ResNet illustrate that a larger number of lower layers in the ResNet are similar to a smaller set of the lowest ViT layers. We compute a CKA heatmap comparing all layers of ViT to all layers of ResNet, for two different ViT models. We observe that the lower half of ResNet layers are similar to around the lowest quarter of ViT layers. The remaining half of the ResNet is similar to approximately the next third of ViT layers, with the highest ViT layers dissimilar to lower and higher ResNet layers. "
+        ],
+        "image_footnote": [],
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+    },
+    {
+        "type": "text",
+        "text": "where HSIC is the Hilbert-Schmidt independence criterion [15]. Given the centering matrix $\\begin{array} { r } { \\pmb { H } = \\pmb { I } _ { n } - \\frac { 1 } { n } \\pmb { 1 } \\pmb { 1 } ^ { \\top } } \\end{array}$ and the centered Gram matrices $K ^ { \\prime } = H K H$ and $L ^ { \\prime } = H L H$ , $\\mathrm { H S I C } ( \\bar { K } , L ) =$ $\\mathrm { v e c } ( K ^ { \\prime } ) \\cdot \\mathrm { v e c } ( L ^ { \\prime } ) / ( m - 1 ) ^ { 2 }$ , the similarity between these centered Gram matrices. CKA is invariant to orthogonal transformation of representations (including permutation of neurons), and the normalization term ensures invariance to isotropic scaling. These properties enable meaningful comparison and analysis of neural network hidden representations. To work at scale with our models and tasks, we approximate the unbiased estimator of HSIC [39] using minibatches, as suggested in [29]. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "4 Representation Structure of ViTs and Convolutional Networks ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We begin our investigation by using CKA to study the internal representation structure of each model. How are representations propagated within the two architectures, and are there signs of functional differences? To answer these questions, we take every pair of layers $X , Y$ within a model and compute their CKA similarity. Note that we take representations not only from outputs of ViT/ResNet blocks, but also from intermediate layers, such as normalization layers and the hidden activations inside a ViT MLP. Figure 1 shows the results as a heatmap, for multiple ViTs and ResNets. We observe clear differences between the internal representation structure between the two model architectures: (1) ViTs show a much more uniform similarity structure, with a clear grid like structure (2) lower and higher layers in ViT show much greater similarity than in the ResNet, where similarity is divided into different (lower/higher) stages. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We also perform cross-model comparisons, where we take all layers $\\boldsymbol { X }$ from ViT and compare to all layers $\\mathbf { Y }$ from ResNet. We observe (Figure 2) that the lower half of 60 ResNet layers are similar to approximately the lowest quarter of ViT layers. In particular, many more lower layers in the ResNet are needed to compute similar representations to the lower layers of ViT. The top half of the ResNet is approximately similar to the next third of the ViT layers. The final third of ViT layers is less similar to all ResNet layers, likely because this set of layers mainly manipulates the CLS token representation, further studied in Section 6. ",
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+    },
+    {
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+        "img_path": "images/386cf223d2ffbb35198c4009d6b4a85458145d4f75ffea87e1a006a2a358ffcf.jpg",
+        "image_caption": [
+            "Figure 3: Plotting attention head mean distances shows lower ViT layers attend both locally and globally, while higher layers primarily incorporate global information. For each attention head, we compute the pixel distance it attends to, weighted by the attention weights, and then average over 5000 datapoints to get an average attention head distance. We plot the heads sorted by their average attention distance for the two lowest and two highest layers in the ViT, observing that the lower layers attend both locally and globally, while the higher layers attend entirely globally. "
+        ],
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+    {
+        "type": "text",
+        "text": "Taken together, these results suggest that (i) ViT lower layers compute representations in a different way to lower layers in the ResNet, (ii) ViT also more strongly propagates representations between lower and higher layers (iii) the highest layers of ViT have quite different representations to ResNet. ",
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+    {
+        "type": "text",
+        "text": "5 Local and Global Information in Layer Representations ",
+        "text_level": 1,
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+        "text": "In the previous section, we observed much greater similarity between lower and higher layers in ViT, and we also saw that ResNet required more lower layers to compute similar representations to a smaller set of ViT lower layers. In this section, we explore one possible reason for this difference: the difference in the ability to incorporate global information between the two models. How much global information is aggregated by early self-attention layers in ViT? Are there noticeable resulting differences to the features of CNNs, which have fixed, local receptive fields in early layers? In studying these questions, we demonstrate the influence of global representations and a surprising connection between scale and self-attention distances. ",
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+    {
+        "type": "text",
+        "text": "Analyzing Attention Distances: We start by analyzing ViT self-attention layers, which are the mechanism for ViT to aggregate information from other spatial locations, and structurally very different to the fixed receptive field sizes of CNNs. Each self-attention layer comprises multiple self-attention heads, and for each head we can compute the average distance between the query patch position and the locations it attends to. This reveals how much local vs global information each self-attention layer is aggregating for the representation. Specifically, we weight the pixel distances by the attention weights for each attention head and average over 5000 datapoints, with results shown in Figure 3. In agreement with Dosovitskiy et al. [14], we observe that even in the lowest layers of ViT, self-attention layers have a mix of local heads (small distances) and global heads (large distances). This is in contrast to CNNs, which are hardcoded to attend only locally in the lower layers. At higher layers, all self-attention heads are global. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Interestingly, we see a clear effect of scale on attention. In Figure 4, we look at attention distances when training only on ImageNet (no large-scale pre-training), which leads to much lower performance in ViT-L/16 and ViT-H/14 [14]. Comparing to Figure 3, we see that with not enough data, ViT does not learn to attend locally in earlier layers. Together, this suggests that using local information early on for image tasks (which is hardcoded into CNN architectures) is important for strong performance. ",
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Does access to global information result in different features? The results of Figure 3 demonstrate that ViTs have access to more global information than CNNs in their lower layers. But does this result in different learned features? As an interventional test, we take subsets of the ViT attention heads from the first encoder block, ranging from the subset corresponding to the most local attention heads to a subset of the representation corresponding to the most global attention heads. We then compute CKA similarity between these subsets and the lower layer representations of ResNet. ",
+        "bbox": [
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+        "page_idx": 3
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+    {
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+        "img_path": "images/3e35bf39b04f38b85758bdc7dde0ef4f00adc22579434f00626ddb89b2b308a2.jpg",
+        "image_caption": [
+            "Figure 4: With less training data, lower attention layers do not learn to attend locally. Comparing the results to Figure 3, we see that training only on ImageNet leads to the lower layers not learning to attend more locally. These models also perform much worse when only trained on ImageNet, suggesting that incorporating local features (which is hardcoded into CNNs) may be important for strong performance. (See also Figure C.5.) "
+        ],
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+        "page_idx": 4
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+        "image_caption": [
+            "Figure 5: Lower layer representations of ResNet are most similar to representations corresponding to local attention heads of ViT. We take subsets of ViT attention heads in the first encoder block, ranging from the most locally attending heads (smallest mean distance) to the most global heads (largest mean distance). We then compute CKA similarity between these subsets and lower layer representations in the ResNet. We observe that lower ResNet layers are most similar to the features learned by local attention heads of ViT, and decrease monotonically in similarity as more global information is incorporated, demonstrating that the global heads learn quantitatively different features. "
+        ],
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+        "type": "text",
+        "text": "The results, shown in Figure 5, which plot the mean distance for each subset against CKA similarity, clearly show a monotonic decrease in similarity as mean attention distance grows, demonstrating that access to more global information also leads to quantitatively different features than computed by the local receptive fields in the lower layers of the ResNet. ",
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+        "type": "text",
+        "text": "Effective Receptive Fields: We conclude by computing effective receptive fields [23] for both ResNets and ViTs, with results in Figure 6 and Appendix C. We observe that lower layer effective receptive fields for ViT are indeed larger than in ResNets, and while ResNet effective receptive fields grow gradually, ViT receptive fields become much more global midway through the network. ViT receptive fields also show strong dependence on their center patch due to their strong residual connections, studied in the next section. As we show in Appendix C, in attention sublayers, receptive fields taken before the residual connection show far less dependence on this central patch. ",
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+        "text": "6 Representation Propagation through Skip Connections ",
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+        "text": "The results of the previous section demonstrate that ViTs learn different representations to ResNets in lower layers due to access to global information, which explains some of the differences in represen tation structure observed in Section 4. However, the highly uniform nature of ViT representations (Figure 1) also suggests lower representations are faithfully propagated to higher layers. But how does this happen? In this section, we explore the role of skip connections in representation propagation across ViTs and ResNets, discovering ViT skip connections are highly influential, with a clear phase transition from preserving the CLS (class) token representation (in lower layers) to spatial token representations (in higher layers). ",
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+            "",
+            "Figure 7: Most information in ViT passes through skip connections. Comparison of representation norms between the skip-connection (identity) and the long branch for ViT-B/16 trained on ImageNet and a ResNet. For ViT, we show the CLS token separately from the rest of the representation. (left) shows the ratios separated for the first few tokens (token 0 is CLS), (right) shows averages over all tokens. "
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+        "type": "text",
+        "text": "Like Transformers, ViTs contain skip (aka identity or shortcut) connections throughout, which are added on after the (i) self-attention layer, and (ii) MLP layer. To study their effect, we plot the norm ratio $\\vert \\vert z _ { i } \\vert \\vert / \\vert \\vert f ( z _ { i } ) \\vert \\vert$ where $z _ { i }$ is the hidden representation of the ith layer coming from the skip connection, and $f ( z _ { i } )$ is the transformation of $z _ { i }$ from the long branch (i.e. MLP or self-attention.) ",
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+        "text": "The results are in Figure 7 (with additional cosine similarity analysis in Figure E.2.) The heatmap on the left shows $\\| z _ { i } \\| / \\| f ( z _ { i } ) \\|$ for different token representations. We observe a striking phase transition: in the first half of the network, the CLS token (token 0) representation is primarily propagated by the skip connection branch (high norm ratio), while the spatial token representations have a large contribution coming from the long branch (lower norm ratio). Strikingly, in the second half of the network, this is reversed. ",
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+        "type": "text",
+        "text": "The right pane, which has line plots of these norm ratios across ResNet50, the ViT CLS token and the ViT spatial tokens additionally demonstrates that skip connection is much more influential in ViT compared to ResNet: we observe much higher norm ratios for ViT throughout, along with the phase transition from CLS to spatial token propagation (shown for the MLP and self-attention layers.) ",
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+        "text": "ViT Representation Structure without Skip Connections: The norm ratio results strongly suggest that skip connections play a key role in the representational structure of ViT. To test this interventionally, we train ViT models with skip connections removed in block $i$ for varying $i$ , and plot the CKA representation heatmap. The results, in Figure 8, illustrate that removing the skip connections in a block partitions the layer representations on either side. (We note a performance drop of $4 \\%$ when removing skip connections from middle blocks.) This demonstrates the importance of representations being propagated by skip connections for the uniform similarity structure of ViT in Figure 1. ",
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+        "image_caption": [
+            "Figure 8: ViT models trained without any skip connections in block $_ { i }$ show very little representation similarity between layers before/after block $_ { i }$ . We train several ViT models without any skip connections at block $_ { i }$ for varying $_ { i }$ to interventionally test the effect on representation structure. For middle blocks without skip connections, we observe a performance drop of $4 \\%$ . We also observe that removing a skip connection at block $i$ partitions similar representations to before/after block $_ { i }$ — this demonstrates the importance of skip connections in ViT’s standard uniform representation structure. "
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+            "ViT-B/32 final block Token at Location(0, 0) Token at Location(2, 1) Token at Location(4, 2) Token at Location(4, 4) ",
+            "Figure 9: Higher layers of ViT maintain spatial location information more faithfully than ResNets. Each heatmap plot shows the CKA similarity between a single token representation in final block of the model and the input images, which are divided into non-overlapping patches. We observe that ViT tokens have strongest similarity to their corresponding spatial location in the image, but tokens corresponding to spatial locations at the edge of the image (e.g. token 0) additionally show similarity to other edge positions. This demonstrates that spatial information from the input is preserved even at the final layer of ViT. By contrast, ResNet “tokens” (features at a specific spatial location) are much less spatially discriminative, showing comparable similarity across a broad set of input spatial locations. See Appendix for additional layers and results. "
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+        "text": "7 Spatial Information and Localization ",
+        "text_level": 1,
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+        "text": "The results so far, on the role of self-attention in aggregating spatial information in ViTs, and skipconnections faithfully propagating representations to higher layers, suggest an important followup question: how well can ViTs perform spatial localization? Specifically, is spatial information from the input preserved in the higher layers of ViT? And how does it compare in this aspect to ResNet? An affirmative answer to this is crucial for uses of ViT beyond classification, such as object detection. ",
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+        "image_caption": [
+            "Figure 10: When trained with global average pooling (GAP) instead of a CLS token, ViTs show less clear localization (compare Figure 9). We plot the same CKA heatmap between a token and different input images patches as in Figure 9, but for a ViT model trained with global average pooling (like ResNet) instead of a CLS token. We observe significantly less localization. "
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+            "Figure 11: Spatial localization experiments with linear probes. We train linear classifiers on 10-shot ImageNet classification from the representations extracted from different layers of ViT-B/32 models. We then plot the accuracy of the probe versus the (normalized) layer number. Left: We train a classifier on each token separately and report the average accuracy over all tokens (excluding the CLS token for the ViT CLS model.) Right: Comparison of ViT models pre-trained with a classification token or with global average pooling (GAP) and then evaluated with different ways of aggregating the token representations. "
+        ],
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+        "type": "text",
+        "text": "We begin by comparing token representations in the higher layers of ViT and ResNet to those of input patches. Recall that ViT tokens have a corresponding input patch, and thus a corresponding input spatial location. For ResNet, we define a token representation to be all the convolutional channels at a particular spatial location. This also gives it a corresponding input spatial location. We can then take a token representation and compute its CKA score with input image patches at different locations. The results are illustrated for different tokens (with their spatial locations labelled) in Figure 9. ",
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+        "type": "text",
+        "text": "For ViT, we observe that tokens corresponding to locations at the edge of the image are similar to edge image patches, but tokens corresponding to interior locations are well localized, with their representations being most similar to the corresponding image patch. By contrast, for ResNet, we see significantly weaker localization (though Figure D.3 shows improvements for earlier layers.) ",
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+        "type": "text",
+        "text": "One factor influencing this clear difference between architectures is that ResNet is trained to classify with a global average pooling step, while ViT has a separate classification (CLS) token. To examine this further, we test a ViT architecture trained with global average pooling (GAP) for localization (see Appendix A for training details). The results, shown in Figure 10, demonstrate that global average pooling does indeed reduce localization in the higher layers. More results in Appendix Section D. ",
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+        "type": "text",
+        "text": "Localization and Linear Probe Classification: The previous results have looked at localization through direct comparison of each token with input patches. To complete the picture, we look at using each token separately to perform classification with linear probes. We do this across different layers of the model, training linear probes to classify image label with closed-form few-shot linear regression similar to Dosovitskiy et al. [14] (details in Appendix A). Results are in Figure 11, with further results in Appendix F. The left pane shows average accuracy of classifiers trained on individual tokens, where we see that ResNet50 and ViT with GAP model tokens perform well at higher layers, while in the standard ViT trained with a CLS token the spatial tokens do poorly – likely because their representations remain spatially localized at higher layers, which makes global classification challenging. Supporting this are results on the right pane, which shows that a single token from the ",
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+        "image_caption": [
+            "Figure 12: Measuring similarity of representations learned with varying amounts of data shows the importance of large datasets for higher layers and larger model representations. We compute the similarity of representations at each block for ViT models that have been trained on smaller subsets of the data to a model that has been trained on the full data on ViT-L/16 (left) and ViT-B/32 (right). We observe that while lower layer representations have high similarity even with $1 0 \\%$ of the data, higher layers and larger models require significantly more data to learn similar representations. "
+        ],
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+    {
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+        "image_caption": [
+            "Figure 13: Experiments with linear probes. We train linear classifiers on 10-shot ImageNet classification from the aggregated representations of different layers of different models. We then plot the accuracy of the probe versus the (normalized) layer number. Left: Comparison of ViTs pre-trained on JFT-300M or ImageNet and evaluated with linear probes on Imagenet. Right: Comparison of ViT and ResNet models trained JFT- $3 0 0 \\mathrm { m }$ evaluated with linear probes on ImageNet. "
+        ],
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+    {
+        "type": "text",
+        "text": "ViT-GAP model achieves comparable accuracy in the highest layer to all tokens pooled together. With the results of Figure 9, this suggests all higher layer tokens in GAP models learn similar (global) representations. ",
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+    {
+        "type": "text",
+        "text": "8 Effects of Scale on Transfer Learning ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Motivated by the results of Dosovitskiy et al. [14] that demonstrate the importance of dataset scale for high performing ViTs, and our earlier result (Figure 4) on needing scale for local attention, we perform a study of the effect of dataset scale on representations in transfer learning. ",
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+    {
+        "type": "text",
+        "text": "We begin by studying the effect on representations as the JFT-300M pretraining dataset size is varied. Figure 12 illustrates the results on ViT-B/32 and ViT-L/16. Even with $3 \\%$ of the entire dataset, lower layer representations are very similar to the model trained on the whole dataset, but higher layers require larger amounts of pretraining data to learn the same representations as at large data scale, especially with the large model size. In Section G, we study how much representations change in finetuning, finding heterogeneity over datasets. ",
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+    {
+        "type": "text",
+        "text": "We next look at dataset size effect on the larger ViT-L/16 and ViT-H/14 models. Specifically, in the left pane of Figure 13, we train linear classifer probes on ImageNet classes for models pretrained on JFT-300M vs models only pretrained on ImageNet. We observe the JFT-300M pretained models achieve much higher accuracies even with middle layer representations, with a $3 0 \\%$ gap in absolute accuracy to the models pretrained only on ImageNet. This suggests that for larger models, the larger dataset is especially helpful in learning high quality intermediate representations. This conclusion is further supported by the results of the right pane of Figure 13, which shows linear probes on different ResNet and ViT models, all pretrained on JFT-300M. We again see the larger ViT models learn much stronger intermediate representations than the ResNets. Additional linear probes experiments in Section F demonstrate this same conclusion for transfer to CIFAR-10 and CIFAR-100. ",
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+    {
+        "type": "text",
+        "text": "9 Discussion ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Limitations: Our study uses CKA [17], which summarizes measurements into a single scalar, to provide quantitative insights on representation similarity. While we have complemented this with interventional tests and other analyses (e.g. linear probes), more fine-grained methods may reveal additional insights and variations in the representations. ",
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+    {
+        "type": "text",
+        "text": "Conclusion: Given the central role of convolutional neural networks in computer vision breakthroughs, it is remarkable that Transformer architectures (almost identical to those used in language) are capable of similar performance. This raises fundamental questions on whether these architectures work in the same way as CNNs. Drawing on representational similarity techniques, we find surprisingly clear differences in the features and internal structures of ViTs and CNNs. An analysis of self-attention and the strength of skip connections demonstrates the role of earlier global features and strong representation propagation in ViTs for these differences, while also revealing that some CNN properties, e.g. local information aggregation at lower layers, are important to ViTs, being learned from scratch at scale. We examine the potential for ViTs to be used beyond classification through a study of spatial localization, discovering ViTs with CLS tokens show strong preservation of spatial information — promising for future uses in object detection. Finally, we investigate the effect of scale for transfer learning, finding larger ViT models develop significantly stronger intermediate representations through larger pretraining datasets. These results are also very pertinent to understanding MLP-based architectures for vision proposed by concurrent work [42, 43], further discussed in Section H, and together answer central questions on differences between ViTs and CNNs, and suggest new directions for future study. From the perspective of societal impact, these findings and future work may help identify potential failures as well as greater model interpretability. ",
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+    {
+        "type": "text",
+        "text": "References ",
+        "text_level": 1,
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+        "text": "[1] G. Alain and Y. Bengio. Understanding intermediate layers using linear classifier probes. arXiv preprint arXiv:1610.01644, 2016.   \n[2] I. Bello, B. Zoph, A. Vaswani, J. Shlens, and Q. V. Le. Attention augmented convolutional networks. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 3286–3295, 2019.   \n[3] S. Bhojanapalli, A. Chakrabarti, D. Glasner, D. Li, T. Unterthiner, and A. Veit. Understanding robustness of transformers for image classification. arXiv preprint arXiv:2103.14586, 2021.   \n[4] N. Carion, F. Massa, G. Synnaeve, N. Usunier, A. Kirillov, and S. Zagoruyko. End-to-end object detection with transformers. In European Conference on Computer Vision, pages 213–229. Springer, 2020.   \n[5] M. Caron, H. Touvron, I. Misra, H. Jégou, J. Mairal, P. Bojanowski, and A. Joulin. Emerging properties in self-supervised vision transformers. arXiv preprint arXiv:2104.14294, 2021.   \n[6] M. Chen, A. Radford, R. Child, J. Wu, H. Jun, D. Luan, and I. Sutskever. Generative pretraining from pixels. In International Conference on Machine Learning, pages 1691–1703. PMLR, 2020.   \n[7] X. Chen, S. Xie, and K. He. An empirical study of training self-supervised vision transformers. arXiv preprint arXiv:2104.02057, 2021.   \n[8] A. Conneau, G. Kruszewski, G. Lample, L. Barrault, and M. Baroni. What you can cram into a single vector: Probing sentence embeddings for linguistic properties. In ACL, 2018.   \n[9] J.-B. Cordonnier, A. Loukas, and M. Jaggi. On the relationship between self-attention and convolutional layers. arXiv preprint arXiv:1911.03584, 2019.   \n[10] C. Cortes, M. Mohri, and A. Rostamizadeh. Algorithms for learning kernels based on centered alignment. The Journal of Machine Learning Research, 13(1):795–828, 2012.   \n[11] S. d’Ascoli, H. Touvron, M. Leavitt, A. Morcos, G. Biroli, and L. Sagun. Convit: Improving vision transformers with soft convolutional inductive biases. arXiv preprint arXiv:2103.10697, 2021.   \n[12] J. Deng, W. Dong, R. Socher, L.-J. Li, K. Li, and L. Fei-Fei. Imagenet: A large-scale hierarchical image database. In 2009 IEEE conference on computer vision and pattern recognition, pages 248–255. Ieee, 2009.   \n[13] J. Devlin, M.-W. Chang, K. Lee, and K. Toutanova. Bert: Pre-training of deep bidirectional transformers for language understanding. arXiv preprint arXiv:1810.04805, 2018.   \n[14] A. Dosovitskiy, L. Beyer, A. Kolesnikov, D. Weissenborn, X. Zhai, T. Unterthiner, M. Dehghani, M. Minderer, G. Heigold, S. Gelly, et al. An image is worth 16x16 words: Transformers for image recognition at scale. arXiv preprint arXiv:2010.11929, 2020.   \n[15] A. Gretton, K. Fukumizu, C. H. Teo, L. Song, B. Schölkopf, A. J. Smola, et al. A kernel statistical test of independence. In Nips, volume 20, pages 585–592. Citeseer, 2007.   \n[16] A. Kolesnikov, L. Beyer, X. Zhai, J. Puigcerver, J. Yung, S. Gelly, and N. Houlsby. Big transfer (bit): General visual representation learning. arXiv preprint arXiv:1912.11370, 6(2):8, 2019.   \n[17] S. Kornblith, M. Norouzi, H. Lee, and G. Hinton. Similarity of neural network representations revisited. In ICML, 2019.   \n[18] S. Kornblith, H. Lee, T. Chen, and M. Norouzi. What’s in a loss function for image classification? arXiv preprint arXiv:2010.16402, 2020.   \n[19] N. Kriegeskorte, M. Mur, and P. A. Bandettini. Representational similarity analysis-connecting the branches of systems neuroscience. Frontiers in systems neuroscience, 2:4, 2008.   \n[20] A. Krizhevsky, I. Sutskever, and G. E. Hinton. Imagenet classification with deep convolutional neural networks. Advances in neural information processing systems, 25:1097–1105, 2012.   \n[21] S. R. Kudugunta, A. Bapna, I. Caswell, N. Arivazhagan, and O. Firat. Investigating multilingual nmt representations at scale. arXiv preprint arXiv:1909.02197, 2019.   \n[22] G. W. Lindsay. Convolutional neural networks as a model of the visual system: past, present, and future. Journal of cognitive neuroscience, pages 1–15, 2020.   \n[23] W. Luo, Y. Li, R. Urtasun, and R. Zemel. Understanding the effective receptive field in deep convolutional neural networks. arXiv preprint arXiv:1701.04128, 2017.   \n[24] N. Maheswaranathan, A. H. Williams, M. D. Golub, S. Ganguli, and D. Sussillo. Universality and individuality in neural dynamics across large populations of recurrent networks. Advances in neural information processing systems, 2019:15629, 2019.   \n[25] A. Merchant, E. Rahimtoroghi, E. Pavlick, and I. Tenney. What happens to bert embeddings during fine-tuning? arXiv preprint arXiv:2004.14448, 2020.   \n[26] A. S. Morcos, M. Raghu, and S. Bengio. Insights on representational similarity in neural networks with canonical correlation. arXiv preprint arXiv:1806.05759, 2018.   \n[27] B. Mustafa, A. Loh, J. Freyberg, P. MacWilliams, M. Wilson, S. M. McKinney, M. Sieniek, J. Winkens, Y. Liu, P. Bui, et al. Supervised transfer learning at scale for medical imaging. arXiv preprint arXiv:2101.05913, 2021.   \n[28] M. Naseer, K. Ranasinghe, S. Khan, M. Hayat, F. S. Khan, and M.-H. Yang. Intriguing properties of vision transformers, 2021.   \n[29] T. Nguyen, M. Raghu, and S. Kornblith. Do wide and deep networks learn the same things? uncovering how neural network representations vary with width and depth. arXiv preprint arXiv:2010.15327, 2020.   \n[30] N. Parmar, A. Vaswani, J. Uszkoreit, L. Kaiser, N. Shazeer, A. Ku, and D. Tran. Image transformer. In International Conference on Machine Learning, pages 4055–4064. PMLR, 2018.   \n[31] S. Paul and P.-Y. Chen. Vision transformers are robust learners. arXiv preprint arXiv:2105.07581, 2021.   \n[32] M. E. Peters, M. Neumann, L. Zettlemoyer, and W.-t. Yih. Dissecting contextual word embeddings: Architecture and representation. In EMNLP, 2018.   \n[33] A. Raghu, M. Raghu, S. Bengio, and O. Vinyals. Rapid learning or feature reuse? towards understanding the effectiveness of maml. arXiv preprint arXiv:1909.09157, 2019.   \n[34] M. Raghu, J. Gilmer, J. Yosinski, and J. Sohl-Dickstein. Svcca: Singular vector canonical correlation analysis for deep learning dynamics and interpretability. arXiv preprint arXiv:1706.05806, 2017.   \n[35] M. Raghu, C. Zhang, J. Kleinberg, and S. Bengio. Transfusion: Understanding transfer learning for medical imaging. arXiv preprint arXiv:1902.07208, 2019.   \n[36] P. Ramachandran, N. Parmar, A. Vaswani, I. Bello, A. Levskaya, and J. Shlens. Stand-alone self-attention in vision models. arXiv preprint arXiv:1906.05909, 2019.   \n[37] O. Russakovsky, J. Deng, H. Su, J. Krause, S. Satheesh, S. Ma, Z. Huang, A. Karpathy, A. Khosla, M. Bernstein, et al. Imagenet large scale visual recognition challenge. International journal of computer vision, 115(3):211–252, 2015.   \n[38] J. Shi, E. Shea-Brown, and M. Buice. Comparison against task driven artificial neural networks reveals functional properties in mouse visual cortex. Advances in Neural Information Processing Systems, 32:5764–5774, 2019.   \n[39] L. Song, A. Smola, A. Gretton, J. Bedo, and K. Borgwardt. Feature selection via dependence maximization. Journal of Machine Learning Research, 13(5), 2012.   \n[40] C. Sun, A. Shrivastava, S. Singh, and A. Gupta. Revisiting unreasonable effectiveness of data in deep learning era. In Proceedings of the IEEE international conference on computer vision, pages 843–852, 2017.   \n[41] Y. Tay, M. Dehghani, J. Gupta, D. Bahri, V. Aribandi, Z. Qin, and D. Metzler. Are pre-trained convolutions better than pre-trained transformers? arXiv preprint arXiv:2105.03322, 2021.   \n[42] I. Tolstikhin, N. Houlsby, A. Kolesnikov, L. Beyer, X. Zhai, T. Unterthiner, J. Yung, D. Keysers, J. Uszkoreit, M. Lucic, et al. Mlp-mixer: An all-mlp architecture for vision. arXiv preprint arXiv:2105.01601, 2021.   \n[43] H. Touvron, P. Bojanowski, M. Caron, M. Cord, A. El-Nouby, E. Grave, A. Joulin, G. Synnaeve, J. Verbeek, and H. Jégou. Resmlp: Feedforward networks for image classification with dataefficient training. arXiv preprint arXiv:2105.03404, 2021.   \n[44] A. Vaswani, N. Shazeer, N. Parmar, J. Uszkoreit, L. Jones, A. N. Gomez, L. Kaiser, and I. Polosukhin. Attention is all you need. arXiv preprint arXiv:1706.03762, 2017.   \n[45] E. Voita, R. Sennrich, and I. Titov. The bottom-up evolution of representations in the transformer: A study with machine translation and language modeling objectives. In EMNLP, 2019.   \n[46] B. Wu, C. Xu, X. Dai, A. Wan, P. Zhang, Z. Yan, M. Tomizuka, J. Gonzalez, K. Keutzer, and P. Vajda. Visual transformers: Token-based image representation and processing for computer vision. arXiv preprint arXiv:2006.03677, 2020.   \n[47] J. M. Wu, Y. Belinkov, H. Sajjad, N. Durrani, F. Dalvi, and J. Glass. Similarity analysis of contextual word representation models. arXiv preprint arXiv:2005.01172, 2020.   \n[48] S. Wu, A. Conneau, H. Li, L. Zettlemoyer, and V. Stoyanov. Emerging cross-lingual structure in pretrained language models. arXiv preprint arXiv:1911.01464, 2019.   \n[49] L. Yuan, Y. Chen, T. Wang, W. Yu, Y. Shi, Z. Jiang, F. E. Tay, J. Feng, and S. Yan. Tokens-to-token vit: Training vision transformers from scratch on imagenet. arXiv preprint arXiv:2101.11986, 2021.   \n[50] X. Zhai, J. Puigcerver, A. Kolesnikov, P. Ruyssen, C. Riquelme, M. Lucic, J. Djolonga, A. S. Pinto, M. Neumann, A. Dosovitskiy, et al. The visual task adaptation benchmark. 2019. ",
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+        "text": "DEEP CONTINUOUS CLUSTERING ",
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+        "text": "ABSTRACT ",
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+        "text": "Clustering high-dimensional datasets is hard because interpoint distances become less informative in high-dimensional spaces. We present a clustering algorithm that performs nonlinear dimensionality reduction and clustering jointly. The data is embedded into a lower-dimensional space by a deep autoencoder. The autoencoder is optimized as part of the clustering process. The resulting network produces clustered data. The presented approach does not rely on prior knowledge of the number of ground-truth clusters. Joint nonlinear dimensionality reduction and clustering are formulated as optimization of a global continuous objective. We thus avoid discrete reconfigurations of the objective that characterize prior clustering algorithms. Experiments on datasets from multiple domains demonstrate that the presented algorithm outperforms state-of-the-art clustering schemes, including recent methods that use deep networks. ",
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+        "text": "1 INTRODUCTION ",
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+        "text": "Clustering is a fundamental procedure in machine learning and data analysis. Well-known approaches include center-based methods and their generalizations (Banerjee et al., 2005; Teboulle, 2007), and spectral methods $\\mathrm { N g }$ et al., 2001; von Luxburg, 2007). Despite decades of progress, reliable clustering of noisy high-dimensional datasets remains an open problem. High dimensionality poses a particular challenge because assumptions made by many algorithms break down in high-dimensional spaces (Ball, 1997; Beyer et al., 1999; Steinbach et al., 2004). ",
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+        "text": "There are techniques that reduce the dimensionality of data by embedding it in a lower-dimensional space (van der Maaten et al., 2009). Such general techniques, based on preserving variance or dissimilarity, may not be optimal when the goal is to discover cluster structure. Dedicated algorithms have been developed that combine dimensionality reduction and clustering by fitting low-dimensional subspaces (Kriegel et al., 2009; Vidal, 2011). Such algorithms can achieve better results than pipelines that first apply generic dimensionality reduction and then cluster in the reduced space. However, frameworks such as subspace clustering and projected clustering operate on linear subspaces and are therefore limited in their ability to handle datasets that lie on nonlinear manifolds. ",
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+        "text": "Recent approaches have sought to overcome this limitation by constructing a nonlinear embedding of the data into a low-dimensional space in which it is clustered (Dizaji et al., 2017; Xie et al., 2016; Yang et al., 2016; 2017). Ultimately, the goal is to perform nonlinear embedding and clustering jointly, such that the embedding is optimized to bring out the latent cluster structure. These works have achieved impressive results. Nevertheless, they are based on classic center-based, divergencebased, or hierarchical clustering formulations and thus inherit some limitations from these classic methods. In particular, these algorithms require setting the number of clusters a priori. And the optimization procedures they employ involve discrete reconfigurations of the objective, such as discrete reassignments of datapoints to centroids or merging of putative clusters in an agglomerative procedure. Thus it is challenging to integrate them with an optimization procedure that modifies the embedding of the data itself. ",
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+        "text": "We seek a procedure for joint nonlinear embedding and clustering that overcomes some of the limitations of prior formulations. There are a number of characteristics we consider desirable. First, we wish to express the joint problem as optimization of a single continuous objective. Second, this optimization should be amenable to scalable gradient-based solvers such as modern variants of SGD. Third, the formulation should not require setting the number of clusters a priori, since this number is often not known in advance. ",
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+        "text": "While any one of these desiderata can be fulfilled by some existing approaches, the combination is challenging. For example, it has long been known that the $k$ -means objective can be optimized by SGD (Bottou & Bengio, 1994). But this family of formulations requires positing the number of clusters $k$ in advance. Furthermore, the optimization is punctuated by discrete reassignments of datapoints to centroids, and is thus hard to integrate with continuous embedding of the data. ",
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+        "text": "In this paper, we present a formulation for joint nonlinear embedding and clustering that possesses all of the aforementioned desirable characteristics. Our approach is rooted in Robust Continuous Clustering (RCC), a recent formulation of clustering as continuous optimization of a robust objective (Shah & Koltun, 2017). The basic RCC formulation has the characteristics we seek, such as a clear continuous objective and no prior knowledge of the number of clusters. However, integrating it with deep nonlinear embedding is still a challenge. For example, Shah & Koltun (2017) presented a formulation for joint linear embedding and clustering (RCC-DR), but this formulation relies on a complex alternating optimization scheme with linear least-squares subproblems, and does not apply to nonlinear embeddings. ",
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+    {
+        "type": "text",
+        "text": "We present an integration of the RCC objective with dimensionality reduction that is simpler and more direct than RCC-DR, while naturally handling deep nonlinear embeddings. Our formulation avoids alternating optimization and the introduction of auxiliary dual variables. A deep nonlinear embedding of the data into a low-dimensional space is optimized while the data is clustered in the reduced space. The optimization is expressed by a global continuous objective and conducted by standard gradient-based solvers. ",
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+        "type": "text",
+        "text": "The presented algorithm is evaluated on high-dimensional datasets of images and documents. Experiments demonstrate that our formulation performs on par or better than state-of-the-art clustering algorithms across all datasets. This includes recent approaches that utilize deep networks and rely on prior knowledge of the number of ground-truth clusters. Controlled experiments confirm that joint dimensionality reduction and clustering is more effective than a stagewise approach, and that the high accuracy achieved by the presented algorithm is stable across different dimensionalities of the latent space. ",
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+        "text": "2 PRELIMINARIES ",
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+        "text": "Let $\\mathbf { X } = [ \\mathbf { x } _ { 1 } , \\dots , \\mathbf { x } _ { N } ]$ be a set of points in $\\mathbb { R } ^ { D }$ that must be clustered. Generic clustering algorithms that operate directly on $\\mathbf { X }$ rely strongly on interpoint distances. When $D$ is high, these distances become less informative (Ball, 1997; Beyer et al., 1999). Hence most clustering algorithms do not operate effectively in high-dimensional spaces. To overcome this problem, we embed the data into a lower-dimensional space $\\mathbb { R } ^ { d }$ . The embedding of the dataset into $\\mathbb { R } ^ { \\bar { d } }$ is denoted by $\\mathbf { Y } = [ \\mathbf { y } _ { 1 } , \\dots , \\mathbf { y } _ { N } ]$ The function that performs the embedding is denoted by $f _ { \\pmb { \\theta } } : \\mathbb { R } ^ { D }  \\mathbb { R } ^ { d }$ . Thus $\\mathbf { y } _ { i } = f _ { \\pmb { \\theta } } ( \\mathbf { x } _ { i } )$ for all $i$ ",
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+        "type": "text",
+        "text": "Our goal is to cluster the embedded dataset $\\mathbf { Y }$ and to optimize the parameters $\\pmb \\theta$ of the embedding as part of the clustering process. This formulation presents an obvious difficulty: if the embedding $f _ { \\theta }$ can be manipulated to assist the clustering of the embedded dataset $\\mathbf { Y }$ , there is nothing that prevents $f _ { \\theta }$ from distorting the dataset such that $\\mathbf { Y }$ no longer respects the structure of the original data. We must therefore introduce a regularizer on $\\pmb \\theta$ that constrains the low-dimensional image $\\mathbf { Y }$ with respect to the original high-dimensional dataset $\\mathbf { X }$ . To this end, we also consider a reverse mapping $g _ { \\omega } : \\mathbb { R } ^ { d }  \\mathbb { R } ^ { D }$ . To constrain $f _ { \\theta }$ to construct a faithful embedding of the original data, we require that the original data be reproducible from its low-dimensional image (Hinton $\\&$ Salakhutdinov, 2006): ",
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+        "type": "equation",
+        "img_path": "images/fe967646dbadc10f2f9521d6cc1f24ad399359e6e88d239c0b53707ab852a0fc.jpg",
+        "text": "$$\n\\operatorname* { m i n i m i z e } \\ \\| \\mathbf { X } - G _ { \\omega } ( \\mathbf { Y } ) \\| _ { F } ^ { 2 } , \\qquad \\mathrm { w h e r e ~ } \\mathbf { Y } = F _ { \\theta } ( \\mathbf { X } ) , \\quad \\Omega = \\{ \\theta , \\omega \\} .\n$$",
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+        "type": "text",
+        "text": "Here $F _ { \\pmb \\theta } ( \\mathbf { X } ) = [ f _ { \\pmb \\theta } ( \\mathbf { x } _ { 1 } ) , \\dots , f _ { \\pmb \\theta } ( \\mathbf { x } _ { N } ) ]$ , $G _ { \\omega } ( { \\mathbf Y } ) = [ g _ { \\omega } ( { \\mathbf y } _ { 1 } ) , \\dots , g _ { \\omega } ( { \\mathbf y } _ { N } ) ]$ , and $\\Vert \\cdot \\Vert _ { F }$ denotes the Frobenius norm. ",
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+    {
+        "type": "text",
+        "text": "Next, we must decide how the low-dimensional embedding $\\mathbf { Y }$ will be clustered. A natural solution is to choose a classic clustering framework: a center-based method such as $k$ -means, a divergence-based formulation, or an agglomerative approach. These are the paths taken in recent work on combining nonlinear dimensionality reduction and clustering (Dizaji et al., 2017; Xie et al., 2016; Yang et al., 2016; 2017). However, the classic clustering algorithms have a discrete structure: associations between centroids and datapoints need to be recomputed or putative clusters need to be merged. In either case, the optimization process is punctuated by discrete reconfigurations. This makes it difficult to coordinate the clustering of $\\mathbf { Y }$ with the optimization of the embedding parameters $\\pmb { \\Omega }$ that modify the dataset $\\mathbf { Y }$ itself. ",
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+        "type": "text",
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "Since we must conduct clustering in tandem with continuous optimization of the embedding, we seek a clustering algorithm that is inherently continuous and performs clustering by optimizing a continuous objective that does not need to be updated during the optimization. The recent RCC formulation provides a suitable starting point (Shah & Koltun, 2017). The key idea of RCC is to introduce a set of representatives $\\mathbf { Z } \\in \\mathbb { R } ^ { d \\times N }$ and optimize the following nonconvex objective: ",
+        "bbox": [
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+        "type": "equation",
+        "img_path": "images/d0c33457783beeaa158217b81b584e4e7c4bed5dd9d94fdb03941b8fea706cd2.jpg",
+        "text": "$$\n\\operatorname* { m i n i m i z e } _ { \\mathbf { z } } \\ \\frac { 1 } { 2 } \\| \\mathbf { Z } - \\mathbf { Y } \\| _ { F } ^ { 2 } + \\frac { \\lambda } { 2 } \\sum _ { ( i , j ) \\in \\mathcal { E } } w _ { i , j } \\rho ( \\| \\mathbf { z } _ { i } - \\mathbf { z } _ { j } \\| _ { 2 } ) ,\n$$",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "where $\\rho$ is a redescending M-estimator, $\\mathcal { E }$ is a graph connecting the datapoints, $\\{ w _ { i , j } \\}$ are appropriately defined weights, and $\\lambda$ is a coefficient that balances the two objective terms. The first term in objective (2) constrains the representatives to remain near the corresponding datapoints. The second term pulls the representatives to each other, encouraging them to merge. This formulation has a number of advantages. First, it reduces clustering to optimization of a fixed continuous objective. Second, each datapoint has its own representative in $\\mathbf { Z }$ and no prior knowledge of the number of clusters is needed. Third, the nonconvex robust estimator $\\rho$ limits the influence of outliers. ",
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+        "type": "text",
+        "text": "To perform nonlinear embedding and clustering jointly, we wish to integrate the reconstruction objective (1) and the RCC objective (2). This idea is developed in the next section. ",
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3 DEEP CONTINUOUS CLUSTERING ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1 OBJECTIVE ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The Deep Continuous Clustering (DCC) algorithm optimizes the following objective: ",
+        "bbox": [
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+            468,
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/4843fe133465e5da08d9681e881c473ea17826038eba8802b196e8b9391a82f6.jpg",
+        "text": "$$\n\\mathcal { L } ( \\Omega , \\mathbf { Z } ) = \\frac { 1 } { D } \\underbrace { \\| \\mathbf { X } - G _ { \\omega } ( \\mathbf { Y } ) \\| _ { F } ^ { 2 } } _ { \\mathrm { r e c o n s i r u c t i o n \\ l o s s } } + \\frac { 1 } { d } \\left( \\sum _ { i } \\rho _ { 1 } \\big ( \\| \\mathbf { z } _ { i } - \\mathbf { y } _ { i } \\| _ { 2 } ; \\mu _ { 1 } \\big ) + \\lambda \\sum _ { ( i , j ) \\in \\mathcal { E } } w _ { i , j } \\rho _ { 2 } \\big ( \\| \\mathbf { z } _ { i } - \\mathbf { z } _ { j } \\| _ { 2 } ; \\mu _ { 2 } \\big ) \\right)\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where $\\mathbf { Y } = F _ { \\pmb { \\theta } } ( \\mathbf { X } )$ ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "This formulation bears some similarity to RCC-DR (Shah & Koltun, 2017), but differs in three major respects. First, RCC-DR only operates on a linear embedding defined by a sparse dictionary, while DCC optimizes a more expressive nonlinear embedding parameterized by $\\pmb { \\Omega }$ . Second, RCC-DR alternates between optimizing dictionary atoms, sparse codes, representatives $\\mathbf { Z }$ , and dual line process variables; in contrast, DCC avoids duality altogether and optimizes the global objective directly. Third, DCC does not rely on closed-form or linear least-squares solutions to subproblems; rather, the joint objective is optimized by modern gradient-based solvers, which are commonly used for deep representation learning and are highly scalable. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "We now discuss objective (3) and its optimization in more detail. The mappings $F _ { \\theta }$ and $G _ { \\omega }$ are performed by an autoencoder with fully-connected or convolutional layers and rectified linear units after each affine projection (Hinton & Salakhutdinov, 2006; Nair & Hinton, 2010). The graph $\\mathcal { E }$ is constructed on $\\mathbf { X }$ using the mutual kNN criterion (Brito et al., 1997), augmented by the minimum spanning tree of the kNN graph to ensure connectivity to all datapoints. The role of M-estimators $\\rho _ { 1 }$ and $\\rho _ { 2 }$ is to pull the representatives of a true underlying cluster into a single point, while disregarding spurious connections across clusters. For both estimators, we use scaled Geman-McClure functions (Geman & McClure, 1987): ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/90e8468ce82da93dcc4901b342468e4dc522e6b3f43b8056b036fee9297a9fb0.jpg",
+        "text": "$$\n\\rho _ { 1 } ( x ; \\mu _ { 1 } ) = { \\frac { \\mu _ { 1 } x ^ { 2 } } { \\mu _ { 1 } + x ^ { 2 } } } \\quad { \\mathrm { a n d } } \\quad \\rho _ { 2 } ( x ; \\mu _ { 2 } ) = { \\frac { \\mu _ { 2 } x ^ { 2 } } { \\mu _ { 2 } + x ^ { 2 } } } .\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The parameters $\\mu _ { 1 }$ and $\\mu _ { 2 }$ control the radii of the convex basins of the estimators. The weights $w _ { i , j }$ are set to balance the contribution of each datapoint to the pairwise loss: ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/a1e506e93df44953c036b23de0dceb4c5e8786420aa829b54e6ee08024c3ff8c.jpg",
+        "text": "$$\nw _ { i , j } = { \\frac { { \\frac { 1 } { N } } \\sum _ { k = 1 } ^ { n } n _ { k } } { \\sqrt { n _ { i } n _ { j } } } } .\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Here $n _ { i }$ is the degree of $\\mathbf { z } _ { i }$ in the graph $\\mathcal { E }$ . The numerator is simply the average degree. The parameter $\\lambda$ balances the relative strength of the data loss and the pairwise loss. To balance the different terms, we set $\\begin{array} { r } { \\lambda = \\frac { \\| \\mathbf { Y } \\| _ { 2 } } { \\| \\mathbf { A } \\| _ { 2 } } } \\end{array}$ , where $\\begin{array} { r } { \\mathbf { A } = \\sum _ { ( i , j ) \\in \\mathcal { E } } w _ { i , j } ( \\mathbf { e } _ { i } - \\mathbf { e } _ { j } ) ( \\mathbf { e } _ { i } - \\mathbf { e } _ { j } ) ^ { \\top } } \\end{array}$ and $\\| \\cdot \\| _ { 2 }$ denotes the spectral norm. In contrast to RCC-DR, the parameter $\\lambda$ need not be updated during the optimization. ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.2 OPTIMIZATION ",
+        "text_level": 1,
+        "bbox": [
+            176,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Objective (3) can be optimized using scalable modern forms of stochastic gradient descent (SGD). Note that each $\\mathbf { z } _ { i }$ is updated only via its corresponding loss and pairwise terms. On the other hand, the autoencoder parameters $\\pmb { \\Omega }$ are updated via all data samples. Thus in a single epoch, there is bound to be a difference between the update rates for $\\mathbf { Z }$ and $\\pmb { \\Omega }$ . To deal with this imbalance, an adaptive solver such as Adam should be used (Kingma & Ba, 2015). ",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Another difficulty is that the graph $\\mathcal { E }$ connects all datapoints such that a randomly sampled minibatch is likely to be connected by pairwise terms to datapoints outside the minibatch. In other words, the objective (3), and more specifically the pairwise loss, does not trivially decompose over datapoints. This requires some care in the construction of minibatches. Instead of sampling datapoints, we sample subsets of edges from $\\mathcal { E }$ . The corresponding minibatch $\\boldsymbol { B }$ is defined by all nodes incident to the sampled edges. However, if we simply restrict the objective (3) to the minibatch and take a gradient step, the reconstruction and data terms will be given additional weight since the same datapoint can participate in different minibatches, once for each incident edge. To maintain balance between the terms, we must weigh the contribution of each datapoint in the minibatch. The rebalanced minibatch loss is given by ",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/f92f47ff2f4c4eff9b2e2bd4c77095b781c39ae57b8e46d28489f2bd94e149f2.jpg",
+        "text": "$$\n\\hat { \\mathbf { \\xi } } _ { B } ( \\mathbf { \\Omega } , \\mathbf { Z } ) = \\frac { 1 } { | B | } \\sum _ { i \\in B } w _ { i } \\left( \\frac { \\| \\mathbf { x } _ { i } - g _ { \\omega } ( \\mathbf { y } _ { i } ) \\| _ { 2 } ^ { 2 } } { D } + \\frac { \\rho _ { 1 } \\left( \\left\\| \\mathbf { z } _ { i } - \\mathbf { y } _ { i } \\right\\| _ { 2 } \\right) } { d } \\right) + \\frac { \\lambda } { | B | } \\sum _ { ( i , j ) \\in \\mathcal { E } _ { B } } w _ { i , j } \\rho _ { 2 } \\left( \\left\\| \\mathbf { z } _ { i } - \\mathbf { z } _ { j } \\right\\| _ { 2 } \\right)\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where $\\mathbf { y } _ { i } = f _ { \\pmb { \\theta } } ( \\mathbf { x } _ { i } ) \\quad \\forall i \\in \\pmb { B }$ . ",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Here $\\begin{array} { r } { w _ { i } = \\frac { n _ { i } ^ { \\mathtt { B } } } { n _ { i } } } \\end{array}$ , where $n _ { i } ^ { B }$ is the number of edges connected to the $i ^ { \\mathrm { t h } }$ node in the subgraph $\\mathcal { E } _ { B }$ ",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The gradients of $\\mathcal { L } _ { B }$ with respect to the low-dimensional embedding $\\mathbf { Y }$ and the representatives $\\mathbf { Z }$ are given by ",
+        "bbox": [
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+            526,
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/240410590e5178293b06b171e9aaa36b6ede8df76bb09fd933c27aa5b51934e0.jpg",
+        "text": "$$\n\\begin{array} { r l } & { \\displaystyle \\frac { \\partial \\mathcal { L } _ { \\mathcal { B } } } { \\partial \\mathbf { y } _ { i } } = \\frac { 1 } { | \\mathcal { B } | } \\left( \\frac { w _ { i } \\mu _ { 1 } ^ { 2 } ( \\mathbf { y } _ { i } - \\mathbf { z } _ { i } ) } { d ( \\mu _ { 1 } + \\| \\mathbf { z } _ { i } - \\mathbf { y } _ { i } \\| _ { 2 } ^ { 2 } ) ^ { 2 } } + \\frac { 2 w _ { i } ( g _ { \\omega } ( \\mathbf { y } _ { i } ) - \\mathbf { x } _ { i } ) } { D } \\frac { \\partial g _ { \\omega } ( \\mathbf { y } _ { i } ) } { \\partial \\mathbf { y } _ { i } } \\right) } \\\\ & { \\displaystyle \\frac { \\partial \\mathcal { L } _ { \\mathcal { B } } } { \\partial \\mathbf { z } _ { i } } = \\frac { 1 } { | \\mathcal { B } | } \\left( \\frac { w _ { i } \\mu _ { 1 } ^ { 2 } ( \\mathbf { z } _ { i } - \\mathbf { y } _ { i } ) } { d ( \\mu _ { 1 } + \\| \\mathbf { z } _ { i } - \\mathbf { y } _ { i } \\| _ { 2 } ^ { 2 } ) ^ { 2 } } + { \\lambda } \\mu _ { 2 } ^ { 2 } \\sum _ { ( i , j ) \\in \\mathcal { E } _ { \\mathcal { B } } } \\frac { w _ { i , j } ( \\mathbf { z } _ { i } - \\mathbf { z } _ { j } ) } { ( \\mu _ { 2 } + \\| \\mathbf { z } _ { i } - \\mathbf { z } _ { j } \\| _ { 2 } ^ { 2 } ) ^ { 2 } } \\right) } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "These gradients are propagated to the parameters $\\pmb { \\Omega }$ . ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.3 INITIALIZATION, CONTINUATION AND STOPPING CRITERION ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Initialization. The embedding parameters $\\pmb { \\Omega }$ are initialized using the stacked denoising autoencoder (SDAE) framework (Vincent et al., 2010). Each pair of corresponding encoding and decoding layers is pretrained in turn. Noise is introduced during pretraining by adding dropout to the input of each affine projection (Srivastava et al., 2014). Encoder-decoder layer pairs are pretrained sequentially, from the outer to the inner. After all layer pairs are pretrained, the entire SDAE is fine-tuned end-to-end using the reconstruction loss. This completes the initialization of the embedding parameters $\\pmb { \\Omega }$ . These parameters are used to initialize the representatives $\\mathbf { Z }$ , which are set to $\\mathbf { Z } = \\mathbf { Y } = F _ { \\pmb { \\theta } } ( \\mathbf { X } )$ . ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Continuation. The price of robustness is the nonconvexity of the estimators $\\rho _ { 1 }$ and $\\rho _ { 2 }$ . One way to alleviate the dangers of nonconvexity is to use a continuation scheme that gradually sharpens the estimator (Blake & Zisserman, 1987; Mobahi & Fisher III, 2015). Following Shah & Koltun (2017), we initially set $\\mu _ { i }$ to a high value that makes the estimator $\\rho _ { i }$ effectively convex in the relevant range. The value of $\\mu _ { i }$ is decreased on a regular schedule until a threshold $\\frac { \\delta _ { i } } { 2 }$ is reached. We set $\\delta _ { 1 }$ to the mean of the distance of each $\\mathbf { y } _ { i }$ to the mean of $\\mathbf { Y }$ , and $\\delta _ { 2 }$ to the mean of the bottom $1 \\%$ of the pairwise distances in $\\mathcal { E }$ at initialization. ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Algorithm 1 Deep Continuous Clustering ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "1: input: Data samples $\\{ { \\bf { x } } _ { i } \\} _ { i }$ .   \n2: output: Cluster assignment $\\{ c _ { i } \\} _ { i }$ .   \n3: Construct a graph $\\mathcal { E }$ on $\\mathbf { X }$ .   \n4: Initialize $\\pmb { \\Omega }$ and $\\mathbf { Z }$ .   \n5: Precompute $\\lambda , w _ { i , j } , \\delta _ { 1 } , \\delta _ { 2 }$ . Initialize $\\mu _ { 1 } , \\mu _ { 2 }$ .   \n6: while stopping criterion not met do   \n7: Every iteration, construct a minibatch $\\boldsymbol { B }$ defined by a sample of edges $\\mathcal { E } _ { B }$ .   \n8: Update $\\{ \\mathbf { z } _ { i } \\} _ { i \\in B }$ and $\\pmb { \\Omega }$ .   \n9: Every $M$ epochs, update $\\begin{array} { r } { \\mu _ { i } = \\operatorname* { m a x } \\left( \\frac { \\mu _ { i } } { 2 } , \\frac { \\delta _ { i } } { 2 } \\right) } \\end{array}$ .   \n10: end while   \n11: Construct graph $\\mathcal { G } = ( \\nu , \\mathcal { F } )$ with $f _ { i , j } = 1$ if $\\| \\mathbf { z } _ { i } ^ { * } - \\mathbf { z } _ { j } ^ { * } \\| _ { 2 } < \\delta _ { 2 }$ .   \n12: Output clusters given by the connected components of $\\mathcal { G }$ . ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Stopping criterion. Once the continuation scheme is completed, DCC monitors the computed clustering. At the end of every epoch, a graph $\\mathcal { G } = ( \\nu , \\mathcal { F } )$ is constructed such that $f _ { i , j } = 1$ if $\\| \\mathbf { z } _ { i } - \\mathbf { z } _ { j } \\| < \\delta _ { 2 }$ . The cluster assignment is given by the connected components of $\\mathcal { G }$ . DCC compares this cluster assignment to the one produced at the end of the preceding epoch. If less than $0 . 1 \\%$ of the edges in $\\mathcal { E }$ changed from intercluster to intracluster or vice versa, DCC outputs the computed clustering and terminates. ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Complete algorithm. The complete algorithm is summarized in Algorithm 1. ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4 EXPERIMENTS ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.1 DATASETS ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We conduct experiments on six high-dimensional datasets, which cover domains such as handwritten digits, objects, faces, and text. We used datasets from Shah & Koltun (2017) that had dimensionality above 100. The datasets are further described in the appendix. All features are normalized to the range [0, 1]. ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Note that DCC is an unsupervised learning algorithm. Unlabelled data is embedded and clustered with no supervision. There is thus no train/test split. ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.2 BASELINES",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The presented DCC algorithm is compared to 12 baselines, which include both classic and deep clustering algorithms. The baselines include $k$ -means $^ { + + }$ (Arthur & Vassilvitskii, 2007), DBSCAN (Ester et al., 1996), two variants of agglomerative clustering: Ward (AC-W) and graph degree linkage (GDL) (Zhang et al., 2012), two variants of spectral clustering: spectral embedded clustering (SEC) (Nie et al., 2011) and local discriminant models and global integration (LDMGI) (Yang et al., 2010), and two variant of robust continuous clustering: RCC and RCC-DR (Shah & Koltun, 2017). ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The deep clustering baselines include four recent approaches that share our basic motivation and use deep networks for clustering: deep embedded clustering (DEC) (Xie et al., 2016), joint unsupervised learning (JULE) (Yang et al., 2016), the deep clustering network (DCN) (Yang et al., 2017), and deep embedded regularized clustering (DEPICT) (Dizaji et al., 2017). These are strong baselines that use deep autoencoders, the same network structure as our approach (DCC). The key difference is in the loss function and the consequent optimization procedure. The prior formulations are built on KLdivergence clustering, agglomerative clustering, and $k$ -means, which involve discrete reconfiguration of the objective during the optimization and rely on knowledge of the number of ground-truth clusters either in the design of network architecture, during the embedding optimization, or in post-processing. In contrast, DCC optimizes a robust continuous loss and does not rely on prior knowledge of the number of clusters. ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.3 IMPLEMENTATION ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We report experimental results for two different autoencoder architectures: one with only fullyconnected layers and one with convolutional layers. This is motivated by prior deep clustering algorithms, some of which used fully-connected architectures and some convolutional. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "For fully-connected autoencoders, we use the same autoencoder architecture as DEC (Xie et al., 2016). Specifically, for all experiments on all datasets, we use an autoencoder with the following dimensions: D–500–500–2000–d–2000–500–500–D. This autoencoder architecture follows parametric t-SNE (van der Maaten, 2009). ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "For convolutional autoencoders, the network architecture is modeled on JULE (Yang et al., 2016). The architecture is specified in the appendix. As in Yang et al. (2016), the number of layers depends on image resolution in the dataset and it is set such that the output resolution of the encoder is about $4 \\times 4$ . ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "In both architectures and for all datasets, the dimensionality of the reduced space is set to $d = 1 0$ . (It is only varied for controlled experiments that analyze stability with respect to $d$ .) No dataset-specific hyperparameter tuning was done. For autoencoder initialization, a minibatch size of 256 and dropout probability of 0.2 are used. SDAE pretraining and finetuning start with a learning rate of 0.1, which is decreased by a factor of 10 every 80 epochs. Each layer is pretrained for 200 epochs. Finetuning of the whole SDAE is performed for 400 epochs. For the fully-connected SDAE, the learning rates are scaled in accordance with the dimensionality of the dataset. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "For m-kNN graph construction, the nearest-neighbor parameter $k$ is set to 10 and the cosine distance metric is used. The Adam solver is used with its default learning rate of 0.001 and momentum 0.99. Minibatches are constructed by sampling 128 edges. DCC was implemented using the PyTorch library. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "For the baselines, we use publicly available implementations. For $k$ -means $^ { + + }$ , DBSCAN and ACW, we use the implementations in the SciPy library and report the best results across ten random restarts. For a number of baselines, we performed hyperparameter search to maximize their reported performance. For DBSCAN, we searched over values of $E p s$ , for LDMGI we searched over values of the regularization constant $\\lambda$ , for SEC we searched over values of the parameter $\\mu$ , and for GDL we tuned the graph construction parameter $a$ . ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "The DCN approach uses a different network architecture for each dataset. Wherever possible, we report results using their dataset-specific architecture. For YTF, Coil100, and YaleB, we use their reference architecture for MNIST. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.4 MEASURES ",
+        "text_level": 1,
+        "bbox": [
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+        "type": "text",
+        "text": "Common measures of clustering accuracy include normalized mutual information (NMI) (Strehl & Ghosh, 2002) and clustering accuracy (ACC). However, NMI is known to be biased in favor of fine-grained partitions and ACC is also biased on imbalanced datasets (Vinh et al., 2010). To overcome these biases, we use adjusted mutual information (AMI) (Vinh et al., 2010), defined as ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "img_path": "images/cfef6f849cfb3917f3eca8275e99a60a0b5c6a66100797df2fb836e480a7d25b.jpg",
+        "text": "$$\n\\mathrm { A M I } ( \\mathbf { c } , \\hat { \\mathbf { c } } ) = \\frac { \\mathbf { M } \\mathrm { I } ( \\mathbf { c } , \\hat { \\mathbf { c } } ) - E [ \\mathbf { M } \\mathrm { I } ( \\mathbf { c } , \\hat { \\mathbf { c } } ) ] } { \\sqrt { \\mathbf { H } ( \\mathbf { c } ) \\mathbf { H } ( \\hat { \\mathbf { c } } ) } - E [ \\mathbf { M } \\mathrm { I } ( \\mathbf { c } , \\hat { \\mathbf { c } } ) ] } .\n$$",
+        "text_format": "latex",
+        "bbox": [
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+            710,
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+            747
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Here $\\mathrm { H } ( \\cdot )$ is the entropy, $\\operatorname { M I } ( \\cdot , \\cdot )$ is the mutual information, and c and cˆ are the two partitions being compared. AMI lies in a range $[ 0 , 1 ]$ . Higher is better. For completeness, results according to ACC are reported in the appendix. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "4.5 RESULTS ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "The results are summarized in Table 1. Among deep clustering methods that use fully-connected networks, DCN and DEC are not as accurate as fully-connected DCC and are also less consistent: the performance of DEC drops on the high-dimensional image datasets, while DCN is far behind on MNIST and YaleB. Among deep clustering methods that use convolutional networks, the performance of DEPICT drops on COIL100 and YTF, while JULE is far behind on YTF. The GDL algorithm failed to scale to the full MNIST dataset and the corresponding measurement is marked as $\\mathrm { \\dot { \\Omega } n / a \\Omega ^ { \\prime } }$ . ",
+        "bbox": [
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+            839,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/deadd05ee4289f29fcab67478ad40072e5a08ce8b0a3acc7eb08e8ab532a44e3.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Algorithm</td><td>MNIST</td><td>Coil100</td><td>YTF</td><td>YaleB</td><td>Reuters</td><td>RCV1</td></tr><tr><td>k-means++</td><td>0.500</td><td>0.803</td><td>0.783</td><td>0.615</td><td>0.516</td><td>0.355</td></tr><tr><td>AC-W</td><td>0.679</td><td>0.853</td><td>0.801</td><td>0.767</td><td>0.471</td><td>0.364</td></tr><tr><td>DBSCAN</td><td>0.000</td><td>0.399</td><td>0.739</td><td>0.456</td><td>0.011</td><td>0.014</td></tr><tr><td>SEC</td><td>0.469</td><td>0.849</td><td>0.745</td><td>0.849</td><td>0.498</td><td>0.069</td></tr><tr><td>LDMGI</td><td>0.761</td><td>0.888</td><td>0.518</td><td>0.945</td><td>0.523</td><td>0.382</td></tr><tr><td>GDL</td><td>n/a</td><td>0.958</td><td>0.655</td><td>0.924</td><td>0.401</td><td>0.020</td></tr><tr><td>RCC</td><td>0.893</td><td>0.957</td><td>0.836</td><td>0.975</td><td>0.556</td><td>0.138</td></tr><tr><td>RCC-DR</td><td>0.828</td><td>0.957</td><td>0.874</td><td>0.974</td><td>0.553</td><td>0.442</td></tr><tr><td colspan=\"7\">Fully-connected</td></tr><tr><td>DCN</td><td>0.570</td><td>0.810</td><td>0.790</td><td>0.590</td><td>0.430</td><td>0.470</td></tr><tr><td>DEC</td><td>0.840</td><td>0.611</td><td>0.807</td><td>0.000</td><td>0.397</td><td>0.500</td></tr><tr><td>DCC</td><td>0.912</td><td>0.952</td><td>0.877</td><td>0.955</td><td>0.572</td><td>0.495</td></tr><tr><td colspan=\"7\">Convolutional</td></tr><tr><td>JULE</td><td>0.900</td><td>0.979</td><td>0.574</td><td>0.990</td><td></td><td></td></tr><tr><td>DEPICT</td><td>0.919</td><td>0.667</td><td>0.785</td><td>0.989</td><td></td><td></td></tr><tr><td>DCC</td><td>0.913</td><td>0.962</td><td>0.903</td><td>0.985</td><td></td><td></td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Table 1: Clustering accuracy of DCC and 12 baselines, measured by AMI. Higher is better. Methods that do no use deep networks are listed first, followed by deep clustering algorithms that use fullyconnected autoencoders (including the fully-connected configuration of DCC) and deep clustering algorithms that use convolutional autoencoders (including the convolutional configuration of DCC). Results that are within $1 \\%$ of the highest accuracy achieved by any method are highlighted in bold. DCC performs on par or better than prior deep clustering formulations, without relying on a priori knowledge of the number of ground-truth clusters. ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "5 ANALYSIS ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Importance of joint optimization. We now analyze the importance of performing dimensionality reduction and clustering jointly, versus performing dimensionality reduction and then clustering the embedded data. To this end, we use the same SDAE architecture and training procedure as fully-connected DCC. We optimize the autoencoder but do not optimize the full DCC objective. This yields a standard nonlinear embedding, using the same autoencoder that is used by DCC, into a space with the same reduced dimensionality $d$ . In this space, we apply a number of clustering algorithms: $k$ -means $^ { + + }$ , AC-W, DBSCAN, SEC, LDMGI, GDL, and RCC. The results are shown in Table 2 (top). ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "These results should be compared to results reported in Table 1. The comparison shows that the accuracy of the baseline algorithms benefits from dimensionality reduction. However, in all cases their accuracy is still lower than that attained by DCC using joint optimization. Furthermore, although RCC and DCC share the same underlying nearest-neighbor graph construction and a similar clustering loss, the performance of DCC far surpasses that achieved by stagewise SDAE embedding followed by RCC. Note also that the relative performance of most baselines drops on Coil100 and YaleB. We hypothesize that the fully-connected SDAE is limited in its ability to discover a good low-dimensional embedding for very high-dimensional image datasets (tens of thousands of dimensions for Coil100 and YaleB). ",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Next, we show the performance of the same clustering algorithms when they are applied in the reduced space produced by DCC. These results are reported in Table 2 (bottom). In comparison to Table 2 (top), the performance of all algorithms improves significantly and some results are now on par or better than the results of DCC as reported in Table 1. The improvement for $k$ -means $^ { + + }$ Ward, and DBSCAN is particularly striking. This indicates that the performance of many clustering algorithms can be improved by first optimizing a low-dimensional embedding using DCC and then clustering in the learned embedding space. ",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/763749ca6c8e9fbc07ce75b1f06942a710148c883620d94013d592fd6bf2ecab.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Dataset</td><td>k-means++</td><td>AC-W</td><td>DBSCAN</td><td>SEC</td><td>LDMGI</td><td>GDL</td><td>RCC</td><td>DCC</td></tr><tr><td colspan=\"9\">Clustering in a reduced space learned by SDAE</td></tr><tr><td>MNIST</td><td>0.669</td><td>0.784</td><td>0.115</td><td>n/a</td><td>0.828</td><td>n/a</td><td>0.881</td><td>0.912</td></tr><tr><td>Coil100</td><td>0.333</td><td>0.336</td><td>0.170</td><td>0.384</td><td>0.318</td><td>0.335</td><td>0.589</td><td>0.952</td></tr><tr><td>YTF</td><td>0.764</td><td>0.831</td><td>0.595</td><td>0.527</td><td>0.612</td><td>0.699</td><td>0.827</td><td>0.877</td></tr><tr><td>YaleB</td><td>0.673</td><td>0.688</td><td>0.503</td><td>0.493</td><td>0.676</td><td>0.742</td><td>0.812</td><td>0.955</td></tr><tr><td>Reuters</td><td>0.501</td><td>0.494</td><td>0.042</td><td>0.435</td><td>0.517</td><td>0.488</td><td>0.542</td><td>0.572</td></tr><tr><td>RCV1</td><td>0.454</td><td>0.430</td><td>0.075</td><td>0.442</td><td>0.060</td><td>0.055</td><td>0.410</td><td>0.495</td></tr><tr><td colspan=\"9\">Clustering in a reduced space learned by DCC</td></tr><tr><td>MNIST</td><td>0.880</td><td>0.883</td><td>0.890</td><td>n/a</td><td>0.868</td><td>n/a</td><td>0.912</td><td>0.912</td></tr><tr><td>Coil100</td><td>0.947</td><td>0.947</td><td>0.569</td><td>0.604</td><td>0.919</td><td>0.915</td><td>0.891</td><td>0.952</td></tr><tr><td>YTF</td><td>0.845</td><td>0.841</td><td>0.896</td><td>0.586</td><td>0.762</td><td>0.658</td><td>0.879</td><td>0.877</td></tr><tr><td>YaleB</td><td>0.811</td><td>0.809</td><td>0.809</td><td>0.584</td><td>0.815</td><td>0.660</td><td>0.814</td><td>0.955</td></tr><tr><td>Reuters</td><td>0.553</td><td>0.554</td><td>0.560</td><td>0.479</td><td>0.586</td><td>0.401</td><td>0.581</td><td>0.572</td></tr><tr><td>RCV1</td><td>0.536</td><td>0.472</td><td>0.496</td><td>0.452</td><td>0.178</td><td>0.326</td><td>0.474</td><td>0.495</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Table 2: Importance of joint optimization. This table shows the accuracy (AMI) achieved by running prior clustering algorithms on a low-dimensional embedding of the data. For reference, DCC results from Table 1 are also listed. Top: The embedding is performed using the same autoencoder architecture as used by fully-connected DCC, into the same target space. However, dimensionality reduction and clustering are performed separately. Clustering accuracy is much lower than the accuracy achieved by DCC. Bottom: Here clustering is performed in the reduced space discovered by DCC. The performance of all clustering algorithms improves significantly. ",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Visualization. A visualization is provided in Figure 1. Here we used Barnes-Hut t-SNE (van der Maaten & Hinton, 2008; van der Maaten, 2014) to visualize a randomly sampled subset of 10K datapoints from the MNIST dataset. We show the original dataset, the dataset embedded by the SDAE into $\\mathbb { R } ^ { d }$ (optimized for dimensionality reduction), and the embedding into $\\mathbb { R } ^ { d }$ produced by DCC. As shown in the figure, the embedding produced by DCC is characterized by well-defined, clearly separated clusters. The clusters strongly correspond to the ground-truth classes (coded by color in the figure), but were discovered with no supervision. ",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/84f1886a5b0333f2664e8a7f3b5a3771f6db9d2bf54131d93821565f9213f235.jpg",
+        "image_caption": [
+            "Figure 1: Effect of joint dimensionality reduction and clustering on the embedding. (a) A randomly sampled subset of 10K points from the MNIST dataset, visualized using t-SNE. (b) An embedding of these points into $\\mathbb { R } ^ { d }$ , performed by an SDAE that is optimized for dimensionality reduction. (c) An embedding of the same points by the same network, optimized with the DCC objective. When optimized for joint dimensionality reduction and clustering, the network produces an embedding with clearly separated clusters. Best viewed in color. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+            613,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Robustness to dimensionality of the latent space. Next we study the robustness of DCC to the dimensionality $d$ of the latent space. For this experiment, we consider fully-connected DCC. We vary $d$ between 5 and 60 and measure AMI on the MNIST and Reuters datasets. For comparison, we report the performance of DEC, which uses the same autoencoder architecture, as well as the accuracy attained by running $k$ -means $^ { + + }$ on the output of the SDAE, optimized for dimensionality reduction. The results are shown in Figure 2. ",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/79c6d1e411b28f9ee42f4ef94bc6f56620b29ef4eaa55555b19d53dac97c81a5.jpg",
+        "image_caption": [
+            "Figure 2: Robustness to dimensionality of the latent space. Clustering accuracy (AMI) as a function of the dimensionality $d$ . Best viewed in color. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            176,
+            111,
+            838,
+            266
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "The results yield two conclusions. First, the accuracy of DCC, DEC, and $\\mathrm { S D A E } { + } k$ -means gradually decreases as the dimensionality $d$ increases. This supports the common view that clustering becomes progressively harder as the dimensionality of the data increases. Second, the results demonstrate that DCC is more robust to increased dimensionality than DEC and SDAE. For example, on MNIST, as the dimensionality $d$ changes from 5 to 60, the accuracy of DEC and SDAE drops by $28 \\%$ and $3 5 \\%$ , respectively, while the accuracy of DCC decreases by only $9 \\%$ . When $d = 6 0$ , the accuracy attained by DCC is higher than the accuracy attained by DEC and SDAE by $27 \\%$ and $40 \\%$ , respectively. ",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "6 CONCLUSION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            446,
+            318,
+            462
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "We have presented a clustering algorithm that combines nonlinear dimensionality reduction and clustering. Dimensionality reduction is performed by a deep network that embeds the data into a lower-dimensional space. The embedding is optimized as part of the clustering process and the resulting network produces clustered data. The presented algorithm does not rely on a priori knowledge of the number of ground-truth clusters. Nonlinear dimensionality reduction and clustering are performed by optimizing a global continuous objective using scalable gradient-based solvers. ",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "REFERENCES ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            582,
+            285,
+            597
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "David Arthur and Sergei Vassilvitskii. k-means $^ { + + }$ : The advantages of careful seeding. In Symposium on Discrete Algorithms (SODA), 2007. ",
+        "bbox": [
+            173,
+            604,
+            825,
+            632
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Keith Ball. An elementary introduction to modern convex geometry. In Flavors of Geometry. 1997. ",
+        "bbox": [
+            173,
+            640,
+            825,
+            656
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Arindam Banerjee, Srujana Merugu, Inderjit S. Dhillon, and Joydeep Ghosh. Clustering with Bregman divergences. Journal of Machine Learning Research (JMLR), 6, 2005. ",
+        "bbox": [
+            176,
+            662,
+            823,
+            693
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Kevin S. Beyer, Jonathan Goldstein, Raghu Ramakrishnan, and Uri Shaft. When is “nearest neighbor” meaningful? In International Conference on Database Theory (ICDT), 1999. ",
+        "bbox": [
+            174,
+            699,
+            823,
+            728
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Andrew Blake and Andrew Zisserman. Visual Reconstruction. MIT Press, 1987. ",
+        "bbox": [
+            174,
+            734,
+            705,
+            751
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Leon Bottou and Yoshua Bengio. Convergence properties of the´ $\\mathbf { k }$ -means algorithms. In Neural Information Processing Systems (NIPS), 1994. ",
+        "bbox": [
+            174,
+            758,
+            818,
+            787
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "M.R. Brito, E.L. Chavez, A.J. Quiroz, and J.E. Yukich. Connectivity of the mutual k-nearest-neighbor ´ graph in clustering and outlier detection. Statistics & Probability Letters, 35, 1997. ",
+        "bbox": [
+            173,
+            794,
+            823,
+            824
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Kamran Ghasedi Dizaji, Amirhossein Herandi, Cheng Deng, Weidong Cai, and Heng Huang. Deep clustering via joint convolutional autoencoder embedding and relative entropy minimization. In International Conference on Computer Vision (ICCV), 2017. ",
+        "bbox": [
+            176,
+            830,
+            821,
+            875
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Martin Ester, Hans-Peter Kriegel, Jorg Sander, and Xiaowei Xu. A density-based algorithm for ¨ discovering clusters in large spatial databases with noise. In Knowledge Discovery and Data Mining (KDD), 1996. ",
+        "bbox": [
+            176,
+            881,
+            823,
+            922
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Stuart Geman and Donald E. McClure. Statistical methods for tomographic image reconstruction. Bulletin of the International Statistical Institute, 52, 1987. ",
+        "bbox": [
+            169,
+            103,
+            825,
+            132
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Athinodoros S. Georghiades, Peter N. Belhumeur, and David J. Kriegman. From few to many: Illumination cone models for face recognition under variable lighting and pose. Pattern Analysis and Machine Intelligence (PAMI), 23(6), 2001. ",
+        "bbox": [
+            176,
+            141,
+            823,
+            185
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Geoffrey E. Hinton and Ruslan Salakhutdinov. Reducing the dimensionality of data with neural networks. Science, 313(5786), 2006. ",
+        "bbox": [
+            174,
+            194,
+            821,
+            223
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Sergey Ioffe and Christian Szegedy. Batch normalization: Accelerating deep network training by reducing internal covariate shift. In International Conference on Machine Learning (ICML), 2015. ",
+        "bbox": [
+            174,
+            233,
+            823,
+            262
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Diederik P. Kingma and Jimmy Ba. Adam: A method for stochastic optimization. In International Conference on Learning Representations (ICLR), 2015. ",
+        "bbox": [
+            173,
+            272,
+            825,
+            301
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Hans-Peter Kriegel, Peer Kroger, and Arthur Zimek. Clustering high-dimensional data: A survey on ¨ subspace clustering, pattern-based clustering, and correlation clustering. ACM Transactions on Knowledge Discovery from Data, 3(1), 2009. ",
+        "bbox": [
+            176,
+            310,
+            823,
+            354
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Yann LeCun, Leon Bottou, Yoshua Bengio, and Patrick Haffner. Gradient-based learning applied to ´ document recognition. Proceedings of the IEEE, 86(11), 1998. ",
+        "bbox": [
+            173,
+            363,
+            825,
+            393
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "David D. Lewis, Yiming Yang, Tony G. Rose, and Fan Li. RCV1: A new benchmark collection for text categorization research. Journal of Machine Learning Research (JMLR), 5, 2004. ",
+        "bbox": [
+            173,
+            401,
+            823,
+            433
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Hossein Mobahi and John W. Fisher III. A theoretical analysis of optimization by Gaussian continuation. In AAAI, 2015. ",
+        "bbox": [
+            173,
+            440,
+            825,
+            470
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Vinod Nair and Geoffrey E. Hinton. Rectified linear units improve restricted Boltzmann machines. In International Conference on Machine Learning (ICML), 2010. ",
+        "bbox": [
+            173,
+            479,
+            825,
+            508
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Sameer A. Nene, Shree K. Nayar, and Hiroshi Murase. Columbia object image library (COIL-100). Technical Report CUCS-006-96, Columbia University, 1996. ",
+        "bbox": [
+            169,
+            518,
+            825,
+            547
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Andrew Y. Ng, Michael I. Jordan, and Yair Weiss. On spectral clustering: Analysis and an algorithm. In Neural Information Processing Systems (NIPS), 2001. ",
+        "bbox": [
+            173,
+            556,
+            823,
+            587
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Feiping Nie, Zinan Zeng, Ivor W. Tsang, Dong Xu, and Changshui Zhang. Spectral embedded clustering: A framework for in-sample and out-of-sample spectral clustering. IEEE Transactions on Neural Networks, 22(11), 2011. ",
+        "bbox": [
+            174,
+            595,
+            823,
+            638
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Sohil Atul Shah and Vladlen Koltun. Robust continuous clustering. Proceedings of the National Academy of Sciences (PNAS), 114(37), 2017. ",
+        "bbox": [
+            171,
+            648,
+            823,
+            678
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Nitish Srivastava, Geoffrey E. Hinton, Alex Krizhevsky, Ilya Sutskever, and Ruslan Salakhutdinov. Dropout: A simple way to prevent neural networks from overfitting. Journal of Machine Learning Research (JMLR), 15(1), 2014. ",
+        "bbox": [
+            176,
+            686,
+            823,
+            731
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Michael Steinbach, Levent Ertoz, and Vipin Kumar. The challenges of clustering high dimensional ¨ data. In New Directions in Statistical Physics. 2004. ",
+        "bbox": [
+            171,
+            739,
+            823,
+            768
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Alexander Strehl and Joydeep Ghosh. Cluster ensembles – A knowledge reuse framework for combining multiple partitions. Journal of Machine Learning Research (JMLR), 3, 2002. ",
+        "bbox": [
+            171,
+            779,
+            823,
+            809
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Marc Teboulle. A unified continuous optimization framework for center-based clustering methods. Journal of Machine Learning Research (JMLR), 8, 2007. ",
+        "bbox": [
+            169,
+            816,
+            825,
+            847
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Laurens van der Maaten. Learning a parametric embedding by preserving local structure. In International Conference on Artificial Intelligence and Statistics (AISTATS), 2009. ",
+        "bbox": [
+            174,
+            856,
+            821,
+            886
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Laurens van der Maaten. Accelerating t-SNE using tree-based algorithms. Journal of Machine Learning Research (JMLR), 15, 2014. ",
+        "bbox": [
+            174,
+            895,
+            821,
+            924
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Laurens van der Maaten and Geoffrey E. Hinton. Visualizing high-dimensional data using t-SNE. Journal of Machine Learning Research (JMLR), 9, 2008. ",
+        "bbox": [
+            169,
+            103,
+            825,
+            132
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Laurens van der Maaten, Eric Postma, and Jaap van den Herik. Dimensionality reduction: A comparative review. Technical Report TiCC-TR 2009-005, Tilburg University, 2009. ",
+        "bbox": [
+            173,
+            140,
+            823,
+            169
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Rene Vidal. Subspace clustering. ´ IEEE Signal Processing Magazine, 28(2), 2011. ",
+        "bbox": [
+            173,
+            176,
+            712,
+            191
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Pascal Vincent, Hugo Larochelle, Isabelle Lajoie, Yoshua Bengio, and Pierre-Antoine Manzagol. Stacked denoising autoencoders: Learning useful representations in a deep network with a local denoising criterion. Journal of Machine Learning Research (JMLR), 11, 2010. ",
+        "bbox": [
+            174,
+            199,
+            821,
+            242
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Nguyen Xuan Vinh, Julien Epps, and James Bailey. Information theoretic measures for clusterings comparison: Variants, properties, normalization and correction for chance. Journal of Machine Learning Research (JMLR), 11, 2010. ",
+        "bbox": [
+            174,
+            250,
+            823,
+            291
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Ulrike von Luxburg. A tutorial on spectral clustering. Statistics and Computing, 17(4), 2007. ",
+        "bbox": [
+            173,
+            299,
+            784,
+            315
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Lior Wolf, Tal Hassner, and Itay Maoz. Face recognition in unconstrained videos with matched background similarity. In Computer Vision and Pattern Recognition (CVPR), 2011. ",
+        "bbox": [
+            174,
+            321,
+            825,
+            352
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Junyuan Xie, Ross B. Girshick, and Ali Farhadi. Unsupervised deep embedding for clustering analysis. In International Conference on Machine Learning (ICML), 2016. ",
+        "bbox": [
+            173,
+            358,
+            823,
+            388
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Bo Yang, Xiao Fu, Nicholas D. Sidiropoulos, and Mingyi Hong. Towards k-means-friendly spaces: Simultaneous deep learning and clustering. In International Conference on Machine Learning (ICML), 2017. ",
+        "bbox": [
+            173,
+            395,
+            825,
+            438
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Jianwei Yang, Devi Parikh, and Dhruv Batra. Joint unsupervised learning of deep representations and image clusters. In Computer Vision and Pattern Recognition (CVPR), 2016. ",
+        "bbox": [
+            171,
+            445,
+            821,
+            474
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Yi Yang, Dong Xu, Feiping Nie, Shuicheng Yan, and Yueting Zhuang. Image clustering using local discriminant models and global integration. IEEE Transactions on Image Processing, 19(10), 2010. ",
+        "bbox": [
+            176,
+            482,
+            825,
+            525
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Wei Zhang, Xiaogang Wang, Deli Zhao, and Xiaoou Tang. Graph degree linkage: Agglomerative clustering on a directed graph. In European Conference on Computer Vision (ECCV), 2012. ",
+        "bbox": [
+            176,
+            532,
+            821,
+            561
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "APPENDIX ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            587,
+            263,
+            602
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "A DATASETS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            618,
+            297,
+            636
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "MNIST (LeCun et al., 1998): This is a popular dataset containing 70,000 images of handwritten digits. Each image is of size $2 8 \\times 2 8$ (784 dimensions). The data is categorized into 10 classes. ",
+        "bbox": [
+            174,
+            650,
+            823,
+            678
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Coil100 (Nene et al., 1996): This dataset consists of 7,200 images of 100 object categories, each captured from 72 poses. Each RGB image is of size $1 2 8 \\times 1 2 8$ (49,152 dimensions). ",
+        "bbox": [
+            176,
+            685,
+            821,
+            713
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "YouTube Faces (Wolf et al., 2011): The YTF dataset contains videos of faces. We use all the video frames of the first 40 subjects sorted in chronological order. Each frame is an RGB image of size $5 5 \\times 5 5$ . The number of datapoints is 10,056 and the dimensionality is 9,075. ",
+        "bbox": [
+            174,
+            719,
+            825,
+            762
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "YaleB (Georghiades et al., 2001): This dataset contains 2,414 images of faces of 28 human subjects taken under different lightning condition. Each image is of size $1 9 2 \\times 1 6 8$ (32,256 dimensions). ",
+        "bbox": [
+            173,
+            768,
+            821,
+            797
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Reuters: This is a popular dataset comprising 21,578 Reuters news articles. We consider the Modified Apte split, which yields a total of 9,082 articles. TF-IDF features on the 2,000 most frequently occurring word stems are computed and normalized. The dimensionality of the data is thus 2,000. ",
+        "bbox": [
+            174,
+            804,
+            825,
+            861
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "RCV1 (Lewis et al., 2004): This is a document dataset comprising 800,000 Reuters newswire articles. Only the four root categories are considered and all articles labeled with more than one root category are pruned. We report results on a randomly sampled subset of 10,000 articles. 2,000 TF-IDF features were extracted as in the case of the Reuters dataset. ",
+        "bbox": [
+            174,
+            867,
+            825,
+            922
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "B CONVOLUTIONAL NETWORK ARCHITECTURE ",
+        "text_level": 1,
+        "bbox": [
+            173,
+            102,
+            589,
+            118
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Table 3 summarizes the architecture of the convolutional encoder used for the convolutional configuration of DCC. Convolutional kernels are applied with a stride of two. The encoder is followed by a fully-connected layer with output dimension $d$ and a convolutional decoder with kernel size that matches the output dimension of conv5. The decoder architecture mirrors the encoder and the output from each layer is appropriately zero-padded to match the input size of the corresponding encoding layer. All convolutional and transposed convolutional layers are followed by batch normalization and rectified linear units (Ioffe & Szegedy, 2015; Nair & Hinton, 2010). ",
+        "bbox": [
+            173,
+            137,
+            826,
+            234
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "table",
+        "img_path": "images/35334d1d67a5ee8606672e2dee3972c40c7540591442fc07e745b4574d7f4e09.jpg",
+        "table_caption": [
+            "Table 3: Convolutional encoder architecture. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>MNIST</td><td>Coil100</td><td>YTF</td><td>YaleB</td></tr><tr><td>conv1</td><td>4×4</td><td>4×4</td><td>4×4</td><td>4×4</td></tr><tr><td>conv2</td><td>5×5</td><td>5×5</td><td>5×5</td><td>5×5</td></tr><tr><td>conv3</td><td>5×5</td><td>5×5</td><td>5×5</td><td>5×5</td></tr><tr><td>conv4</td><td>1</td><td>5×5</td><td>5×5</td><td>5×5</td></tr><tr><td>conv5</td><td>1</td><td>5×5</td><td>1</td><td>5×5</td></tr><tr><td>output</td><td>4×4</td><td>4×4</td><td>4×4</td><td>6×6</td></tr></table>",
+        "bbox": [
+            328,
+            253,
+            665,
+            372
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "C HYPERPARAMETERS ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            434,
+            380,
+            450
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "DCC uses three hyperparameters: the nearest neighbor graph (mkNN) parameter $k$ , the embedding dimensionality $d$ , and the update period $M$ for graduated nonconvexity. For fair comparison to RCC and RCC-DR, we fix $k = 1 0$ (the setting used in Shah & Koltun (2017)). The other two hyperparameters were set to $d = 1 0$ and $M = 2 0$ based on grid search on MNIST. The hyperparameters are fixed at these values across all datasets. No dataset-specific tuning is done. However, note that the hyperparameter $M$ is architecture-specific. We set $M = 1 0$ for convolutional autoencoders and it is varied for varying dimensionality $d$ during the controlled experiment reported in Figures 2 and 3. The other hyperparameters such as $\\lambda , \\delta _ { i } , \\mu _ { i }$ are set automatically as described in Sections 3.2 and 3.3 and in Shah & Koltun (2017). ",
+        "bbox": [
+            173,
+            469,
+            826,
+            594
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "D ACC MEASURE ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            621,
+            343,
+            637
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "For completeness, we report results according to the ACC measure. Table 4 provides the ACC counterpart to Table 1. Figure 3 provides the ACC counterpart to Figure 2. ",
+        "bbox": [
+            174,
+            656,
+            823,
+            685
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "image",
+        "img_path": "images/b838c3a50548ae1f08e98f9c4463720173e59ef8bcb61b037a0809d2557070ad.jpg",
+        "image_caption": [
+            "Figure 3: Clustering accuracy (ACC) as a function of the dimensionality $d$ of the latent space. This is the ACC counterpart to Figure 2. Best viewed in color. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            176,
+            715,
+            823,
+            867
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "table",
+        "img_path": "images/74047421811d45c20768891b4de068cda76d7e57930900b8c318b5dae500d66f.jpg",
+        "table_caption": [],
+        "table_footnote": [
+            "Table 4: Clustering accuracy of DCC and 12 baselines, measured by ACC. Higher is better. This is the ACC counterpart to Table 1. "
+        ],
+        "table_body": "<table><tr><td>Algorithm</td><td>MNIST</td><td>Coil100</td><td>YTF</td><td>YaleB</td><td>Reuters</td><td>RCV1</td></tr><tr><td>k-means++</td><td>0.532</td><td>0.621</td><td>0.624</td><td>0.514</td><td>0.236</td><td>0.529</td></tr><tr><td>AC-W</td><td>0.571</td><td>0.697</td><td>0.647</td><td>0.614</td><td>0.261</td><td>0.554</td></tr><tr><td>DBSCAN</td><td>0.000</td><td>0.921</td><td>0.675</td><td>0.632</td><td>0.700</td><td>0.571</td></tr><tr><td>SEC</td><td>0.545</td><td>0.648</td><td>0.562</td><td>0.721</td><td>0.434</td><td>0.425</td></tr><tr><td>LDMGI</td><td>0.723</td><td>0.763</td><td>0.332</td><td>0.901</td><td>0.465</td><td>0.667</td></tr><tr><td>GDL</td><td>n/a</td><td>0.825</td><td>0.497</td><td>0.783</td><td>0.463</td><td>0.444</td></tr><tr><td>RCC</td><td>0.876</td><td>0.831</td><td>0.484</td><td>0.939</td><td>0.381</td><td>0.356</td></tr><tr><td>RCC-DR</td><td>0.698</td><td>0.825</td><td>0.579</td><td>0.945</td><td>0.437</td><td>0.676</td></tr><tr><td colspan=\"7\">Fully Connected</td></tr><tr><td>DCN</td><td>0.560</td><td>0.620</td><td>0.620</td><td>0.430</td><td>0.220</td><td>0.730</td></tr><tr><td>DEC</td><td>0.867</td><td>0.815</td><td>0.643</td><td>0.027</td><td>0.168</td><td>0.683</td></tr><tr><td>DCC</td><td>0.962</td><td>0.842</td><td>0.605</td><td>0.861</td><td>0.596</td><td>0.563</td></tr><tr><td colspan=\"7\">Fully Convolutional</td></tr><tr><td>JULE</td><td>0.800</td><td>0.911</td><td>0.342</td><td>0.970</td><td></td><td></td></tr><tr><td>DEPICT</td><td>0.968</td><td>0.420</td><td>0.586</td><td>0.965</td><td></td><td></td></tr><tr><td>DCC</td><td>0.963</td><td>0.858</td><td>0.699</td><td>0.964</td><td></td><td></td></tr></table>",
+        "bbox": [
+            274,
+            101,
+            718,
+            390
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "E NMI MEASURE ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            453,
+            339,
+            469
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "table",
+        "img_path": "images/69ebfeb2a269d790d2a0782af33d6f7def64da78996a96fa4f4c32e3f0af9c5d.jpg",
+        "table_caption": [
+            "We also report results according to the NMI measure. Table 5 provides the NMI counterpart to Table 1. "
+        ],
+        "table_footnote": [
+            "Table 5: Clustering accuracy of DCC and 12 baselines, measured by NMI. Higher is better. This is the NMI counterpart to Table 1. "
+        ],
+        "table_body": "<table><tr><td>Algorithm</td><td>MNIST</td><td>Coil100</td><td>YTF</td><td>YaleB</td><td>Reuters</td><td>RCV1</td></tr><tr><td>k-means++</td><td>0.500</td><td>0.835</td><td>0.788</td><td>0.650</td><td>0.536</td><td>0.355</td></tr><tr><td>AC-W</td><td>0.679</td><td>0.876</td><td>0.806</td><td>0.788</td><td>0.492</td><td>0.364</td></tr><tr><td>DBSCAN</td><td>0.000</td><td>0.458</td><td>0.756</td><td>0.535</td><td>0.022</td><td>0.017</td></tr><tr><td>SEC</td><td>0.469</td><td>0.872</td><td>0.760</td><td>0.863</td><td>0.498</td><td>0.069</td></tr><tr><td>LDMGI</td><td>0.761</td><td>0.906</td><td>0.532</td><td>0.950</td><td>0.523</td><td>0.382</td></tr><tr><td>GDL</td><td>n/a</td><td>0.965</td><td>0.664</td><td>0.931</td><td>0.401</td><td>0.020</td></tr><tr><td>RCC</td><td>0.893</td><td>0.963</td><td>0.850</td><td>0.978</td><td>0.556</td><td>0.138</td></tr><tr><td>RCC-DR</td><td>0.827</td><td>0.963</td><td>0.882</td><td>0.976</td><td>0.553</td><td>0.442</td></tr><tr><td colspan=\"7\">Fully-connected</td></tr><tr><td>DCN</td><td>0.570</td><td>0.830</td><td>0.810</td><td>0.630</td><td>0.460</td><td>0.470</td></tr><tr><td>DEC</td><td>0.853</td><td>0.645</td><td>0.811</td><td>0.000</td><td>0.409</td><td>0.504</td></tr><tr><td>DCC</td><td>0.912</td><td>0.961</td><td>0.886</td><td>0.959</td><td>0.588</td><td>0.498</td></tr><tr><td colspan=\"7\">Convolutional</td></tr><tr><td>JULE</td><td>0.900</td><td>0.983</td><td>0.587</td><td>0.991</td><td></td><td></td></tr><tr><td>DEPICT</td><td>0.919</td><td>0.678</td><td>0.790</td><td>0.990</td><td></td><td></td></tr><tr><td>DCC</td><td>0.915</td><td>0.967</td><td>0.908</td><td>0.987</td><td></td><td></td></tr></table>",
+        "bbox": [
+            274,
+            523,
+            718,
+            813
+        ],
+        "page_idx": 12
+    }
+]

parse/train/rkMW1hRqKX/rkMW1hRqKX.md

@@ -0,0 +1,377 @@
+# OPTIMAL COMPLETION DISTILLATIONFOR SEQUENCE LEARNING
+
+Sara Sabour, William Chan, Mohammad Norouzi
+
+{sasabour, williamchan, mnorouzi}@google.com Google Brain
+
+# ABSTRACT
+
+We present Optimal Completion Distillation (OCD), a training procedure for optimizing sequence to sequence models based on edit distance. OCD is efficient, has no hyper-parameters of its own, and does not require pretraining or joint optimization with conditional log-likelihood. Given a partial sequence generated by the model, we first identify the set of optimal suffixes that minimize the total edit distance, using an efficient dynamic programming algorithm. Then, for each position of the generated sequence, we define a target distribution that puts an equal probability on the first token of each optimal suffix. OCD achieves the state-of-theart performance on end-to-end speech recognition, on both Wall Street Journal and Librispeech datasets, achieving ${ \mathrm { { \bar { 9 } . 3 \% } } }$ and $\bar { 4 } . 5 \%$ word error rates, respectively.
+
+# 1 INTRODUCTION
+
+Recent advances in natural language processing and speech recognition hinge on the development of expressive neural network architectures for sequence to sequence (seq2seq) learning (Sutskever et al., 2014; Bahdanau et al., 2015). Such encoder-decoder architectures are adopted in both machine translation (Bahdanau et al., 2015; Wu et al., 2016; Hassan et al., 2018) and speech recognition systems (Chan et al., 2016; Bahdanau et al., 2016a; Chiu et al., 2017) achieving impressive performance above traditional multi-stage pipelines (Koehn et al., 2007; Povey et al., 2011). Improving the building blocks of seq2seq models can fundamentally advance machine translation and speech recognition, and positively impact other domains such as image captioning (Xu et al., 2015), parsing (Vinyals et al., 2015), summarization (Rush et al., 2015), and program synthesis (Zhong et al., 2017).
+
+To improve the key components of seq2seq models, one can either design better architectures, or develop better learning algorithms. Recent architectures using convolution (Gehring et al., 2017) and self attention (Vaswani et al., 2017) have proved to be useful, especially to facilitate efficient training. On the other hand, despite many attempts to mitigate the limitations of Maximum Likelihood Estimation (MLE) (Ranzato et al., 2016; Wiseman and Rush, 2016; Norouzi et al., 2016; Bahdanau et al., 2017; Leblond et al., 2018), MLE is still considered the dominant approach for training seq2seq models. Current alternative approaches require pre-training or joint optimization with conditional log-likelihood. They are difficult to implement and require careful tuning of new hyper-parameters (e.g. mixing ratios). In addition, alternative approaches typically do not offer a substantial performance improvement over a well tuned MLE baseline, especially when label smoothing (Pereyra et al., 2017; Edunov et al., 2018) and scheduled sampling (Bengio et al., 2015) are used.
+
+In this paper, we borrow ideas from search-based structured prediction (Daumé et al., 2009; Ross et al., 2011) and policy distillation (Rusu et al., 2016) and develop an efficient algorithm for optimizing seq2seq models based on edit distance1. Our key observation is that given an arbitrary prefix (e.g. a partial sequence generated by sampling from the model), we can exactly and efficiently identify all of the suffixes that result in a minimum total edit distance (v.s. the ground truth target). Our training procedure, called Optimal Completion Distillation (OCD), is summarized as follows:
+
+1. We always train on prefixes generated by sampling from the model that is being optimized.   
+2. For each generated prefix, we identify all of the optimal suffixes that result in a minimum total edit distance v.s. the ground truth target using an efficient dynamic programming algorithm.   
+3. We teach the model to optimally extend each generated prefix by maximizing the average log probability of the first token of each optimal suffix identified in step 2.
+
+The proposed OCD algorithm is efficient, straightforward to implement, and has no tunable hyperparameters of its own. Our key contributions include:
+
+• We propose OCD, a stand-alone algorithm for optimizing seq2seq models based on edit distance. OCD is scalable to real-world datasets with long sequences and large vocabularies, and consistently outperforms Maximum Likelihood Estimation (MLE) by a large margin. • Given a target sequence of length $m$ and a generated sequence of length $n$ , we present an $O ( n m )$ algorithm that identifies all of the optimal extensions for each prefix of the generated sequence. We demonstrate the effectiveness of OCD on end-to-end speech recognition using attentionbased seq2seq models. On the Wall Street Journal dataset, OCD achieves a Character Error Rate (CER) of $3 . 1 \%$ and a Word Error Rate (WER) of $9 . 3 \%$ without language model rescoring, outperforming all prior work (Table 4). On Librispeech, OCD achieves state-of-the-art WER of $4 . 5 \%$ on “test-clean” and $1 3 . 3 \%$ on “test-other” sets (Table 5).
+
+# 2 BACKGROUND: SEQUENCE LEARNING WITH MLE
+
+Given a dataset of input output pairs $\mathcal { D } \equiv \{ ( \mathbf { x } , \mathbf { y } ^ { * } ) _ { i } \} _ { i = 1 } ^ { N }$ , we are interested in learning a mapping $\mathbf x \to \mathbf y$ from an input $\mathbf { x }$ to a target output sequence $\mathbf { y } ^ { \ast } \in \mathcal { V }$ . Let $\mathcal { V }$ denote the set of all sequences of tokens from a finite vocabulary $\nu$ with variable but finite lengths. Often learning a mapping $\mathbf x \to \mathbf y$ is formulated as optimizing the parameters of a conditional distribution $p _ { \theta } ( \mathbf { y } \mid \mathbf { x } )$ . Then, the final sequence prediction under the probabilistic model $p _ { \theta }$ is performed by exact or approximate inference (e.g. via beam search) as:
+
+$$
+{ \hat { \mathbf { y } } } \approx \operatorname { a r g m a x } _ { \mathbf { y } \in \mathcal { Y } } p _ { \theta } ( \mathbf { y } \mid \mathbf { x } ) ~ .
+$$
+
+Similar to the use of log loss for supervised classification, the standard approach to optimize the parameters $\theta$ of the conditional probabilistic model entails maximizing a conditional log-likelihood objective, $\mathcal { O } _ { \mathrm { M L E } } ( \theta ) = \mathbb { E } _ { ( \mathbf { x } , \mathbf { y } ^ { * } ) \sim p _ { \mathcal { D } } } \log p _ { \theta } ( \mathbf { y } ^ { * } \mid \mathbf { x } )$ . This approach to learning the parameters is called Maximum Likelihood Estimation (MLE) and is commonly used in sequence to sequence learning.
+
+Sutskever et al. (2014) propose the use of recurrent neural networks (RNNs) for autoregressive seq2seq modeling to tractably optimize ${ \mathcal { O } } _ { \mathrm { M L E } } ( \theta )$ . An autoregressive model estimates the conditional probability of the target sequence given the source one token at a time, often from left-to-right. A special end-of-sequence token is appended at the end of all of target sequences to handle variable length. The conditional probability of $\mathbf { y } ^ { * }$ given $\mathbf { x }$ is decomposed via the chain rule as,
+
+$$
+p _ { \boldsymbol \theta } ( \mathbf { y } ^ { * } \mid \mathbf { x } ) \equiv \prod _ { t = 1 } ^ { | \mathbf { y } ^ { * } | } p _ { \boldsymbol \theta , t } ( y _ { t } ^ { * } \mid \mathbf { y } _ { < t } ^ { * } , \mathbf { x } ) ,
+$$
+
+where $\mathbf { y } _ { < t } ^ { * } \equiv ( y _ { 1 } ^ { * } , \dots , y _ { t - 1 } ^ { * } )$ denotes a prefix of the sequence $\mathbf { y } ^ { * }$ . To estimate the probability of a token $a$ given a prefix $\mathbf { y } _ { < t } ^ { * }$ and an input $\mathbf { x }$ , denoted $p _ { \theta , t } ( a \mid \mathbf { y } _ { < t } ^ { * } , \mathbf { x } )$ , different architectures have been proposed. Some papers (e.g. Britz et al. (2017)) have investigated the use of LSTM (Hochreiter and Schmidhuber, 1997) and GRU (Cho et al., 2014) cells, while others proposed new architecturs based on soft attention (Bahdanau et al., 2015), convolution (Gehring et al., 2017), and self-attention (Vaswani et al., 2017). Nonetheless, all of these techniques rely on MLE for learning,
+
+$$
+\mathcal { O } _ { \mathrm { M L E } } ( \theta ) = \mathbb { E } _ { ( \mathbf { x } , \mathbf { y } ^ { * } ) \sim p _ { D } } \sum _ { t = 1 } ^ { | \mathbf { y } ^ { * } | } \log p _ { \theta , t } ( y _ { t } ^ { * } \mid \mathbf { y } _ { < t } ^ { * } , \mathbf { x } ) ,
+$$
+
+where $p _ { \mathcal { D } }$ denotes the empirical data distribution, uniform across the dataset $\mathcal { D }$ . We present a new objective function for optimizing autoregressive seq2seq models applicable to any neural architecture.
+
+# 2.1 LIMITATIONS OF MLE FOR AUTOREGRESSIVE MODELS
+
+In order to maximize the conditional log-likelihood (3) of an autoregressive seq2seq model (2), one provides the model with a prefix of $t - 1$ tokens from the ground truth target sequence, denoted $\mathbf { y } _ { < t } ^ { * }$ and maximizes the log-probability of $y _ { t } ^ { * }$ as the next token. This resembles a teacher walking a student through a sequence of perfect decisions, where the student learns as a passive observer. However, during inference one uses beam search (1), wherein the student needs to generate each token $\hat { \mathbf { y } } _ { t }$ by conditioning on its own previous outputs, i.e. $\hat { \mathbf { y } } _ { < t }$ instead of $\mathbf { y } _ { < t } ^ { * }$ . This creates a discrepancy between training and test known as exposure bias (Ranzato et al., 2016). Appendix B expands this further.
+
+Concretely, we highlight two limitations with the use of MLE for autoregressive seq2seq modeling:
+
+1. There is a mismatch between the prefixes seen by the model during training and inference. When the distribution of $\hat { \mathbf { y } } _ { < t }$ is different from the distribution of $\mathbf { y } _ { < t } ^ { * }$ , then the student will find themselves in a novel situation that they have not been trained for. This can result in poor generalization, especially when the training set is small or the model size is large. 2. There is a mismatch between the training loss and the task evaluation metric. During training, one optimizes the log-probability of the ground truth output sequence, which is often different from the task evaluation metric (e.g. edit distance for speech recognition).
+
+There has been a recent surge of interest in understanding and mitigating the limitations of MLE for autoregressive seq2seq modeling. In Section 4 we discuss prior work in detail after presenting our approach below.
+
+# 3 OPTIMAL COMPLETION DISTILLATION
+
+To alleviate the mismatch between inference and training, we never train on ground truth target sequences. Instead, we always train on sequences generated by sampling from the current model that is being optimized. Let $\widetilde { \mathbf { y } }$ denote a sequence generated by sampling from the current model, and $\mathbf { y } ^ { * }$ edenote the ground truth target. Applying MLE to autoregressive models casts the problem of sequence learning as optimizing a mapping $( \mathbf { x } , \mathbf { y } _ { < t } ^ { * } ) \to y _ { t } ^ { * }$ from ground truth prefixes to correct next tokens. By contrast, the key question that arises when training on model samples is the choice of targets for learning a similar mapping $( { \bf x } , \widetilde { { \bf y } } _ { < t } )  \ ? \ ?$ from generated prefixes to next tokens. Instead eof using a set of pre-specified targets, OCD solves a prefix-specific problem to find optimal extensions that lead to the best completions according to the task evaluation metric. Then, OCD encourages the model to extend each prefix with the set of optimal choices for the next token.
+
+Our notion of optimal completion depends on the task evaluation metric denoted $R ( \cdot , \cdot )$ , which measures the similarity between two complete sequences, e.g. the ground truth target v.s. a generated sequence. Edit distance is a common task metric. Our goal in sequence learning is to train a model, which achieves high scores of $R ( \mathbf { y } ^ { * } , \widetilde { \mathbf { y } } )$ . Drawing connection with the goal of reinforcement elearning (Sutton and Barto, 1998), let us recall the notion of optimal $\mathbf { Q }$ -values. Optimal Q-values for a state-action pair $( s , a )$ , denoted $Q ^ { * } ( s , a )$ , represent the maximum future reward that an agent can accumulate after taking an action $a$ at a state $s$ by following with optimal subsequent actions. Similarly, we define Q-values for a prefix $\widetilde { \mathbf { y } } _ { < t }$ and the extending token $a$ , as the maximum score attainable by concatenating $[ \widetilde { \mathbf { y } } _ { < t } , a ]$ ewith an optimal suffix $\mathbf { y }$ to create a full sequence $[ \widetilde { \mathbf { y } } _ { < t } , a , \mathbf { y } ]$ Formally,
+
+$$
+\forall a \in \mathcal { V } , \qquad Q ^ { * } ( \widetilde { \mathbf { y } } _ { < t } , a ) = \operatorname* { m a x } _ { \mathbf { y } \in \mathcal { V } } R ( \mathbf { y } ^ { * } , [ \widetilde { \mathbf { y } } _ { < t } , a , \mathbf { y } ] ) .
+$$
+
+Then, the optimal extension for a prefix $\widetilde { \mathbf { y } } _ { < t }$ can be defined as tokens that attain the maximal Q-values, i.e. argmax $a ^ { Q ^ { * } } ( \widetilde { \mathbf { y } } _ { < t } , a )$ e. This formulation allows for a prefix $\widetilde { \mathbf { y } } _ { < t }$ to be sampled on-policy from the model $p _ { \theta }$ e e, or drawn off-policy in any way. Table 1 includes an example ground truth target from the Wall Street Journal dataset and the corresponding generated sample from a model. We illustrate that for some prefixes there exist more than a single optimal extension leading to the same edit distance.
+
+Given $Q$ -values for our prefix-token pairs, we use an exponential transform followed by normalization to convert $\mathbf { Q }$ -values to a soft optimal policy over the next token extension,
+
+$$
+\pi ^ { * } ( a \mid \widetilde { \mathbf { y } } _ { < t } ) = \frac { \exp ( Q ^ { * } ( \widetilde { \mathbf { y } } _ { < t } , a ) / \tau ) } { \sum _ { a ^ { \prime } } \exp \left( Q ^ { * } ( \widetilde { \mathbf { y } } _ { < t } , a ^ { \prime } ) / \tau \right) } ,
+$$
+
+where $\tau \geq 0$ is a temperature parameter. Note the similarity of $\tau$ and the label smoothing parameter helpful within MLE. In our experiments, we used the limit of $\tau  0$ resulting in hard targets and no hyper-parameter tuning.
+
+Given a training example $\left( \mathbf { x } , \mathbf { y } ^ { * } \right)$ , we first draw a full sequence $\widetilde { \mathbf { y } } \sim p _ { \theta } ( \cdot \mid \mathbf { x } )$ i.i.d. from the current model, and then minimize a per-step KL divergence between the optimal policy and the model distribution over the next token extension at each time step $t$ . The OCD objective is expressed as,
+
+$$
+\begin{array} { r l r } { \mathcal { O } _ { \mathrm { O C D } } ( \theta ) } & { = } & { \mathbb { E } _ { ( \mathbf { x } , \mathbf { y } ^ { * } ) \sim p _ { \mathcal { D } } } \mathbb { E } _ { \widetilde { \mathbf { y } } \sim p _ { \theta } ( \cdot | \mathbf { x } ) } \sum _ { t = 1 } ^ { | \widetilde { \mathbf { y } } | } \mathrm { K L } \left( \pi ^ { * } ( \cdot | \widetilde { \mathbf { y } } _ { < t } ) \parallel p _ { \theta , t } ( \cdot | \widetilde { \mathbf { y } } _ { < t } , \mathbf { x } ) \right) . } \end{array}
+$$
+
+For every prefix $\widetilde { \mathbf { y } } _ { < t }$ , we compute the optimal $Q$ -values and use (5) to construct the optimal policy distribution $\pi ^ { * }$ e. Then, we distill the knowledge of the optimal policy for each prefix $\widetilde { \mathbf { y } } _ { < t }$ into the eparametric model using a KL loss. For the important class of sequence learning problems where edit
+
+<table><tr><td>Target sequence y*</td><td>ａｓ_ｈｅ_ｔａlkｓ_ｈis_wifｅ</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Generated sequence y</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>ａｓ_ｅｅ_ｔａlks_wｈoｓｅ_wifｅ</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Optimal extensions for</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>ａｓ_ｈｅ_ｔａlｋｓ_ｈiiｓ＿_𝑤ifｅ</td></tr><tr><td>edit distance (OCD targets)</td><td></td><td></td><td></td><td>ｈ</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>ｈiw</td><td></td><td></td><td></td><td></td><td></td></tr></table>
+
+Table 1: A sample sequence $\mathbf { y } ^ { * }$ from the Wall Street Journal dataset, where the model’s prediction $\widetilde { \mathbf { y } }$ is not perfect. The optimal next characters for each prefix of $\widetilde { \mathbf { y } }$ based on edit distance are shown in blue. For example, for the prefix “as $\mathbf { e } ^ { \prime \prime }$ e there are 3 optimal next characters of “e”, “h”, and $\underline { { { \bf \hat { \Pi } } } } ( \mathbf { \Delta } ) \mathbf { \Delta } ,$ . All of these 3 characters when combined with proper suffixes will result in a total edit distance of 1.
+
+distance is the evaluation metric, we develop a dynamic programming algorithm to calculate optimal $Q$ -values exactly and efficiently for all prefixes of a sequence $\widetilde { \mathbf { y } }$ , discussed below.
+
+# 3.1 OPTIMAL Q-VALUES FOR EDIT DISTANCE
+
+We propose a dynamic programming algorithm to calculate optimal Q-values exactly and efficiently for the reward metric of negative edit distance, i.e. $R ( \mathbf { y } ^ { * } , \widetilde { \mathbf { y } } ) \overset { - } { = } - \mathrm { D } _ { \mathrm { e d i t } } ( \mathbf { y } ^ { * } , \widetilde { \mathbf { y } } )$ . Given two sequences $\mathbf { y } ^ { * }$ and $\widetilde { \mathbf { y } }$ , we compute the Q-values for every prefix $\widetilde { \mathbf { y } } _ { < t }$ e eand any extending token $a \in \nu$ with an easymptotic complexity of $O ( | \mathbf { y } ^ { * } | . | \widetilde { \mathbf { y } } | + | \mathcal { V } | . | \widetilde { \mathbf { y } } | )$ e. Assuming that $| \mathbf { y } ^ { * } | \approx | \widetilde { \mathbf { y } } | \leq | \nu |$ , our algorithm does e e enot increase the time complexity over MLE, since computing the cross-entropy losses in MLE also requires a complexity of $O ( | \mathbf { y } ^ { * } | . | \nu | )$ . When this assumption does not hold, e.g. genetic applications, OCD is less efficient than MLE. However, in practice, the wall clock time is dominated by the forward and backward passes of a neural networks, and the OCD cost is often negligible. We discuss the efficiency of OCD further in Appendix A.
+
+Recall the Levenshtein algorithm (Levenshtein, 1966) for calculating the minimum number of edits (insertion, deletion and substitution) required to convert sequences $\widetilde { \mathbf { y } }$ and $\mathbf { y } ^ { * }$ to each other based on,
+
+$$
+\{ \begin{array} { l l } { \mathrm { D } _ { \mathrm { e d i f } } ( \widetilde { \mathbf { y } } _ { < - 1 } , : ) = \infty } \\ { \mathrm { D } _ { \mathrm { e d i f } } ( \cdot , \mathbf { y } _ { < - 1 } ^ { * } ) = \infty } &  D _ { \mathrm { e d i f } } ( \widetilde { \mathbf { y } } _ { < i } , \mathbf { y } _ { < j } ^ { * } ) = \operatorname* { m i n } \{ \begin{array} { l l } { D _ { \mathrm { e d i f } } ( \widetilde { \mathbf { y } } _ { < i - 1 } , \mathbf { y } _ { < j } ^ { * } ) + 1 } \\ { D _ { \mathrm { e d i f } } ( \widetilde { \mathbf { y } } _ { < i } , \mathbf { y } _ { < j - 1 } ^ { * } ) + 1 } \\ { D _ { \mathrm { e d i f } } ( \widetilde { \mathbf { y } } _ { < i - 1 } , \mathbf { y } _ { < j - 1 } ^ { * } ) + \mathbb { 1 } [ \widetilde { y } _ { i } \neq y _ { j } ^ { * } ] . } \end{array}  \end{array}
+$$
+
+Table 2 shows an example edit distance table for sequences “Satrapy” and “Sunday”. Our goal is to identify the set of all optimal suffixes $\mathbf { y } \in \mathcal { V }$ that result in a full sequences $[ \widetilde { \mathbf { y } } _ { < i } , \mathbf { y } ]$ with a minimum edit distance v.s. $\mathbf { y } ^ { * }$ .
+
+Lemma 1. The edit distance resulting from any potential suffix $\mathbf { y } \in \mathcal { V }$ is lower bounded by $m _ { i }$
+
+$$
+\forall \mathbf { y } \in \mathcal { V } , \ D _ { e d i t } \big ( [ \widetilde { \mathbf { y } } _ { < i } , \mathbf { y } ] , \mathbf { y } ^ { * } \big ) \ \ge \ \operatorname* { m i n } _ { 0 \le j \le | \mathbf { y } ^ { * } | } \ D _ { e d i t } \big ( \widetilde { \mathbf { y } } _ { < i } , \mathbf { y } _ { < j } ^ { * } \big ) \ = \ m _ { i } .
+$$
+
+Proof. Let’s consider the path $P$ that traces $\mathrm { D } _ { \mathrm { e d i t } } \big ( [ \widetilde { \mathbf { y } } _ { < i } , \mathbf { y } ] , \mathbf { y } ^ { \ast } \big )$ back to $\mathrm { D } _ { \mathrm { e d i t } } \big ( \widetilde { \mathbf { y } } _ { < 0 } , \mathbf { y } _ { < 0 } ^ { * } \big )$ connecting each cell to an adjacent parent cell, which provides the minimum value among the three options in (7). Such a path for tracing edit distance between “Satrapy” and “Sunday” is shown in Table 2.
+
+Table 2: Each row corresponds to a prefix of “SATRAPY” and shows edit distances with all prefixes of “SUNDAY”. We also show OCD targets (optimal extensions) for each prefix, and minimum value along each row, denoted $m _ { i }$ (see (8)). We highlight the trace path for $\mathrm { D } _ { \mathrm { e d i t } }$ (“Satrapy”, “Sunday”).   
+
+<table><tr><td rowspan=1 colspan=8>Edit Distance Table</td><td rowspan=1 colspan=1> OCD Targets</td><td rowspan=1 colspan=1>mi</td></tr><tr><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>S</td><td rowspan=1 colspan=1>U</td><td rowspan=1 colspan=1>N</td><td rowspan=1 colspan=1>D</td><td rowspan=1 colspan=1>A</td><td rowspan=1 colspan=1>Y</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td></tr><tr><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>0</td><td rowspan=1 colspan=1>1</td><td rowspan=1 colspan=1>2</td><td rowspan=1 colspan=1>3</td><td rowspan=1 colspan=1>4</td><td rowspan=1 colspan=1>5</td><td rowspan=1 colspan=1>6</td><td rowspan=1 colspan=1>S</td><td rowspan=1 colspan=1>0</td></tr><tr><td rowspan=1 colspan=1>S</td><td rowspan=1 colspan=1>1</td><td rowspan=1 colspan=1>0</td><td rowspan=1 colspan=1>1</td><td rowspan=1 colspan=1>2</td><td rowspan=1 colspan=1>3</td><td rowspan=1 colspan=1>4</td><td rowspan=1 colspan=1>5</td><td rowspan=1 colspan=1>U</td><td rowspan=1 colspan=1>0</td></tr><tr><td rowspan=1 colspan=1>A</td><td rowspan=1 colspan=1>2</td><td rowspan=1 colspan=1>1</td><td rowspan=1 colspan=1>1</td><td rowspan=1 colspan=1>2</td><td rowspan=1 colspan=1>3</td><td rowspan=1 colspan=1>3</td><td rowspan=1 colspan=1>4</td><td rowspan=1 colspan=1>U,N</td><td rowspan=1 colspan=1>1</td></tr><tr><td rowspan=1 colspan=1>T</td><td rowspan=1 colspan=1>3</td><td rowspan=1 colspan=1>2</td><td rowspan=1 colspan=1>2</td><td rowspan=1 colspan=1>2</td><td rowspan=1 colspan=1>3</td><td rowspan=1 colspan=1>4</td><td rowspan=1 colspan=1>4</td><td rowspan=1 colspan=1>U, N, D</td><td rowspan=1 colspan=1>2</td></tr><tr><td rowspan=1 colspan=1>R</td><td rowspan=1 colspan=1>4</td><td rowspan=1 colspan=1>3</td><td rowspan=1 colspan=1>3</td><td rowspan=1 colspan=1>3</td><td rowspan=1 colspan=1>3</td><td rowspan=1 colspan=1>4</td><td rowspan=1 colspan=1>5</td><td rowspan=1 colspan=1>U, N, D,A</td><td rowspan=1 colspan=1>3</td></tr><tr><td rowspan=1 colspan=1>A</td><td rowspan=1 colspan=1>5</td><td rowspan=1 colspan=1>4</td><td rowspan=1 colspan=1>4</td><td rowspan=1 colspan=1>4</td><td rowspan=1 colspan=1>4</td><td rowspan=1 colspan=1>3</td><td rowspan=1 colspan=1>4</td><td rowspan=1 colspan=1>Y</td><td rowspan=1 colspan=1>3</td></tr><tr><td rowspan=1 colspan=1>P</td><td rowspan=1 colspan=1>6</td><td rowspan=1 colspan=1>5</td><td rowspan=1 colspan=1>5</td><td rowspan=1 colspan=1>5</td><td rowspan=1 colspan=1>5</td><td rowspan=1 colspan=1>4</td><td rowspan=1 colspan=1>4</td><td rowspan=1 colspan=1>Y,&lt;/s&gt;</td><td rowspan=1 colspan=1>4</td></tr><tr><td rowspan=1 colspan=1>Y</td><td rowspan=1 colspan=1>7</td><td rowspan=1 colspan=1>6</td><td rowspan=1 colspan=1>6</td><td rowspan=1 colspan=1>6</td><td rowspan=1 colspan=1>6</td><td rowspan=1 colspan=1>5</td><td rowspan=1 colspan=1>4</td><td rowspan=1 colspan=1>&lt;s&gt;</td><td rowspan=1 colspan=1>4</td></tr></table>
+
+Suppose the path $P$ crosses row $i$ at a cell $( i , k )$ . Since the operations in (7) are non-decreasing, the edit distance along the path cannot decrease, so $\mathrm { D } _ { \mathrm { e d i t } } \bigl ( \bigl [ \widetilde { \mathbf { y } } _ { < i } , \mathbf { y } \bigr ] , \mathbf { y } ^ { * } \bigr ) \geq \mathrm { D } _ { \mathrm { e d i t } } \bigl ( \widetilde { \mathbf { y } } _ { < i } , \mathbf { y } _ { < k } ^ { * } \bigr ) \geq m _ { i }$ . □
+
+Then, consider any $k$ such that $\mathrm { D } _ { \mathrm { e d i t } } \big ( \widetilde { \mathbf { y } } _ { < i } , \mathbf { y } _ { < k } ^ { * } \big ) = m _ { i }$ . Let $\mathbf { y } _ { \geq k } ^ { * } \equiv ( y _ { k } ^ { * } , \ldots , y _ { | \mathbf { y } ^ { * } | } ^ { * } )$ denote a suffix of $\mathbf { y } ^ { * }$ . We conclude that $\mathrm { D } _ { \mathrm { e d i t } } \big ( [ \widetilde { \mathbf { y } } _ { < i } , \mathbf { y } _ { > k } ^ { * } ] , \mathbf { y } ^ { * } \big ) = m _ { i }$ , because on the one hand there is a particular edit path that results in $m _ { i }$ eedits, and on the other hand $m _ { i }$ is a lower bound according to Lemma 1. Hence any such $\mathbf { y } _ { \geq k } ^ { * }$ is an optimal suffix for $\widetilde { \mathbf { y } } _ { < i }$ . Further, it is straightforward to prove by contradiction that ethe set of optimal suffixes is limited to suffixes $\mathbf { y } _ { \geq k } ^ { * }$ corresponding to $\mathrm { D } _ { \mathrm { e d i t } } ( \widetilde { \mathbf { y } } _ { < i } , \mathbf { y } _ { < k } ^ { * } ) = m _ { i }$ .
+
+Since the set of optimal completions for $\widetilde { \mathbf { y } } _ { < i }$ is limited to $\mathbf { y } _ { \geq k } ^ { * }$ , the only extensions that can lead to maximum reward are the starting token of such suffixes $( y _ { k } ^ { * } )$ . Since $\mathrm { D } _ { \mathrm { e d i t } } ( \widetilde { \mathbf { y } } _ { < i } , \mathbf { y } _ { < k } ^ { * } ) = m _ { i }$ as well, we can identify the optimal extensions by calculating the edit distances between all prefixes of $\widetilde { \mathbf { y } }$ and all prefixes of $\mathbf { y } ^ { * }$ which can be efficiently calculated by dynamic programming in $\mathcal { O } ( | \widetilde { \mathbf { y } } | . | \mathbf { y } ^ { * } | )$ . For a prefix $\widetilde { \mathbf { y } } _ { < i }$ after we calculate the minimum edit distance $m _ { i }$ among all prefixes of $\mathbf { y } ^ { * }$ e, we set the $Q ^ { * } ( \widetilde { \mathbf { y } } _ { < i } , y _ { k } ^ { * } ) = - m _ { i }$ for all $k$ where $\mathbf { y } _ { < k } ^ { * }$ has edit distance equal to $m _ { i }$ . We set the $Q ^ { * }$ for any eother token to $- m _ { i } - 1$ . We provide the details of our modified Levenshtein algorithm to efficiently compute the $Q ^ { * } ( \widetilde { \mathbf { y } } _ { < i } , a )$ for all $i$ and $a$ in Appendix A.
+
+# 4 RELATED WORK
+
+Our work builds upon Learning to Search (Daumé III and Marcu, 2005) and Imitation Learning techniques (Ross et al., 2011; Ross and Bagnell, 2014; Sun et al., 2018), where a student policy is optimized to imitate an expert teacher. DAgger (Ross et al., 2011) in particular is closely related, where a dataset of trajectories from an expert teacher is aggregated with samples from past student models, and a policy is optimized to mimic a given expert policy $\pi ^ { * }$ at various states. Similarly, OCD aims to mimic an optimal policy $\pi ^ { * }$ at all prefixes, but in OCD, the behavior policy is directly obtained from an online student. Further, the oracle policy is not provided during training, and we obtain the optimal policy by finding optimal $Q$ -values. AggreVaTeD (Sun et al., 2017) assumes access to an unbiased estimate of Q-values and relies on variance reduction techniques and conjugate gradients to address a policy optimization problem. OCD calculates exact Q-values and uses regular SGD for optimization. Importantly, our roll-in prefixes are drawn only from the student model, and we do not require mixing in ground truth (a.k.a. expert) samples. Cheng and Boots (2018) showed that mixing in ground truth samples is an essential regularizer for value aggregation convergence in imitation learning.
+
+Our work is closely related to Policy Distillation (Rusu et al., 2016), where a Deep Q-Network (DQN) agent (Mnih et al., 2015) that is previously optimized is used as the expert teacher. Then, action sequences are sampled from the teacher and the learned Q-value estimates are distilled (Hinton et al., 2014) into a smaller student network using a KL loss. OCD adopts a similar loss function, but rather than estimating Q-values using bootstrapping, we estimate exact $Q$ -values using dynamic programming. Moreover, we draw samples from the student rather than the teacher.
+
+Similar to OCD, the learning to search (L2S) techniques such as LOLS (Chang et al., 2015) and Goodman et al. (2016) also attempt to estimate the Q-values for each state-action pair. Such techniques examine multiple roll-outs of a generated prefix and aggregate the return values. SeaRNN (Leblond et al., 2018) approximates the cost-to-go for each token by computing the task loss for as many roll-outs as the vocabulary size at each time step with a per step complexity of $O ( V T )$ . It is often difficult to scale approaches based on multiple roll-outs to real world datasets, where either the sequences are long or the vocabulary is large. OCD exploits the special structure in edit distance and find exact Q-values efficiently in $O ( V + T )$ per step. Unlike L2S and SeaRNN, which require ground truth prefixes to stabilize training, we solely train on model samples.
+
+Approaches based on Reinforcement Learning (RL) have also been applied to sequence prediction problems, including REINFORCE (Ranzato et al., 2016), Actor-Critic (Bahdanau et al., 2017) and Self-critical Sequence Training (Rennie et al., 2017). These methods sample sequences from the model’s distribution and backpropagate a sequence-level task objective (e.g. edit distance). Beam Search Optimization (Wiseman and Rush, 2016) and Edit-based Minimum Bayes Risk (EMBR) (Prabhavalkar et al., 2018) is similar, but the sampling procedure is replaced with beam search. These training methods suffer from high variances and credit assignment problems. By contrast, OCD takes advantage of the decomposition of the sequence-level objective into token level optimal completion targets. This reduces the variance of the gradient and stabilizes the model. Crucially, unlike most
+
+![](images/e41a06c08d271a6940d4c5688a21f71510dfc6b1911f489e3ddb1480351aa5d3.jpg)  
+Figure 1: Fraction of OCD training prefix tokens on WSJ which does not match ground truth.
+
+![](images/b3e172ed3797811b59a2d7f6bad5cc0e5db8ac7ab284df0c18bd1f130f5ea01d.jpg)  
+Figure 2: WSJ validation Character Error Rate (CER) per training CER for MLE and OCD.
+
+RL-based approaches, we neither need MLE pretraining or joint optimization with log-likelihood. Bahdanau et al. (2016b) also noticed some of the nice structure of edit distance, but they optimize the model by regressing its outputs to edit distance values leading to suboptimal performance. Rather, we first construct the optimal policy and then use knowledge distillation for training. Independently, Karita et al. (2018) also decomposed edit distance into the contribution of individual tokens and used this decomposition within the EMBR framework. That said, Karita et al. (2018) do not theoretically justify this particular choice of decomposition and report high variance in their gradient estimates.
+
+Reward Augmented Maximum Likelihood (RAML) (Norouzi et al., 2016) and its variants (Ma et al., 2017; Elbayad et al., 2018; Wang et al., 2018) are also similiar to RL-based approaches. Instead of sampling from the model’s distribution, RAML samples sequences from the true exponentiated reward distribution. However, sampling from the true distribution is often difficult and intractable. RAML suffers from the same problems as RL-based methods in credit assignment. SPG (Ding and Soricut, 2017) changes the policy gradient formulation to sample from a reward shaped model distribution. Therefore, its samples are closer than RAML to the model’s samples. In order to facilitate sampling from their proposed distribution SPG provides a heuristic to decompose ROUGE score. Although SPG has a lower variance due to their biased samples, it suffers from the same problems as RAML and RL-based methods in credit assignment.
+
+Generally, OCD excels at training from scratch, which makes it an ideal substitution for MLE. Hence, OCD is orthogonal to methods which require MLE pretraining or joint optimization.
+
+# 5 EXPERIMENTS
+
+We conduct our experiments on speech recogntion on the Wall Street Journal (WSJ) (Paul and Baker, 1992) and Librispeech (Panayotov et al., 2015) benchmarks. We only compare end-to-end speech recognition approaches that do not incorporate language model rescoring. On both WSJ and Librispeech, our proposed OCD (Optimal Completion Distillation) algorithm significantly outperforms our own strong baselines including MLE (Maximum Likelihood Estimation with label smoothing) and SS (scheduled sampling with a well-tuned schedule). Moreover, OCD significantly outperforms all prior work, achieving a new state-of-the-art on two competitive benchmarks.
+
+# 5.1 WALL STREET JOURNAL
+
+The WSJ dataset is readings of three separate years of the Wall Street Journal. We use the standard configuration of si284 for training, dev93 for validation and report both test Character Error Rate (CER) and Word Error Rate (WER) on eval92. We tokenize the dataset to English characters and punctuation. Our model is an attention-based seq2seq network with a deep convolutional frontend as used in Zhang et al. (2017). During inference, we use beam search with a beam size of 16 for all of our models. We describe the architecture and hyperparameter details in Appendix C. We first analyze some key characteristics of the OCD model separately, and then compare our results with other baselines and state-of-the-art methods.
+
+Training prefixes and generalization. We emphasize that during training, the generated prefixes sampled from the model do not match the ground truth sequence, even at the end of training. We define OCD prefix mismatch as the fraction of OCD training tokens that do not match corresponding ground truth training tokens at each position. Assuming that the generated prefix sequence is perfectly matched with the ground truth sequence, then the OCD targets would simply be the following tokens of the ground truth sequence. Hence, OCD becomes equivalent to MLE. Figure 1 shows that OCD prefixes mismatch is more than $2 5 \%$ for the most of the training. This suggests that OCD and MLE are training on very different input prefix trajectories. Further, Figure 2 depicts validation CER as a function of training CER for different model checkpoints during training, where we use beam search on both training and validation sets to obtain CER values. Even at the same training CER, we observe better validation error for OCD, which suggests that OCD improves generalization of MLE, possibly because OCD alleviates the mismatch between training and inference.
+
+Table 3: WSJ Character Error Rate (CER) and Word Error Rate (WER) of different baselines. Schedule Sampling optimizes for Hamming distance and mixes samples from the model and ground truth with a probability schedule (start-of-training end-of-training). OCD always samples from the model and optimizes for all characters which minimize Edit distance. Optimal Completion Target optimizes for one character which minimizes edit distance and another criteria (shortest or same #words).   
+
+<table><tr><td>Training Strategy</td><td>CER</td><td>WER</td></tr><tr><td>Schedule Sampling (1.0 →1.0)</td><td>12.1</td><td>35.6</td></tr><tr><td>Schedule Sampling (0.0 → 1.0)</td><td>3.8</td><td>11.7</td></tr><tr><td>Schedule Sampling (0.0 → 0.55)</td><td>3.6</td><td>10.2</td></tr><tr><td>Optimal Completion &#x27; Target (Shortest)</td><td>3.8</td><td>12.7</td></tr><tr><td>Optimal Completion Target (Same #Words)</td><td>3.3</td><td>10.2</td></tr><tr><td>Optimal Completion Distillation</td><td>3.1</td><td>9.3</td></tr></table>
+
+Table 4: Character Error Rate (CER) and Word Error Rate (WER) results on the end-to-end speech recognition WSJ task. We report results of our Optimal Completion Distillation (OCD) model, and well-tuned implementations of maximum likelihood estimation (MLE) and Scheduled Sampling (SS).   
+
+<table><tr><td>Model</td><td>CER</td><td>WER</td></tr><tr><td>Prior Work</td><td></td><td></td></tr><tr><td>CTC (Graves and Jaitly; 2014)</td><td>9.2</td><td>30.1</td></tr><tr><td>CTC +REINFORCE (Graves and Jaitly; 2014)</td><td>8.4</td><td>27.3</td></tr><tr><td>Gram-CTC (Liu et al.; 2017)</td><td>1</td><td>16.7</td></tr><tr><td>seq2seq (Bahdanau et al.; 2016a)</td><td>6.4</td><td>18.6</td></tr><tr><td>seq2seq + TLE (Bahdanau et al.; 2016b)</td><td>5.9</td><td>18.0</td></tr><tr><td>seq2seq + LS (Chorowski and Jaitly; 2017)</td><td>-</td><td>10.6</td></tr><tr><td>seq2seq + CNN (Zhang et al.; 2017)</td><td>-</td><td>10.5</td></tr><tr><td>seq2seq + LSD (Chan et al.; 2017)</td><td>=</td><td>9.6</td></tr><tr><td>seq2seq + CTC (Kim et al.; 2017)</td><td>7.4</td><td>-</td></tr><tr><td>seq2seq + TwinNet (Serdyuk et al.; 2018)</td><td>6.2</td><td></td></tr><tr><td>seq2seq + MLE + REINFORCE (Tjandra et al.; 2018)</td><td>6.1</td><td>=</td></tr><tr><td>Our Implementation</td><td></td><td></td></tr><tr><td>seq2seq +MLE</td><td>3.6</td><td>10.6</td></tr><tr><td>seq2seq + SS</td><td>3.6</td><td>10.2</td></tr><tr><td>seq2seq + OCD</td><td>3.1</td><td>9.3</td></tr></table>
+
+Impact of edit distance. We further investigate the role of the optimizer by experimenting with different losses. Table 3 compares the test CER and WER of the schedule sampling with a fixed probability schedule of $( 1 . 0  1 . 0 $ ) and OCD model. Both of the models are trained only on sampled trajectories. The main difference is their optimizers, where the S ${ \bf S } ( 1 . 0  1 . 0 $ ) model is optimizing the log likelihood of ground truth (a.k.a. Hamming distance). The significant drop in CER of $\mathrm { S S } ( 1 . 0  1 . 0 $ ) emphasizes the necessity of pretraining or joint training with MLE for models such as SS. OCD is trained from random initialization and does not require MLE pretraining, nor does it require joint optimization with MLE. We also emphasize that unlike SS, we do not need to tune an exploration schedule, OCD prefixes are simply always sampled from the model from the start of training. We note that even fine tuning a pre-trained SS model which achieves $3 . 6 \%$ CER with $1 0 0 \%$ sampling increases the CER to $3 . 8 \%$ . This emphasizes the importance of making the loss a function of the model input prefixes, as opposed to the ground truth prefixes. Appendix D covers another aspect of optimizing Edit distance rather than Hamming distance.
+
+![](images/71ce5958b2f21055b87b6a5f0239d2cd27dff707a2ea4dc7b8b5d16daf8edde3.jpg)  
+Figure 3: Librispeech training and validation WER per training epoch for OCD and MLE.
+
+Target distribution. Another baseline which is closer to MLE framework is selecting only one correct target. Table 3 compares OCD with several Optimal Completion Target (OCT) models. In OCT, we optimize the log-likelihood of one target, which at each step we pick dynamically based on the minimum edit distance completion similar to OCD. We experiment with several different strategies when there is more than one character that can lead to minimum CER. In the OCT (Shortest), we select the token that would minimize the CER and the final length of the sequence. In the OCT (Same #Words), we select the token that in addition to minimum CER, would lead to the closest number of words to the target sequence. We show that OCD achieves significantly better CER and WER over the other optimization strategies compared in Table 3. This highlights the importance of optimizing for the entire set of optimal completion targets, as opposed to a single target.
+
+State-of-the-art. Our model trained with OCD optimizes for CER; we achieve $3 . 1 \%$ CER and $9 . 3 \%$ WER, substantially outperforming our baseline by $14 \%$ relatively on CER and $12 \%$ relatively on WER. In terms of CER, our work substantially outperforms prior work as compared in Table 4, with the closest being Tjandra et al. (2018) trained with policy gradients on CER. In terms of WER, our work is also outperforming Chan et al. (2017), which uses subword units while our model emits characters.
+
+# 5.2 LIBRISPEECH
+
+For the Librispeech dataset, we train on the full training set (960h audio data) and validate our results on the dev-other set. We report the results both on the “clean” and “other” test set. We use Byte Pair Encoding (BPE) (Sennrich et al., 2016) for the output token segmentation. BPE token set is an open vocabulary set since it includes the characters as well as common words and n-grams. We use 10k BPE tokens and report both CER and WER as the evaluation metric. We describe the architecture and hyperparameter details in Appendix C.
+
+Table 5: Character Error Rate (CER) and Word Error Rate (WER) on LibriSpeech test sets.   
+
+<table><tr><td>Model</td><td colspan="2">test-clean</td><td colspan="2">test-other</td></tr><tr><td></td><td>CER</td><td>WER</td><td>CER</td><td>WER</td></tr><tr><td>Prior Work</td><td></td><td></td><td></td><td></td></tr><tr><td>Wav2letter (Collobert et al., 2016)</td><td>6.9</td><td>7.2</td><td></td><td></td></tr><tr><td>Gated ConvNet (Liptchinsky etal., 2017)</td><td>1</td><td>6.7</td><td>1</td><td>20.8</td></tr><tr><td>Cold Fusion (Sriram et al., 2018)</td><td>3.9</td><td>7.5</td><td>9.3</td><td>17.0</td></tr><tr><td>Invariant Representation Learning (Liang et al.,2018)</td><td>3.3</td><td>1</td><td>11.0</td><td>1</td></tr><tr><td>Pretraining+seq2seq+CTC (Zeyer et al.,2018)</td><td>1</td><td>4.9</td><td>1</td><td>15.4</td></tr><tr><td>Our Implementation</td><td></td><td></td><td></td><td></td></tr><tr><td>seq2seq +MLE</td><td>2.9</td><td>5.7</td><td>8.4</td><td>15.4</td></tr><tr><td>seq2seq + OCD</td><td>1.7</td><td>4.5</td><td>6.4</td><td>13.3</td></tr></table>
+
+Fig. 3 shows the validation and training WER curves for MLE and OCD. OCD starts outperforming MLE on training decodings after training for 13 epochs and on validation decodings after 9 epochs. Our MLE baseline achieves $5 . 7 \%$ WER, while OCD achieves $4 . 5 \%$ WER on test-clean ( $2 1 \%$ improvement) and improves the state-of-the-art results over Zeyer et al. (2018). test-other is the more challenging test split ranked by the WER of a model trained on WSJ (Panayotov et al., 2015) mainly because readers accents deviate more from US-English accents. On test-other our MLE baseline achieves $1 5 . 4 \%$ , while our OCD model achieves $1 3 . 3 \%$ WER, outperforming the $1 5 . 4 \%$ WER of Zeyer et al. (2018). Table 5 compares our results with other recent works and the MLE baseline on Librispeech.
+
+# 6 CONCLUSION
+
+This paper presents Optimal Completion Distillation (OCD), a training procedure for optimizing autoregressive sequence models base on edit distance. OCD is applicable to on-policy or off-policy trajectories, and in this paper, we demonstrate its effectiveness on samples drawn from the model in an online fashion. Given any prefix, OCD creates an optimal extension policy by computing the exact optimal Q-values via dynamic programming. The optimal extension policy is distilled by minimizing a KL divergence between the optimal policy and the model. OCD does not require MLE initialization or joint optimization with conditional log-likelihood. OCD achieves $3 . 1 \%$ CER and $9 . 3 \%$ WER on the competitive WSJ speech recognition task, and $4 . 5 \%$ WER on Librispeech without any language model. OCD outperforms all published work on end-to-end speech recognition, including our own well-tuned MLE and scheduled sampling baselines without introducing new hyper-parameters.
+
+# ACKNOWLEDGEMENTS
+
+We thank Geoffrey Hinton for his valuable feedback and reviews. We thank Samy Bengio, Navdeep Jaitly, and Jamie Kiros for their help in reviewing the manuscript as well. We thank Zhifeng Chen and Yonghui Wu for their generous technical help.
+
+# REFERENCES
+
+Martín Abadi, Paul Barham, Jianmin Chen, Zhifeng Chen, Andy Davis, Jeffrey Dean, Matthieu Devin, Sanjay Ghemawat, Geoffrey Irving, Michael Isard, et al. Tensorflow: a system for large-scale machine learning. In OSDI, volume 16, pages 265–283, 2016.
+
+Dzmitry Bahdanau, Kyunghyun Cho, and Yoshua Bengio. Neural machine translation by jointly learning to align and translate. ICLR, 2015.
+
+Dzmitry Bahdanau, Jan Chorowski, Dmitriy Serdyuk, Philemon Brakel, and Yoshua Bengio. End-toEnd Attention-based Large Vocabulary Speech Recognition. ICASSP, 2016a.
+
+Dzmitry Bahdanau, Dmitriy Serdyuk, Philemon Brakel, Nan Rosemary Ke, Jan Chorowski, Aaron Courville, and Yoshua Bengio. Task Loss Estimation for Sequence Prediction. ICLR Workshop, 2016b.
+
+Dzmitry Bahdanau, Philemon Brakel, Kelvin Xu, Anirudh Goyal, Ryan Lowe, Joelle Pineau, Aaron Courville, and Yoshua Bengio. An Actor-Critic Algorithm for Sequence Prediction. ICLR, 2017.
+
+Samy Bengio, Oriol Vinyals, Navdeep Jaitly, and Noam M. Shazeer. Scheduled Sampling for Sequence Prediction with Recurrent Neural Networks. NIPS, 2015.
+
+Denny Britz, Anna Goldie, Minh-Thang Luong, and Quoc Le. Massive exploration of neural machine translation architectures. arXiv:1703.03906, 2017.
+
+William Chan, Navdeep Jaitly, Quoc Le, and Oriol Vinyals. Listen, Attend and Spell: A Neural Network for Large Vocabulary Conversational Speech Recognition. ICASSP, 2016.
+
+William Chan, Yu Zhang, and Navdeep Jaitly. Latent Sequence Decompositions. ICLR, 2017.
+
+Kai-Wei Chang, Akshay Krishnamurthy, Alekh Agarwal, Hal Daumé III, and John Langford. Learning to Search Better Than Your Teacher. In ICML, 2015.
+
+Ching-An Cheng and Byron Boots. Convergence of value aggregation for imitation learning. arXiv preprint arXiv:1801.07292, 2018.
+
+Chung-Cheng Chiu, Tara N Sainath, Yonghui Wu, Rohit Prabhavalkar, Patrick Nguyen, Zhifeng Chen, Anjuli Kannan, Ron J Weiss, Kanishka Rao, Katya Gonina, et al. State-of-the-art speech recognition with sequence-to-sequence models. arXiv:1712.01769, 2017.
+
+Kyunghyun Cho, Bart Van Merriënboer, Caglar Gulcehre, Dzmitry Bahdanau, Fethi Bougares, Holger Schwenk, and Yoshua Bengio. Learning phrase representations using rnn encoder-decoder for statistical machine translation. EMNLP, 2014.
+
+Jan Chorowski and Navdeep Jaitly. Towards better decoding and language model integration in sequence to sequence models. INTERSPEECH, 2017.
+
+Ronan Collobert, Christian Puhrsch, and Gabriel Synnaeve. Wav2letter: an end-to-end convnet-based speech recognition system. arXiv preprint arXiv:1609.03193, 2016.
+
+Hal Daumé, III, John Langford, and Daniel Marcu. Search-based structured prediction. Mach. Learn. J., 2009.
+
+Hal Daumé III and Daniel Marcu. Learning as search optimization: Approximate large margin methods for structured prediction. ICML, 2005.
+
+Nan Ding and Radu Soricut. Cold-Start Reinforcement Learning with Softmax Policy Gradient. In Advances in Neural Information Processing Systems, pages 2817–2826, 2017.
+
+Sergey Edunov, Myle Ott, Michael Auli, David Grangier, and Marc’Aurelio Ranzato. Classical structured prediction losses for sequence to sequence learning. NAACL, 2018.
+
+Maha Elbayad, Laurent Besacier, and Jakob Verbeek. Token-level and sequence-level loss smoothing for rnn language models. ACL, 2018.
+
+Jonas Gehring, Michael Auli, David Grangier, Denis Yarats, and Yann N. Dauphin. Convolutional Sequence to Sequence Learning. In arXiv:1705.03122, 2017.
+
+Xavier Glorot and Yoshua Bengio. Understanding the difficulty of training deep feedforward neural networks. In Proceedings of the thirteenth international conference on artificial intelligence and statistics, pages 249–256, 2010.
+
+James Goodman, Andreas Vlachos, and Jason Naradowsky. Noise reduction and targeted exploration in imitation learning for abstract meaning representation parsing. In Proceedings of the 54th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), volume 1, pages 1–11, 2016.
+
+Alex Graves and Navdeep Jaitly. Towards End-to-End Speech Recognition with Recurrent Neural Networks. ICML, 2014.
+
+Hany Hassan, Anthony Aue, Chang Chen, Vishal Chowdhary, Jonathan Clark, Christian Federmann, Xuedong Huang, Marcin Junczys-Dowmunt, William Lewis, Mu Li, et al. Achieving human parity on automatic chinese to english news translation. arXiv:1803.05567, 2018.
+
+Geoffrey Hinton, Oriol Vinyals, and Jeff Dean. Distilling the Knowledge in a Neural Network. In Neural Information Processing Systems: Workshop Deep Learning and Representation Learning Workshop, 2014.
+
+Sepp Hochreiter and Jurgen Schmidhuber. Long Short-Term Memory. Neural Comput., 9, 1997.
+
+Shigeki Karita, Atsunori Ogawa, Marc Delcroix, and Tomohiro Nakatani. Sequence Training of Encoder-decoder Model Using Policy Gradient for End- To-end Speech Recognition. In ICASSP, 2018.
+
+Suyoun Kim, Takaaki Hori, and Shinji Watanabe. Joint CTC-Attention based End-to-End Speech Recognition using Multi-task Learning. ICASSP, 2017.
+
+Philipp Koehn, Hieu Hoang, Alexandra Birch, Chris Callison-Burch, Marcello Federico, Nicola Bertoldi, Brooke Cowan, Wade Shen, Christine Moran, Richard Zens, et al. Moses: Open source toolkit for statistical machine translation. Proceedings of the 45th annual meeting of the ACL on interactive poster and demonstration sessions, 2007.
+
+Rémi Leblond, Jean-Baptiste Alayrac, Anton Osokin, and Simon Lacoste-Julien. SEARNN: Training RNNs with global-local losses. ICLR, 2018.
+
+Vladimir I Levenshtein. Binary codes capable of correcting deletions, insertions, and reversals. Soviet Physics Doklady, 10(8):707–710, 1966.
+
+Davis Liang, Zhiheng Huang, and Zachary C Lipton. Learning noise-invariant representations for robust speech recognition. arXiv preprint arXiv:1807.06610, 2018.
+
+Vitaliy Liptchinsky, Gabriel Synnaeve, and Ronan Collobert. Letter-Based Speech Recognition with Gated ConvNets. In arXiv:1712.09444, 2017.
+
+Hairong Liu, Zhenyao Zhu, Xiangang Li, and Sanjeev Satheesh. Gram-CTC: Automatic Unit Selection and Target Decomposition for Sequence Labelling. ICML, 2017.
+
+Xuezhe Ma, Pengcheng Yin, Jingzhou Liu, Graham Neubig, and Eduard Hovy. Softmax q-distribution estimation for structured prediction: A theoretical interpretation for raml. arXiv:1705.07136, 2017.
+
+Volodymyr Mnih, Koray Kavukcuoglu, David Silver, Andrei A. Rusu, Joel Veness, Marc G. Bellemare, Alex Graves, Martin Riedmiller, Andreas K. Fidjeland, Georg Ostrovski, Stig Petersen, Charles Beattie, Amir Sadik, Ioannis Antonoglou, Helen King, Dharshan Kumaran, Daan Wierstra, Shane Legg, and Demis Hassabis. Human-level control through deep reinforcement learning. Nature, 2015.
+
+Mohammad Norouzi, Samy Bengio, Zhifeng Chen, Navdeep Jaitly, Mike Schuster, Yonghui Wu, and Dale Schuurmans. Reward Augmented Maximum Likelihood for Neural Structured Prediction. NIPS, 2016.
+
+Vassil Panayotov, Guoguo Chen, Daniel Povey, and Sanjeev Khudanpur. Librispeech: an asr corpus based on public domain audio books. In Acoustics, Speech and Signal Processing (ICASSP), 2015 IEEE International Conference on, pages 5206–5210. IEEE, 2015.
+
+Douglas B Paul and Janet M Baker. The design for the wall street journal-based csr corpus. In Proceedings of the workshop on Speech and Natural Language, pages 357–362. Association for Computational Linguistics, 1992.
+
+Gabriel Pereyra, George Tucker, Jan Chorowski, Łukasz Kaiser, and Geoffrey Hinton. Regularizing Neural Networks by Penalizing Confident Output Distributions. ICLR Workshop, 2017.
+
+Daniel Povey, Arnab Ghoshal, Gilles Boulianne, et al. The Kaldi Speech Recognition Toolkit. ASRU, 2011.
+
+Rohit Prabhavalkar, Tara N. Sainath, Yonghui Wu, Patrick Nguyen, Zhifeng Chen, Chung-Cheng Chiu, and Anjuli Kannan. Minimum Word Error Rate Training for Attention-based Sequence-toSequence Models. In ICASSP, 2018.
+
+Marc’Aurelio Ranzato, Sumit Chopra, Michael Auli, and Wojciech Zaremba. Sequence Level Training with Recurrent Neural Networks. ICLR, 2016.
+
+Steven J. Rennie, Etienne Marcheret, Youssef Mroueh, Jarret Ross, and Vaibhava Goel. Self-critical Sequence Training for Image Captioning. In CVPR, 2017.
+
+Stephane Ross and J Andrew Bagnell. Reinforcement and imitation learning via interactive no-regret learning. arXiv preprint arXiv:1406.5979, 2014.
+
+Stephane Ross, Geoffrey J Gordon, and J Andrew Bagnell. A Reduction of Imitation Learning and Structured Prediction to No-Regret Online Learning. AISTATS, 2011.
+
+Alexander M. Rush, Sumit Chopra, and Jason Weston. A Neural Attention Model for Abstractive Sentence Summarization. In EMNLP, 2015.
+
+Andrei A. Rusu, Sergio Gomez Colmenarejo, Caglar Gulcehre, Guillaume Desjardins, James Kirkpatrick, Razvan Pascanu, Volodymyr Mnih, Koray Kavukcuoglu, and Raia Hadsell. Policy Distillation. ICLR, 2016.
+
+Rico Sennrich, Barry Haddow, and Alexandra Birch. Neural Machine Translation of Rare Words with Subword Units. ACL, 2016.
+
+Dmitriy Serdyuk, Nan Rosemary Ke, Alessandro Sordoni, Adam Trischler, Chris Pal, and Yoshua Bengio. Twin Networks: Matching the Future for Sequence Generation. ICLR, 2018.
+
+Anuroop Sriram, Heewoo Jun, Sanjeev Satheesh, and Adam Coates. Cold fusion: Training seq2seq models together with language models. In INTERSPEECH, 2018.
+
+Wen Sun, Arun Venkatraman, Geoffrey J Gordon, Byron Boots, and J Andrew Bagnell. Deeply aggrevated: Differentiable imitation learning for sequential prediction. arXiv preprint arXiv:1703.01030, 2017.
+
+Wen Sun, J Andrew Bagnell, and Byron Boots. Truncated horizon policy search: Combining reinforcement learning & imitation learning. arXiv preprint arXiv:1805.11240, 2018.
+
+Ilya Sutskever, Oriol Vinyals, and Quoc V. Le. Sequence to Sequence Learning with Neural Networks. NIPS, 2014.
+
+Richard S. Sutton and Andrew G. Barto. Reinforcement Learning: An Introduction. MIT Press, 1998.
+
+Andros Tjandra, Sakriani Sakti, and Satoshi Nakamura. Sequence-to-Sequence ASR Optimization via Reinforcement Learning. ICASSP, 2018.
+
+Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Łukasz Kaiser, and Illia Polosukhin. Attention is all you need. NIPS, 2017.
+
+Oriol Vinyals, Lukasz Kaiser, Terry Koo, Slav Petrov, Ilya Sutskever, and Geoffrey Hinton. Grammar as a Foreign Language. NIPS, 2015.
+
+Xinyi Wang, Hieu Pham, Zihang Dai, and Graham Neubig. Switchout: an efficient data augmentation algorithm for neural machine translation. EMNLP, 2018.
+
+Sam Wiseman and Alexander M. Rush. Sequence-to-Sequence Learning as Beam-Search Optimization. EMNLP, 2016.
+
+Yonghui Wu, Mike Schuster, Zhifeng Chen, Quoc V Le, Mohammad Norouzi, Wolfgang Macherey, Maxim Krikun, Yuan Cao, Qin Gao, Klaus Macherey, et al. Google’s neural machine translation system: Bridging the gap between human and machine translation. arXiv:1609.08144, 2016.
+
+Kelvin Xu, Jimmy Ba, Ryan Kiros, Kyunghyun Cho, Aaron Courville, Ruslan Salakhutdinov, Richard Zemel, and Yoshua Bengio. Show, Attend and Tell: Neural Image Caption Generation with Visual Attention. ICML, 2015.
+
+Albert Zeyer, Kazuki Irie, Ralf Schlüter, and Hermann Ney. Improved training of end-to-end attention models for speech recognition. arXiv preprint arXiv:1805.03294, 2018.
+
+Yu Zhang, William Chan, and Navdeep Jaitly. Very Deep Convolutional Networks for End-to-End Speech Recognition. ICASSP, 2017.
+
+Victor Zhong, Caiming Xiong, and Richard Socher. Seq2SQL: Generating Structured Queries from Natural Language using Reinforcement Learning. arXiv:1709.00103, 2017.
+
+Procedure 1 EditDistanceQ op returns Q-values of the tokens at each time step based on the minimum edit distance between a reference sequence $r$ and a hypothesis sequence $h$ of length $t$ .   
+
+<table><tr><td>1: for j in (0..t) do</td><td></td></tr><tr><td>2:</td><td>dj←j+1</td></tr><tr><td>3:</td><td>for i in (1..t) do</td></tr><tr><td>4:</td><td>minDist←i</td></tr><tr><td>5:</td><td>subCost←i-1</td></tr><tr><td>6:</td><td>insCost←i+1</td></tr><tr><td>7:</td><td>for j in (0..t -1) do</td></tr><tr><td>8:</td><td>if hi-1=rj then</td></tr><tr><td>9: 10:</td><td>repCost ←0</td></tr><tr><td>11:</td><td>else repCost ←1</td></tr><tr><td></td><td></td></tr><tr><td>12: 13:</td><td>cheapest ← min(subCost+repCost,dj +1,insCost)</td></tr><tr><td>14:</td><td>subCost ←dj</td></tr><tr><td>15:</td><td>insCost ← cheapest +1</td></tr><tr><td>16:</td><td>dj←cheapest</td></tr><tr><td>17:</td><td>if dj&lt;minDist then minDist ← dj</td></tr><tr><td>18:</td><td></td></tr><tr><td>19:</td><td>if minDist=ithen Qi,r←1</td></tr><tr><td>20:</td><td>for j in (1..t) do</td></tr><tr><td>21:</td><td>if dj = minDist then</td></tr><tr><td>22:</td><td>Qi,rj+1←1</td></tr><tr><td>23:</td><td>for all tokens k do</td></tr><tr><td>24:</td><td>Qi,k ← Qi,k -1-minDist</td></tr></table>
+
+# APPENDIX A OCD ALGORITHM
+
+Complexity. The total time complexity for calculating the sequence loss using OCD is $O ( T ^ { 2 } + | V | T )$ where $V$ is the vocabulary size and $T$ is the sequence length. MLE loss has a time complexity of $O ( | V | T )$ for calculating the softmax loss at each step. Therefore, assuming that $O ( T ) \leq O ( | V | )$ OCD does not change the time complexity compared to the baseline seq2seq+MLE. The memory cost of the OCD algorithm is $O ( T + | V | T ) = O ( | V | T ) , O ( 2$ for the dynamic programming in line 4 - line 13 of Proc. 1 and $O ( | V | T )$ for storing the stepwise $Q$ values. MLE also stores the one-hot encoding of targets at each step with a cost of $O ( | V | T )$ . Therefore, the memory complexity does not change compared to the MLE baseline either.
+
+Although the loss calculation has the same complexity as MLE, online sampling from the model to generate the input of next RNN cell (as in OCD and SS) is generally slower than reading the ground truth (as in MLE). Therefore, overall a naive implementation of OCD is $\leq 2 0 \%$ slower than our baseline MLE in terms of number of step time. However, since OCD is stand alone and can be trained off-policy, we can also train on stale samples and untie the input generation worker from the training workers. In this case it is as fast as the MLE baseline.
+
+Run through. As an example of how this algorithm works, consider the sequence “SUNDAY” as reference and “SATURDAY” as hypothesis. Table A.1 first shows how to extract optimal targets and their respective $Q ^ { * }$ -values from the table of edit distances between all prefixes of reference and all prefixes of hypothesis. At each row highlighted cells indicate the prefixes which has minimum edit distance in the row. The next character at these indices are the Optimal targets for that row. At each step the $Q ^ { * }$ -value for the optimal targets is negative of the minimum edit distance and for the non-optimal characters it is one smaller.
+
+Table A.1 also illustrates how appending the optimal completions for the prefix “SA” of the hypothesis can lead to the minimum total edit distance. Concatenating with both reference suffixes, “UNDAY”
+
+and “NDAY” will result in an edit distance of 1. Therefore, predicting “U” or “N” at step 2 can lead to the maximum attainable reward of $( - 1 )$ .
+
+Table A.1: Top: Each row corresponds to a prefix of “SATURDAY” and shows edit distances with all prefixes of “SUNDAY”, along with the optimal targets and their $Q ^ { * }$ -value at that step. The highlighted cells indicate cells with minimum edit distance at each row. Bottom: An example of appending suffixes of “SUNDAY” with minimum edit distance to the prefix “SA”.
+
+<table><tr><td rowspan=1 colspan=1></td><td rowspan=1 colspan=7>Edit Distance</td><td rowspan=1 colspan=1>OCD Targets</td><td rowspan=1 colspan=1>Q-values</td></tr><tr><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>S</td><td rowspan=1 colspan=1>U</td><td rowspan=1 colspan=1>N</td><td rowspan=1 colspan=1>D</td><td rowspan=1 colspan=1>A</td><td rowspan=1 colspan=1>Y</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td></tr><tr><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>0</td><td rowspan=1 colspan=1>1</td><td rowspan=1 colspan=1>2</td><td rowspan=1 colspan=1>3</td><td rowspan=1 colspan=1>4</td><td rowspan=1 colspan=1>5</td><td rowspan=1 colspan=1>6</td><td rowspan=1 colspan=1>S</td><td rowspan=1 colspan=1>0</td></tr><tr><td rowspan=1 colspan=1>S</td><td rowspan=1 colspan=1>1</td><td rowspan=1 colspan=1>0</td><td rowspan=1 colspan=1>1</td><td rowspan=1 colspan=1>2</td><td rowspan=1 colspan=1>3</td><td rowspan=1 colspan=1>4</td><td rowspan=1 colspan=1>5</td><td rowspan=1 colspan=1>U</td><td rowspan=1 colspan=1>0</td></tr><tr><td rowspan=1 colspan=1>A</td><td rowspan=1 colspan=1>2</td><td rowspan=1 colspan=1>1</td><td rowspan=1 colspan=1>1</td><td rowspan=1 colspan=1>2</td><td rowspan=1 colspan=1>3</td><td rowspan=1 colspan=1>3</td><td rowspan=1 colspan=1>4</td><td rowspan=1 colspan=1>U,N</td><td rowspan=1 colspan=1>-1</td></tr><tr><td rowspan=1 colspan=1>T</td><td rowspan=1 colspan=1>3</td><td rowspan=1 colspan=1>2</td><td rowspan=1 colspan=1>2</td><td rowspan=1 colspan=1>2</td><td rowspan=1 colspan=1>3</td><td rowspan=1 colspan=1>4</td><td rowspan=1 colspan=1>4</td><td rowspan=1 colspan=1>U,N,D</td><td rowspan=1 colspan=1>-2</td></tr><tr><td rowspan=1 colspan=1>U</td><td rowspan=1 colspan=1>4</td><td rowspan=1 colspan=1>3</td><td rowspan=1 colspan=1>2</td><td rowspan=1 colspan=1>3</td><td rowspan=1 colspan=1>3</td><td rowspan=1 colspan=1>4</td><td rowspan=1 colspan=1>5</td><td rowspan=1 colspan=1>N</td><td rowspan=1 colspan=1>-2</td></tr><tr><td rowspan=1 colspan=1>R</td><td rowspan=1 colspan=1>5</td><td rowspan=1 colspan=1>4</td><td rowspan=1 colspan=1>3</td><td rowspan=1 colspan=1>3</td><td rowspan=1 colspan=1>4</td><td rowspan=1 colspan=1>4</td><td rowspan=1 colspan=1>5</td><td rowspan=1 colspan=1>N,D</td><td rowspan=1 colspan=1>-3</td></tr><tr><td rowspan=1 colspan=1>D</td><td rowspan=1 colspan=1>6</td><td rowspan=1 colspan=1>5</td><td rowspan=1 colspan=1>4</td><td rowspan=1 colspan=1>4</td><td rowspan=1 colspan=1>3</td><td rowspan=1 colspan=1>4</td><td rowspan=1 colspan=1>5</td><td rowspan=1 colspan=1>A</td><td rowspan=1 colspan=1>-3</td></tr><tr><td rowspan=1 colspan=1>A</td><td rowspan=1 colspan=1>7</td><td rowspan=1 colspan=1>6</td><td rowspan=1 colspan=1>5</td><td rowspan=1 colspan=1>5</td><td rowspan=1 colspan=1>4</td><td rowspan=1 colspan=1>3</td><td rowspan=1 colspan=1>4</td><td rowspan=1 colspan=1>Y</td><td rowspan=1 colspan=1>-3</td></tr><tr><td rowspan=1 colspan=1>Y</td><td rowspan=1 colspan=1>8</td><td rowspan=1 colspan=1>7</td><td rowspan=1 colspan=1>6</td><td rowspan=1 colspan=1>6</td><td rowspan=1 colspan=1>5</td><td rowspan=1 colspan=1>4</td><td rowspan=1 colspan=1>3</td><td rowspan=1 colspan=1>&lt;/s&gt;</td><td rowspan=1 colspan=1>-3</td></tr></table>
+
+<table><tr><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>S</td><td rowspan=1 colspan=1>U</td><td rowspan=1 colspan=1>N</td><td rowspan=1 colspan=1>D</td><td rowspan=1 colspan=1>A</td><td rowspan=1 colspan=1>Y</td></tr><tr><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>0</td><td rowspan=1 colspan=1>1</td><td rowspan=1 colspan=1>2</td><td rowspan=1 colspan=1>3</td><td rowspan=1 colspan=1>4</td><td rowspan=1 colspan=1>5</td><td rowspan=1 colspan=1>6</td></tr><tr><td rowspan=1 colspan=1>S</td><td rowspan=1 colspan=1>1</td><td rowspan=1 colspan=1>0</td><td rowspan=1 colspan=1>1</td><td rowspan=1 colspan=1>2</td><td rowspan=1 colspan=1>3</td><td rowspan=1 colspan=1>4</td><td rowspan=1 colspan=1>5</td></tr><tr><td rowspan=1 colspan=1>A</td><td rowspan=1 colspan=1>2</td><td rowspan=1 colspan=1>1</td><td rowspan=1 colspan=1>1</td><td rowspan=1 colspan=1>2</td><td rowspan=1 colspan=1>3</td><td rowspan=1 colspan=1>3</td><td rowspan=1 colspan=1>4</td></tr><tr><td rowspan=1 colspan=1>U</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>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></td></tr><tr><td rowspan=1 colspan=1>N</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>1</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td></tr><tr><td rowspan=1 colspan=1>D</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>+</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td></tr><tr><td rowspan=1 colspan=1>A</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></td><td rowspan=1 colspan=1>1</td><td rowspan=1 colspan=1></td></tr><tr><td rowspan=1 colspan=1>Y</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></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td></tr></table>
+
+<table><tr><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>S</td><td rowspan=1 colspan=1>U</td><td rowspan=1 colspan=1>N</td><td rowspan=1 colspan=1>D</td><td rowspan=1 colspan=1>A</td><td rowspan=1 colspan=1>Y</td></tr><tr><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>0</td><td rowspan=1 colspan=1>1</td><td rowspan=1 colspan=1>2</td><td rowspan=1 colspan=1>3</td><td rowspan=1 colspan=1>4</td><td rowspan=1 colspan=1>5</td><td rowspan=1 colspan=1>6</td></tr><tr><td rowspan=1 colspan=1>S</td><td rowspan=1 colspan=1>1</td><td rowspan=1 colspan=1>0</td><td rowspan=1 colspan=1>1</td><td rowspan=1 colspan=1>2</td><td rowspan=1 colspan=1>3</td><td rowspan=1 colspan=1>4</td><td rowspan=1 colspan=1>5</td></tr><tr><td rowspan=1 colspan=1>A</td><td rowspan=1 colspan=1>2</td><td rowspan=1 colspan=1>1</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>2</td><td rowspan=1 colspan=1>3</td><td rowspan=1 colspan=1>3</td><td rowspan=1 colspan=1>4</td></tr><tr><td rowspan=1 colspan=1>N</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></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td></tr><tr><td rowspan=1 colspan=1>D</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>1</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td></tr><tr><td rowspan=1 colspan=1>A</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></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td></tr><tr><td rowspan=1 colspan=1>Y</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></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>1</td></tr></table>
+
+# APPENDIX B EXPOSURE BIAS
+
+A key limitation of teacher forcing for sequence learning stems from the discrepancy between the training and test objectives. One trains the model using conditional log-likelihood $\mathcal { O } _ { \mathrm { C L L } }$ , but evaluates the quality of the model using empirical reward $\mathcal { O } _ { \mathrm { E R } }$ .
+
+Unlike teacher forcing and Scheduled Sampling (SS), policy gradient approaches (e.g. Ranzato et al. (2016); Bahdanau et al. (2017)) and OCD aim to optimize the empirical reward objective (4) on the training set. We illustrate four different training strategies of MLE, SS, Policy Gradient and OCD in Figure B.1. The drawback of policy gradient techniques is twofold: 1) they cannot easily incorporate ground truth sequence information except through the reward function, and 2) they have difficulty reducing the variance of the gradients to perform proper credit assignment. Accordingly, most policy gradient approaches Ranzato et al. (2016); Bahdanau et al. (2017); Wu et al. (2016) pre-train the model using teacher forcing. By contrast, the OCD method proposed in this paper defines an optimal completion policy $\pi _ { t } ^ { * }$ for any off-policy prefix by incorporating the ground truth information. Then, OCD optimizes a token level log-loss and alleviates the credit assignment problem. Finally, training is much more stable, and we do not require initialization nor joint optimization with MLE.
+
+There is an intuitive notion of exposure bias Ranzato et al. (2016) discussed in the literature as a limitation of teacher forcing. We formalize this notion as follows. One can think of the optimization of the log loss (3) in an autoregressive models as a classification problem, where the input to the classifier is a tuple $( \mathbf { s } , \mathbf { y } _ { < t } ^ { * } )$ and the correct output is $y _ { i } ^ { * }$ , where $\mathbf { y } _ { < t } ^ { * } \equiv ( y _ { 1 } ^ { * } , \dots , y _ { t - 1 } ^ { * } )$ . Then the training dataset comprises different examples and different prefixes of the ground truth sequence. The key challenge is that once the model is trained, one should not expect the model to generalize to a new prefix $\mathbf { y } _ { < t }$ that does not come from the training distribution of $P ( \mathbf { y } _ { < t } ^ { * } )$ . This problem can become severe as $\mathbf { y } _ { < t }$ becomes more dissimilar to correct prefixes. During inference, when one conducts beam search with a large beam size then one is more likely to discover wrong generalization of $p _ { \theta } ( \hat { y } _ { t } | \hat { \mathbf { y } } _ { < t } , \mathbf { x } )$ , because the sequence is optimized globally. A natural strategy to remedy this issue is to train on arbitrary prefixes. Unlike the aforementioned techniques OCD can train on any prefix given its off-policy nature.
+
+![](images/a6422f8a30c76b8784cd0fa15cedce9e663005b9c29f310a57f8b98e1c660728.jpg)  
+Figure B.1: Illustration of different training strategies for autoregressive sequence models. (a) Teacher Forcing: the model conditions on correct prefixes and is taught to predict the next ground truth token. (b) Scheduled Sampling: the model conditions on tokens either from ground truth or drawn from the model and is taught to predict the next ground truth token regardless. (c) Policy Gradient: the model conditions on prefixes drawn from the model and is encouraged to reinforce sequences with a large sequence reward $R ( \tilde { y } )$ . (d) Optimal Completion Distillation: the model conditions on prefixes drawn from the model and is taught to predict an optimal completion policy $\pi ^ { * }$ specific to the prefix.
+
+Figure B.2 illustrates how increasing the beam size for MLE and SS during inference decreases their performance on WSJ datasets to above $1 1 \%$ WER. OCD suffers a degradation in the performance too but it never gets above $1 0 \%$ WER.
+
+![](images/2f28827fab90427338d033646de972d4f4ec1e63a5a83aca41a88ff214c88977.jpg)  
+Figure B.2: Word Error Rate (WER) of WSJ with MLE, SS and OCD for different beam sizes.
+
+# APPENDIX C ARCHITECTURE
+
+WSJ. The input audio signal is converted into 80-dimensional filterbank features computed every $1 0 \mathrm { m s }$ with delta and delta-delta acceleration, normalized with per-speaker mean and variance generated by Kaldi (Povey et al., 2011). Our encoder uses 2-layers of convolutions with $3 \times 3$ filters, stride $2 \times 2$ and 32 channels, followed by a convolutional LSTM with 1D-convolution of filter width 3, followed by 3 LSTM layers with 256 cell size. We also apply batch-normalization between each layer in the encoder. The attention-based decoder is a 1-layer LSTM with 256 cell size with content-based attention. We use Xavier initializer (Glorot and Bengio, 2010) and train our models for 300 epochs of batch size 8 with 8 async workers. We separately tune the learning rate for our baseline and OCD model, 0.0007 for OCD vs 0.001 for baseline. We apply a single 0.01 drop of learning rate when validation CER plateaus, the same as for our baseline. Both happen around 225 epoch. We implemented our experiments2 in TensorFlow (Abadi et al., 2016).
+
+Librispeech. Since the dataset is larger than WSJ, we use a larger batch size of 16, smaller learning rate of 0.0005 for baseline and 0.0003 for OCD. Models are trained for 70 epochs. We remove the convolutional LSTM layers of the encoder, increase the number of LSTM layers in the encoder to 6, and increase the LSTM cell size to 384. All other configs are the same as the WSJ setup.
+
+# APPENDIX D HAMMING DISTANCE VS EDIT DISTANCE DURING TRAINING
+
+Figure D.3 plots the edit distance on training data of OCD and MLE for fixed hamming distances during training. The plot shows that for a fixed Hamming distance (which is the metric that MLE correlates with more), OCD achieves a lower edit distance compared to MLE. This gives evidence that OCD is indeed optimizing for edit distance as intended.
+
+![](images/78ef8e2bb60a4c5ce394e0ec73fd87257c53534b596e8505d6a9256ada4d11d9.jpg)  
+Figure D.3: WSJ training Character Error Rate (CER) of MLE and OCD over Character Accuracy at different checkpoints during training.

parse/train/rylWVnR5YQ/rylWVnR5YQ.md

@@ -0,0 +1,253 @@
+# CONTEXT DEPENDENT MODULATION OF ACTIVATIONFUNCTION
+
+Anonymous authors Paper under double-blind review
+
+# ABSTRACT
+
+We propose a modification to traditional Artificial Neural Networks (ANNs), which provides the ANNs with new aptitudes motivated by biological neurons. Biological neurons work far beyond linearly summing up synaptic inputs and then transforming the integrated information. A biological neuron change firing modes accordingly to peripheral factors (e.g., neuromodulators) as well as intrinsic ones. Our modification connects a new type of ANN nodes, which mimic the function of biological neuromodulators and are termed modulators, to enable other traditional ANN nodes to adjust their activation sensitivities in run-time based on their input patterns. In this manner, we enable the slope of the activation function to be context dependent. This modification produces statistically significant improvements in comparison with traditional ANN nodes in the context of Convolutional Neural Networks and Long Short-Term Memory networks.
+
+# 1 INTRODUCTION
+
+Artificial neural networks (ANNs), such as convolutional neural networks (CNNs) (LeCun et al., 1998) and long short-term memory (LSTM) cells (Hochreiter & Schmidhuber, 1997), have incredible capabilities and are applied in a variety of applications including computer vision, natural language analysis, and speech recognition among others. Historically, the development of ANNs (e.g., network architectures and learning algorithms) has benefited significantly from collaborations with Psych-Neuro communities (Churchland & Sejnowski, 1988; Hebb, 1949; Hinton et al., 1984; Hopfield, 1982; McCulloch & Pitts, 1943; Turing, 1950; Hassabis et al., 2017; Elman, 1990; Hopfield & Tank, 1986; Jordan, 1997; Hassabis et al., 2017). The information processing capabilities of traditional ANN nodes are rather rigid when compared to the plasticity of real neurons. A typical traditional ANN node linearly integrate its input signals and run the integration through a transformation called an activation function, which simply takes in a scalar value and outputs another. Of the most popular Activation Functions are sigmoid (Mikolov et al., 2010), tanh (Kalman & Kwasny, 1992) and ReLU (Nair & Hinton, 2010).
+
+Researchers have shown that it could be beneficial to deploy layer-/node- specific activation functions in a deep ANN (Chen & Chang, 1996; Solazzi & Uncini, 2000; Goh & Mandic, 2003; He et al., 2015; Agostinelli et al., 2014). However, each ANN node is traditionally stuck with a fixed activation function once trained. Therefore, the same input integration will always produce the same output. This fails to replicate the amazing capability of individual biological neurons to conduct complex nonlinear mappings from inputs to outputs (Antic et al., 2010; Hassabis et al., 2017; Marblestone et al., 2016). In this study, we propose one new modification to ANN architectures by adding a new type of node, termed modulators, to modulate the activation sensitivity of the ANN nodes targeted by modulators (see Figures 1-3 for examples). In one possible setting, a modulator and its target ANN nodes share the same inputs. The modulator maps the input into a modulation signal, which is fed into each target node. Each target node multiples its input integration by the modulator signal prior to transformation by its traditional activation function. Examples of neuronal principles that may be captured by our new modification include intrinsic excitability, diverse firing modes, type 1 and type 2 forms of firing rate integration, activity dependent facilitation and depression and, most notably, neuromodulation (Marder et al., 1996; Sherman, 2001; Ward, 2003; Ringrose & Paro, 2004).
+
+Our modulator is relevant to the attention mechanism (Larochelle & Hinton, 2010; Mnih et al., 2014), which dynamically restricts information pathways and has been found to be very useful in practice. Attention mechanisms apply the attention weights, which are calculated in run-time, to the outputs of ANN nodes or LSTM cells. Notably, the gating mechanism in a Simple LSTM cell can also be viewed as a dynamical information modifier. A gate takes the input of the LSTM cell and outputs gating signals for filtering the outputs of its target ANN nodes in the same LSTM cell. A similar gating mechanism was proposed in the Gated Linear Unit (Dauphin et al., 2016) for CNNs. Different from the attention and gating mechanisms, which are applied to the outputs of the target nodes, our modulation mechanism adjusts the sensitivities of the target ANN nodes in run-time by changing the slopes of the corresponding activation functions. Hence, the modulator can also be used as a complement to the attention and gate mechanisms.
+
+Below we will explain our modulator mechanism in detail. Experimentation shows that the modulation mechanism can help achieve better test stability and higher test performance using easy to implement and significantly simpler models. Finally, we conclude the paper with discussions on the relevance to the properties of actual neurons.
+
+# 2 METHODS
+
+We designed two modulation mechanisms, one for CNNs and the other for LSTMs. In modulating CNNs, our modulator (see Figure 1) is a layer-specific one that is best compared to the biological phenomenon of neuromodulation. Each CNN layer before activation has one modulator, which shares the input $\vec { x }$ with other CNN nodes in the same layer (Figure 1Left). The modulator (Figure 1Right) of the ${ { l } ^ { t h } }$ CNN layer calculates a scalar modulation signal as $s _ { l } = \tau _ { l } ( \vec { w } _ { l } ^ { T } \vec { x } )$ , where $\tau _ { l } ( \cdot )$ is the activation function of the ${ { l } ^ { t h } }$ modulator, and feeds $s _ { l }$ to every other CNN node in the same layer. The $k ^ { t h }$ modulated CNN node in the $l ^ { t h }$ layer linearly integrates its inputs as a traditional ANN nodes $v _ { l , k } = \vec { w } _ { l , k } ^ { T } \vec { x }$ and modulates the integration to get $u _ { l , k } = s _ { l } \cdot v _ { l , k }$ prior to its traditional activation step $\varphi _ { l , k } ( \cdot )$ . The final output is $o _ { l , k } = \varphi _ { l , k } \big ( \tau _ { l } \big ( \vec { w } _ { l } ^ { T } \vec { x } \big ) \cdot \vec { w } _ { l , k } ^ { T } \vec { x } \big )$ . The above modulation mechanism is slightly modified to expand Densely Connected CNNs (Iandola et al., 2014)(see Figure 2). A modulator is added to each dense block layer to modulate the outputs of its convolution nodes. Given a specific input, the modulator outputs a scalar modulation signal that is multiplied to the scalar outputs of the target convolution nodes in the same layer.
+
+In addition to the Cellgate, there are three modifying gates (Forget, Input, and Output) in a traditional LSTM cell. Each gate is a full layer of ANN nodes. Each of ANN node in a gate uses sigmoid to transform the integration of the input into regulation signals. The traditional LSTM cell transforms the input integration to an intermediate output (i.e., $\tilde { C } _ { t }$ in Figure 3). The Forget gate regulates what is removed from the old cell state (i.e., $t - 1$ in Figure 3), and the Input gate what in $\tilde { C } _ { t }$ is added to obtain the new cell state (i.e., $_ t )$ . The new cell state is transformed and then regulated by the output gate to become part of the input of the next time point. In modulating LSTM (see Figure 3), for the purpose of easier implementation, we create a new ”modulation gate” (the round dash rectangle in Figure 3) for node-specific sensitivity-adjustment which is most analogous to neuronal facilitation and depression. Different from a conventional LSTM that calculates $\tilde { C } _ { t } ~ = ~ \varphi ( W _ { c } [ \vec { x } _ { t } , \vec { h } _ { t - 1 } ] )$ , a modulated LSTM calculates $\tilde { C } _ { t } = \varphi ( \tau ( W _ { M } [ \vec { x } _ { t } , \vec { h } _ { t - 1 } ] ) \cdot ( W _ { c } [ \vec { x } _ { t } , \vec { h } _ { t - 1 } ] ) )$ .
+
+In the above designs, both a multi-layer CNN and single-layer LSTM had multiple modulator nodes within each model. A generalization to the above designs is to allow a modulator to take the outputs from other CNN layers or those of the LSTM cell at other time points as the inputs.
+
+![](images/c5c160d685633168dd2635293a5acbfdb7626255f33b162ce5d04a56e73223d9.jpg)  
+Figure 1: Modulator expansion to CNN. Left: Each CNN layer before activation layer has a modulator, whose input $\vec { x }$ is the same to that of other CNN nodes in the same layer. Right: The modulator maps the input into a scalar modulation signal, which is fed to every other CNN node in the same layer. Every modulated node multiples the integration of its inputs by the modulation signal prior to traditional activation.
+
+![](images/b984fc11468aabad40e054698845a113db29818d4254c47f352299cfa6a51783.jpg)  
+Figure 2: Modulator expansion to a dense block in a DenseNet. Left: A dense block example that contains two dense block layers. Right: A dense block layer transforms its input element-wisely before convolution. Hence, the modulation applied to the previous dense block layer affects the transformation activity of the next dense block layer. Modulation is applied to the output of each node in the target convolution layer. We ignore other steps (e.g, batch normalization and drop-out) in a dense block layer for visualization purpose.
+
+![](images/37043457478b59922e080e7107e2727a9d8066360814232945774db4a645b73b.jpg)  
+Figure 3: Modulator expansion to a Simple LSTM cell. A Simple LSTM cell wraps the Input Integration and Activation steps in the orange box into one node. Our modification adds a modulator (the green box) that maps $[ \vec { x _ { t } } , \vec { h } _ { t - 1 } ]$ , i.e., the concatenation of the input at time $t$ and the LSTM output at time $t - 1$ , into modulation signals that are used to adjust the sensitivity of transforming the integration of $[ \vec { x } _ { t } , \vec { h } _ { t - 1 } ]$ .
+
+# 3 EXPERIMENTAL RESULTS
+
+# 3.1 MODULATED CNNS
+
+In our experiments with CNNs, the activation functions of the traditional CNN nodes was ReLU, with our modulator nodes using a sigmoid. We tested six total settings: a vanilla CNN vs a modulated vanilla CNN, a vanilla DenseNet vs a modulated DenseNet, and a vanilla DenseNet-lite vs a modulated DenseNet-lite. The vanilla CNN has 2 convolution blocks, each of which contains two sequential convolution layers, a pooling layer, and a dropout layer. A fully connected layer of 512 nodes is appended at the very end of the model. The convolution layers in the first block have 32 filters with a size of 3x3 while the convolution layers in the second block have 64 filters with a size of 3x3. We apply a dropout of 0.25 to each block. The vanilla DenseNet used the structure (40 in depth and 12 in growth-rate) reported in the original DenseNet paper (Iandola et al., 2014) and a dropout of 0.5 is used in our experiment. The vanilla DenseNet-lite has a similar structure to the vanilla DenseNet, however, uses a smaller growth-rate of 10 instead of 12 in the original configuration, which results in $28 \%$ fewer parameters. The modulators are added to the vanilla CNN, the vanilla DenseNet, and the vanilla DenseNet-lite in the way described in Figures 1 and 2 to obtain their modulated versions, respectively. Table 1 summarizes the numbers of the parameters in the above models to indicate their complexities. The modulated networks have slightly more parameters than their vanilla versions do. All the experiments were run for 150 epochs on 4 NVIDIA Titan $\mathrm { X p }$ GPUs with a mini-batch size of 128.
+
+Table 1: Compare the numbers of parameters in the CNNs.   
+
+<table><tr><td>Model</td><td>Total parameters</td></tr><tr><td>vanilla CNN</td><td></td></tr><tr><td>modulated CNN</td><td>1.25M 1.25 M</td></tr><tr><td>vanilla DenseNet</td><td>1.00 M</td></tr><tr><td>modulated DenseNet</td><td>1.07 M</td></tr><tr><td>vanilla DenseNet-lite</td><td>0.71M</td></tr><tr><td>modulatedDenseNet-lite</td><td>0.77 M</td></tr></table>
+
+CIFAR-10 dataset (Krizhevsky & Hinton, 2009) was used in this experiment. CIFAR-10 consists of colored images at a resolution of $3 2 \mathrm { x } 3 2 $ pixels. The training and test set are containing 50000 and 10000 images respectively. We held $20 \%$ of the training data for validation and applied data augmentation of shifting and mirroring on the training data. All the CNN models are trained using the Adam (Kingma & Ba, 2014) optimization method with a learning rate of 1e-3 and shrinks by a factor of 10 at $50 \%$ and $80 \%$ of the training progress.
+
+As shown in Figure 4, the vanilla CNN model begins to overfit after 80 training epochs. Although the modulated CNN model is slightly more complex, it is less prone to overfitting and excels its vanilla counterpart by a large margin (see Table 2). Modulation also significantly helps DenseNets in training, validation, and test. The modulated DenseNet/DenseNet-lite models consistently outperform their vanilla counterparts by a noticeable margin (see Figures 5(a) and 5(b)) during training. The validation and test results of the modulated DenseNet/DenseNet-lite models are also better than those of their vanilla counterparts. It is not surprising that the vanilla DenseNet-lite model underperforms the vanilla DenseNet model. Interestingly, despite having $28 \%$ fewer parameters than the vanilla DenseNet model, the modulated DenseNet-lite model outperforms the vanilla DenseNet model (see the dash orange curve vs the solid blue curve in Figure 5(b) and Table 2).
+
+![](images/979c87cb2f3f0b3a1b3068b4bfd1be3c0d7bbe08a776b1d76f191d2c7fd63fd1.jpg)  
+Figure 4: Modulation increases the robustness of CNNs. The $\mathbf { X }$ -axis is the validation epoch, and the y-axis is the top-1 accuracy. The vanilla CNN begins to show sign of overfitting after 80 epochs, while the modulated CNN keeps improving.
+
+![](images/005016e265e18dafa5641d8072937f4ac5f97e4cba6489b0f02819040bbf558b.jpg)
+
+(a) Comparison of the training results of vanilla DenseNet, moduldate DenseNet, vanilla DenseNet-lite, and modulate DenseNet-lite. The $\mathbf { X }$ -axis is the training epoch, and the y-axis is the top-1 accuracy.
+
+![](images/6d639b58dc79209a9d619b326596c135a56127c47df24efce99b702b9aa4eb0b.jpg)  
+(b) Comparison of the validation results of vanilla DenseNet, modulate DenseNet, vanilla DenseNet-lite, and modulate DenseNet-lite. The $\mathbf { X }$ -axis is the validation epoch, and the y-axis is the top-1 accuracy.
+
+Figure 5: Modulation improves the performance of DenseNets. Both training and validation results show that the modulated versions perform better than their vanilla versions. In addition, modulated DenseNet-lite clearly outperforms vanilla DenseNet even though the former has $28 \%$ less parameters than the latter.
+
+Table 2: Test results (top-1 classification accuracy) of vanilla and modulated CNNs.   
+
+<table><tr><td>Model</td><td>Training</td><td>Validation</td><td>Test</td></tr><tr><td></td><td></td><td></td><td></td></tr><tr><td>vanilla CNN</td><td>0.649</td><td>0.694</td><td>0.690</td></tr><tr><td>modulated CNN</td><td>0.775</td><td>0.782</td><td>0.782</td></tr><tr><td>vanilla DenseNet</td><td>0.889</td><td>0.888</td><td>0.889</td></tr><tr><td>modulatedDenseNet</td><td>0.905</td><td>0.902</td><td>0.902</td></tr><tr><td>vanilla DenseNet-lite</td><td>0.881</td><td>0.885</td><td>0.885</td></tr><tr><td>modulatedDenseNet-lite</td><td>0.894</td><td>0.893</td><td>0.894</td></tr></table>
+
+# 3.2 MODULATED LSTM
+
+Two datasets were used in the LSTM experiments. The first one is the NAMES dataset (Sean, 2016), in which the goal is to take a name as a string and classify its ethnicity or country of origin. Approximately $10 \%$ of the data-set was reserved for testing. The second experiment used the SST2 data-set (Socher et al., 2013), which requires a trained model to classify whether a movie review is positive or negative based on the raw text in the review. The SST2 is identical to the SST1 with the exception of the neutral category removed (Socher et al., 2013), leaving only positive and negative reviews. About $20 \%$ of the data-set was reserved for testing.
+
+Since modulators noticeably increase the parameters in a modulated LSTM, to perform fair comparisons, we create three versions of vanilla LSTMs (see Controls 1, 2, & 3 in Figure 6). Control 1 has an identical total LSTM cell size. Control 2 has the identical number of nodes per layer. Control 3 has an extra Input gate so that it has both an identical total number of nodes and identical nodes per layer. The numbers of parameters in the modulated LSTM and control LSTMs are listed in Table 3 for comparison.
+
+![](images/d442f3647890830ca9aa78beeb8caf14b332eab9759ecf37d412295c66ce6703.jpg)  
+Figure 6: The configurations of the modulated LSTM and three control versions of the vanilla LSTMs.
+
+Modulated condition has $5 \mathrm { N }$ total LSTM nodes,N nodes per gate& N linear layer nodes (hidden_dim $= \mathbf { N } ]$ Control1 has $5 \mathrm { N }$ totalLSTM nodes, $5 / 4 \mathrm { N }$ per (standard LSTM) gate& 5/4Nlinear nodes (hidden_dim $= 5 / 4 \mathrm { N }$ Control 2 has $4 \mathrm { N }$ totalLSTM nodes,Nper (standardLSTM) gate&Nlinear nodes (hidden_dim $\mathbf { \tau } = \mathbf { N } .$ ） Control 3 has $5 \mathrm { N }$ total LSTM nodes,N per(with extra Ingate) gate &N linear nodes (hidden_dim $\mathbf { \tau } = \mathbf { N }$
+
+The hyper-parameters for the first experiment were set as following: the hidden dimension was set to 32, batch size to 32, embedding dimension to 128, initial learning rate to .01, learning rate decay to 1e-4, an SGD optimizer was used, with dropout of 0.2 applied to the last hidden state of the LSTM and 100 epochs were collected. This condition was tested on the name categorization data-set. The number of parameters in this model ranged from $4 . 1 \ \mathrm { K }$ to $6 . 4 ~ \mathrm { K }$ , depending on the condition. We repeated the experimental runs 30 times. Based on the simplicity of the data-set and the relative sparsity of parameters, this condition will be referred to as Simple-LSTM. As for the second experiment: the hidden dimension was set to 150, he batch size was set to 5, the embedding dimension was set to 300, the initial learning rate was set to 1e-3, there was no learning rate decay, an Adam optimizer was used with no dropout and 100 epochs were collected. The number of parameters in this model ranged from $5 7 . 6 \mathrm { ~ K ~ }$ to $9 0 ~ \mathrm { K }$ , depending on the control setup. This experiment was repeated 100 times. Based on the complexity of the data-set and the relatively large amount of parameters, this condition will be referred to as Advanced-LSTM. In all experiments, the models were trained for 100 epochs.
+
+Table 3: The number of parameters in a LSTM cell.   
+
+<table><tr><td>Base Model</td><td>Modulated</td><td>Control 1</td><td>Control 2</td><td>Control 3</td></tr><tr><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Simple-LSTM</td><td>5.1K</td><td>6.4K</td><td>4.1 K</td><td>5.1K</td></tr><tr><td>Advanced-LSTM</td><td>72K</td><td>90K</td><td>57.6K</td><td>72K</td></tr></table>
+
+Table 4: Modulation Performance Tests on LSTM   
+Table 5: LSTM node Activation function visualizations   
+
+<table><tr><td>Model Dataset</td><td>Modulator Activation</td><td>Performance Statistics</td><td>Modulated</td><td>Control 1</td><td>Control 2</td><td>Control 3</td></tr><tr><td rowspan="4">Simple-LSTM NAMES</td><td rowspan="4">Sigmoid</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>mean</td><td>0.77898</td><td>0.77490</td><td>0.77516</td><td>0.77602</td></tr><tr><td>std</td><td>0.00526</td><td>0.00565 0.74778</td><td>0.00531</td><td>0.00650</td></tr><tr><td>Hedge&#x27;s G p-value</td><td>1</td><td>p&lt;.006</td><td>0.72173 p&lt;.007</td><td>0.49924 p&lt;.06</td></tr><tr><td rowspan="5">Advanced-LSTM SST2</td><td rowspan="5">Tanhshrink</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>mean</td><td>0.77482</td><td>0.73629</td><td>0.74327</td><td>0.73628</td></tr><tr><td>std</td><td>0.01150</td><td>0.04855</td><td>0.04687</td><td>0.04701</td></tr><tr><td>Hedge&#x27;s G</td><td>1</td><td>1.09182</td><td>0.92435</td><td>1.12593</td></tr><tr><td>p-value</td><td></td><td>p&lt;.001</td><td>p&lt;.001</td><td>p&lt;.001</td></tr></table>
+
+![](images/f47bd4f498d318f62a2008330bc634096126d73a31d334867935dab7d6588ad3.jpg)  
+Simple-LSTM (sigmoid t1)
+
+In this node, the Ingate produces diverse clusters of potential outputs fora given input.However,specific input-output relationships seem somewhat poorly defined, illustrated by the low density of the clusters.
+
+The added source of variability from the adjustable slope appears to finetune the Activation clusters in a homeostatic manner. Four Activation clusters and three Activation Function modes are distinguishable.
+
+![](images/1f531c91ae66605d5e3d2e5aa236b73d669991611c0624393cda687eeaafcc9e.jpg)  
+Advanced-LSTM (tanhshrink τ1)
+
+![](images/1eac2efc6843f2a4c4427f87031f2800cde860bc50d55297d518044bb09f0c51.jpg)
+
+In this node, the Activation clusters produced by the Ingate appear to be rather undefined. This approach may be interpretable as explorative, since the two dimensional space is being examined,but this comes at the cost of having poorly-defined boundaries.
+
+The boundaries of the input-output relationship are well-defined since the Activation clusters are denser.Due to the potential for negative slopes, this node has learned an input-modulator interaction that produces only negative outputs,akin to an inhibitory neuron
+
+We can observe from the results in Table 4 that, the mean test performance of both modulated LSTMs outperformed all three control groups and achieved the highest validation performance. Statistical significance varied between the two LSTM models. In the Vanilla-LSTM $\left( \mathbf { n } = 3 0 \right)$ ), with $\tau _ { l } ( \cdot )$ set to sigmoid, statistical significance ranged between $\mathbf { p } { < } . 0 6$ (Control 3) and $\mathrm { P } { < } . 0 0 1$ (Control 2). In the Advanced-LSTM $( \mathbf { n } = 1 0 0 )$ ), with $\tau _ { l } ( \cdot )$ set to tanhshrink, statistical significance was a consistently $\mathrm { P } { < } . 0 0 1$ in all conditions. In all cases, variance was lowest in the modulated condition. We further zoom in the activation data-flow and visualized the the effect of our modulation in Table 3.2. The control condition and modulated condition was compared side by side. On the left we can observe the impact of the Ingate on the amplitude of the tanh activation function, on the right we can observe our modulation adjust the slope as well. Each input generates a context dependent activation as shown in continuous lines and specific activations are represented by the blue dots which corresponded to a point on a specific line. Our modulation modification provides new aptitudes for the model to learn, generalize and appears to add a stabilizing feature to the dynamic input-output relationship.
+
+# 4 CONCLUSION
+
+We propose a modulation mechanism addition to traditional ANNs so that the shape of the activation function can be context dependent. Experimental results show that the modulated models consistently outperform their original versions. Our experiment also implied adding modulator can reduce overfitting. We demonstrated even with fewer parameters, the modulated model can still perform on par with it vanilla version of a bigger size. This modulation idea can also be expanded to other setting, such as, different modulator activation or different structure inside the modulator.
+
+# 5 DISCUSSION
+
+It was frequently observed in preliminary testing that arbitrarily increasing model parameters actually hurt network performance, so future studies will be aimed at investigating the relationship between the number of model parameters and the performance of the network. Additionally, it will be important to determine the interaction between specific network implementations and the ideal Activation Function wrapping for slope-determining neurons. Lastly, it may be useful to investigate layer-wide single-node modulation on models with parallel LSTM’s.
+
+Epigenetics refers to the activation and inactivation of genes (Weinhold, 2006), often as a result of environmental factors. These changes in gene-expression result in modifications to the generation and regulation of cellular proteins, such as ion channels, that regulate how the cell controls the flow of current through the cell membrane (Meadows et al., 2016). The modulation of these proteins will strongly influence the tendency of a neuron to fire and hence affect the neurons function as a single computational node. These proteins, in turn, can influence epigenetic expression in the form of dynamic control (Kawasaki et al., 2004).
+
+Regarding the effects of these signals, we can compare the output of neurons and nodes from a variety of perspectives. First and foremost, intrinsic excitability refers to the ease with which a neurons electrical potential can increase, and this feature has been found to impact plasticity itself (Desai et al., 1999). From this view, the output of a node in an artificial neural network would correspond to a neurons firing rate, which Intrinsic Excitability is a large contributor to, and our extra gate would be setting the node’s intrinsic excitability. With the analogy of firing rate, another phenomenon can be considered. Neurons may experience various modes of information integration, typically labeled Type 1 and Type 2. Type 1 refers to continuous firing rate integration, while Type 2 refers to discontinuous information (Tateno et al., 2004). This is computationally explained as a function of interneuron communication resulting in neuron-activity nullclines with either heavy overlap or discontinuous saddle points (Miller, 2016). In biology, a neuron may switch between Type 1 and Type 2 depending on the presence of neuromodulator (Stiefel & Gutkin, 2012). Controlling the degree to which the tanh function encodes to a binary space, our modification may be conceived as determining the form of information integration. The final possible firing rate equivalence refers to the ability of real neurons to switch between different firing modes. While the common mode of firing, Tonic firing, generally encodes information in rate frequency, neurons in a Bursting mode (though there are many types of bursts) tend to encode information in a binary mode - either firing bursts or not (Tateno et al., 2004). Here too, our modification encompasses a biological phenomenon by enabling the switch between binary and continuous information.
+
+Another analogy to an ANN nodes output would be the neurotransmitter released. With this view, our modification is best expressed as an analogy to Activity Dependent Facilitation and Depression, phenomena which cause neurons to release either more or less neurotransmitter. Facilitation and depression occur in response to the same input: past activity (Reyes et al., 1998). Our modification enables a network to use previous activity to determine its current sensitivity to input, allowing for both Facilitation and Depression. On the topic of neurotransmitter release, neuromodulation is the most relevant topic to the previously shown experiments. Once again, Marblestone et al. (2016) explains the situation perfectly, expressing that research (Bargmann, 2012; Bargmann & Marder, 2013) has shown ”the same neuron or circuit can exhibit different input-output responses depending on a global circuit state, as reflected by the concentrations of various neuromodulators”. Relating to our modification, the slope of the activation function may be conceptualized as the mechanism of neuromodulation, with the new gate acting analogously to a source of neuromodulator for all nodes in the network.
+
+Returning to a Machine Learning approach, the ability to adjust the slope of an Activation Function has an immediate benefit in making the back-propagation gradient dynamic. For example, for Activations near 0, where the tanh Function gradient is largest, the effect of our modification on node output is minimal. However, at this point, our modification has the ability to decrease the gradient, perhaps acting as pseudo-learning-rate. On the other hand, at activations near 1 and -1, where the tanh Function gradient reaches 0, our modification causes the gradient to reappear, allowing for information to be extracted from inputs outside of the standard range. Additionally, by implementing a slope that is conditional on node input, the node has the ability to generate a wide range of functional Activation Functions, including asymmetric functions. Lastly, injecting noise has been found to help deep neural networks with noisy datasets (Zheng et al., 2016), which is noteworthy since noise may act as a stabilizer for neuronal firing rates, (Touboul et al., 2012). With this in mind, Table 3.2 demonstrates increased clustering in two-dimensional node-Activation space, when the Activation Function slope is made to be dynamic. This indicates that noise may be a mediator of our modification, improving network performance through stabilization, induced by increasing the variability of the input-output relationship.
+
+In summary, we have shown evidence that nodes in LSTMs and CNNs benefit from added complexity to their input-output dynamic. Specifically, having a node that adjusts the slope of the main layer’s nodes’ activation functions mimics the functionality of neuromodulators and is shown to benefit the network. The exact mechanism by which this modification improves network performance remains unknown, yet it is possible to support this approach from both a neuroscientific and machine-learning perspective. We believe this demonstrates the need for further research into discovering novel non-computationally-demanding methods of applying principles of neuroscience to artificial networks.
+
+# REFERENCES
+
+Forest Agostinelli, Matthew Hoffman, Peter Sadowski, and Pierre Baldi. Learning activation functions to improve deep neural networks. arXiv preprint arXiv:1412.6830, 2014.
+
+Srdjan D Antic, Wen-Liang Zhou, Anna R Moore, Shaina M Short, and Katerina D Ikonomu. The decade of the dendritic nmda spike. Journal of neuroscience research, 88(14):2991–3001, 2010.
+
+Cornelia I Bargmann. Beyond the connectome: how neuromodulators shape neural circuits. Bioessays, 34(6):458–465, 2012.
+
+Cornelia I Bargmann and Eve Marder. From the connectome to brain function. Nature methods, 10 (6):483, 2013.
+
+Chyi-Tsong Chen and Wei-Der Chang. A feedforward neural network with function shape autotuning. Neural networks, 9(4):627–641, 1996.
+
+Patricia S Churchland and Terrence J Sejnowski. Perspectives on cognitive neuroscience. Science, 242(4879):741–745, 1988.
+
+Yann N Dauphin, Angela Fan, Michael Auli, and David Grangier. Language modeling with gated convolutional networks. arXiv preprint arXiv:1612.08083, 2016.
+
+Niraj S Desai, Lana C Rutherford, and Gina G Turrigiano. Plasticity in the intrinsic excitability of cortical pyramidal neurons. Nature neuroscience, 2(6):515, 1999.
+
+Jeffrey L Elman. Finding structure in time. Cognitive science, 14(2):179–211, 1990.
+
+Su Lee Goh and Danilo P Mandic. Recurrent neural networks with trainable amplitude of activation functions. Neural Networks, 16(8):1095–1100, 2003.
+
+Demis Hassabis, Dharshan Kumaran, Christopher Summerfield, and Matthew Botvinick. Neuroscience-inspired artificial intelligence. Neuron, 95(2):245–258, 2017.
+
+Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Delving deep into rectifiers: Surpassing human-level performance on imagenet classification. In Proceedings of the IEEE international conference on computer vision, pp. 1026–1034, 2015.
+
+Donald O Hebb. The organization of behavior: A neurophysiological approach, 1949.
+
+Geoffrey E Hinton, James L McClelland, David E Rumelhart, et al. Distributed representations. Carnegie-Mellon University Pittsburgh, PA, 1984.
+
+Sepp Hochreiter and Jurgen Schmidhuber. Long short-term memory. ¨ Neural computation, 9(8): 1735–1780, 1997.
+
+John J Hopfield. Neural networks and physical systems with emergent collective computational abilities. Proceedings of the national academy of sciences, 79(8):2554–2558, 1982.
+
+John J Hopfield and David W Tank. Computing with neural circuits: A model. Science, 233(4764): 625–633, 1986.
+
+Forrest Iandola, Matt Moskewicz, Sergey Karayev, Ross Girshick, Trevor Darrell, and Kurt Keutzer. Densenet: Implementing efficient convnet descriptor pyramids. arXiv preprint arXiv:1404.1869, 2014.
+
+Michael I Jordan. Serial order: A parallel distributed processing approach. In Advances in psychology, volume 121, pp. 471–495. Elsevier, 1997.
+
+Barry L Kalman and Stan C Kwasny. Why tanh: choosing a sigmoidal function. In Neural Networks, 1992. IJCNN., International Joint Conference on, volume 4, pp. 578–581. IEEE, 1992.
+
+Yasuhiko Kawasaki, Tatsuro Kohno, Zhi-Ye Zhuang, Gary J Brenner, Haibin Wang, Catrien Van Der Meer, Katia Befort, Clifford J Woolf, and Ru-Rong Ji. Ionotropic and metabotropic receptors, protein kinase a, protein kinase c, and src contribute to c-fiber-induced erk activation and camp response element-binding protein phosphorylation in dorsal horn neurons, leading to central sensitization. Journal of Neuroscience, 24(38):8310–8321, 2004.
+
+Diederik P Kingma and Jimmy Ba. Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980, 2014.
+
+Alex Krizhevsky and Geoffrey Hinton. Learning multiple layers of features from tiny images. Technical report, Citeseer, 2009.
+
+Hugo Larochelle and Geoffrey E Hinton. Learning to combine foveal glimpses with a third-order boltzmann machine. In Advances in neural information processing systems, pp. 1243–1251, 2010.
+
+Yann LeCun, Leon Bottou, Yoshua Bengio, and Patrick Haffner. Gradient-based learning applied to ´ document recognition. Proceedings of the IEEE, 86(11):2278–2324, 1998.
+
+Adam H Marblestone, Greg Wayne, and Konrad P Kording. Toward an integration of deep learning and neuroscience. Frontiers in computational neuroscience, 10:94, 2016.
+
+Mitchell P Marcus, Mary Ann Marcinkiewicz, and Beatrice Santorini. Building a large annotated corpus of english: The penn treebank. Computational linguistics, 19(2):313–330, 1993.
+
+Eve Marder, LF Abbott, Gina G Turrigiano, Zheng Liu, and Jorge Golowasch. Memory from the dynamics of intrinsic membrane currents. Proceedings of the national academy of sciences, 93 (24):13481–13486, 1996.
+
+Warren S McCulloch and Walter Pitts. A logical calculus of the ideas immanent in nervous activity. The bulletin of mathematical biophysics, 5(4):115–133, 1943.
+
+Jarrod P Meadows, Mikael C Guzman-Karlsson, Scott Phillips, Jordan A Brown, Sarah K Strange, J David Sweatt, and John J Hablitz. Dynamic dna methylation regulates neuronal intrinsic membrane excitability. Sci. Signal., 9(442):ra83–ra83, 2016.
+
+Stephen Merity, Nitish Shirish Keskar, and Richard Socher. Regularizing and Optimizing LSTM Language Models. arXiv preprint arXiv:1708.02182, 2017.
+
+Stephen Merity, Nitish Shirish Keskar, and Richard Socher. An Analysis of Neural Language Modeling at Multiple Scales. arXiv preprint arXiv:1803.08240, 2018.
+
+Toma´s Mikolov, Martin Karafi ˇ at, Luk ´ a´s Burget, Jan ˇ Cernock ˇ y, and Sanjeev Khudanpur. Recurrent \` neural network based language model. In Eleventh Annual Conference of the International Speech Communication Association, 2010.
+
+Paul Miller. Dynamical systems, attractors, and neural circuits. F1000Research, 5, 2016.
+
+Volodymyr Mnih, Nicolas Heess, Alex Graves, et al. Recurrent models of visual attention. In Advances in neural information processing systems, pp. 2204–2212, 2014.
+
+Vinod Nair and Geoffrey E Hinton. Rectified linear units improve restricted boltzmann machines. In Proceedings of the 27th international conference on machine learning (ICML-10), pp. 807–814, 2010.
+
+Alex Reyes, Rafael Lujan, Andrej Rozov, Nail Burnashev, Peter Somogyi, and Bert Sakmann. Target-cell-specific facilitation and depression in neocortical circuits. Nature neuroscience, 1 (4):279, 1998.
+
+Leonie Ringrose and Renato Paro. Epigenetic regulation of cellular memory by the polycomb and trithorax group proteins. Annu. Rev. Genet., 38:413–443, 2004.
+
+Robertson Sean. Names dataset. https://github.com/spro/practical-pytorch/ tree/master/data/names, 2016.
+
+S Murray Sherman. Tonic and burst firing: dual modes of thalamocortical relay. Trends in neurosciences, 24(2):122–126, 2001.
+
+Richard Socher, Alex Perelygin, Jean Wu, Jason Chuang, Christopher D Manning, Andrew $\mathrm { N g }$ , and Christopher Potts. Recursive deep models for semantic compositionality over a sentiment treebank. In Proceedings of the 2013 conference on empirical methods in natural language processing, pp. 1631–1642, 2013.
+
+Mirko Solazzi and Aurelio Uncini. Artificial neural networks with adaptive multidimensional spline activation functions. In Neural Networks, 2000. IJCNN 2000, Proceedings of the IEEE-INNSENNS International Joint Conference on, volume 3, pp. 471–476. IEEE, 2000.
+
+Klaus M Stiefel and Boris S Gutkin. Cholinergic neuromodulation controls prc type in cortical pyramidal neurons. In Phase response curves in neuroscience, pp. 279–305. Springer, 2012.
+
+T Tateno, A Harsch, and HPC Robinson. Threshold firing frequency–current relationships of neurons in rat somatosensory cortex: type 1 and type 2 dynamics. Journal of neurophysiology, 92(4): 2283–2294, 2004.
+
+Jonathan Touboul, Geoffroy Hermann, and Olivier Faugeras. Noise-induced behaviors in neural mean field dynamics. SIAM Journal on Applied Dynamical Systems, 11(1):49–81, 2012.
+
+A. M. Turing. I.computing machinery and intelligence. Mind, LIX(236):433460, 1950. doi: 10. 1093/mind/lix.236.433.
+
+Lawrence M Ward. Synchronous neural oscillations and cognitive processes. Trends in cognitive sciences, 7(12):553–559, 2003.
+
+Bob Weinhold. Epigenetics: the science of change. Environmental health perspectives, 114(3): A160, 2006.
+
+Stephan Zheng, Yang Song, Thomas Leung, and Ian Goodfellow. Improving the robustness of deep neural networks via stability training. In Proceedings of the ieee conference on computer vision and pattern recognition, pp. 4480–4488, 2016.
+
+# 6 APPENDIX
+
+# 6.1 SUPPLEMENTARY DATA METHODOLOGY
+
+Additionally we tested our modulator gate, with $\tau _ { l } ( \cdot )$ set to sigmoid, on a much more computationally demanding three-layered LSTM network with weight drop method named awd-lstm-lm (Merity et al., 2017; 2018). This model was equipped to handle the Penn-Treebank dataset (Marcus et al., 1993) and was trained to minimize word perplexity. The network was trained for 500 epochs, however, the sample size was limited due to extremely long training times.
+
+Table 6: Network parameters per cell   
+
+<table><tr><td>Model</td><td>Modulated</td><td>Control</td></tr><tr><td></td><td></td><td></td></tr><tr><td>awd-lstm-lm</td><td>6.61 M</td><td>5.29 M</td></tr></table>
+
+# 6.2 SUPPLEMENTARY DATA RESULTS
+
+On the Penn-Treebank dataset with the awd-lstm-lm implementation, sample size was restricted to 2 per condition, due to long training times and limited resources. However on the data collected, our model outperformed template perplexity, achieving an average of 58.4730 compared to the template average 58.7115. Due to the lack of a control for model parameters, interpretation of these results rests on the assumption that the author fine-tuned network parameters such that the template parameters maximized performance.
+
+# 7 SUPPLEMENTARY DATA FIGURES & TABLES
+
+# 7.1 AWD-LSTM-LM ON PENN-TREEBANK
+
+Table 7: Comparison of mean test Perplexities lower $=$ better   
+
+<table><tr><td>Model</td><td>Epochs</td><td>Modulated</td><td>Control</td><td>Statistical Analysis</td></tr><tr><td></td><td></td><td></td><td></td><td>T: 1.842</td></tr><tr><td rowspan="3">awd-lstm-lm on Penn-Treebank</td><td>500</td><td>58.4730</td><td>58.7115</td><td>DOF: 1.9</td></tr><tr><td></td><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td><td>Hedges&#x27;s G:1.853</td></tr></table>
+
+![](images/a3b3373fc615d43ca4c37975c1996f570d182eb7e80e00687a999c483d972ed1.jpg)  
+Figure 7: Validation Perplexity progress (lowe $r = b _ { \mathrm { { \ell } } }$ etter)
+
+# 7.2 SUPPLEMENTAL LSTM DATA
+
+Table 8: LSTM test performance histograms illustrating improved test-retest reliability
+
+<table><tr><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>Simple- LSTM(Names categorization)</td><td rowspan=1 colspan=1> Advanced- LSTM(SST2)</td></tr><tr><td rowspan=1 colspan=1>Modulated</td><td rowspan=1 colspan=1>Prenbegg0.76 0.77 0.78 0.79Accuracy</td><td rowspan=3 colspan=1>14irenbeg120.60 0.650.700.750.80Accuracy14Pirenbeng1210 0.600.650.700.750.8Accuracy14 Prranbeg30.600.650.700.750.8Accuracy</td></tr><tr><td rowspan=1 colspan=1>Control 1</td><td rowspan=1 colspan=1>Pirenbee0.76 0.77 0.78 0.79Accuracy</td></tr><tr><td rowspan=1 colspan=1>Control 2</td><td rowspan=1 colspan=1>Pireneeng. 0.77 0.78 0.79Accuracy</td></tr><tr><td rowspan=1 colspan=1>Control 3</td><td rowspan=1 colspan=1>Prenbeng0.76 0.77 0.78 0.79Accuracy</td><td rowspan=1 colspan=1>14rrenbeng1210 0.600.650.700.750.80Accuracy</td></tr></table>

parse/train/rylWVnR5YQ/rylWVnR5YQ_content_list.json

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+[
+    {
+        "type": "text",
+        "text": "CONTEXT DEPENDENT MODULATION OF ACTIVATIONFUNCTION",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Anonymous authors Paper under double-blind review ",
+        "bbox": [
+            183,
+            195,
+            398,
+            223
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "ABSTRACT ",
+        "text_level": 1,
+        "bbox": [
+            454,
+            260,
+            544,
+            275
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "We propose a modification to traditional Artificial Neural Networks (ANNs), which provides the ANNs with new aptitudes motivated by biological neurons. Biological neurons work far beyond linearly summing up synaptic inputs and then transforming the integrated information. A biological neuron change firing modes accordingly to peripheral factors (e.g., neuromodulators) as well as intrinsic ones. Our modification connects a new type of ANN nodes, which mimic the function of biological neuromodulators and are termed modulators, to enable other traditional ANN nodes to adjust their activation sensitivities in run-time based on their input patterns. In this manner, we enable the slope of the activation function to be context dependent. This modification produces statistically significant improvements in comparison with traditional ANN nodes in the context of Convolutional Neural Networks and Long Short-Term Memory networks. ",
+        "bbox": [
+            233,
+            290,
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+            457
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            483,
+            336,
+            498
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Artificial neural networks (ANNs), such as convolutional neural networks (CNNs) (LeCun et al., 1998) and long short-term memory (LSTM) cells (Hochreiter & Schmidhuber, 1997), have incredible capabilities and are applied in a variety of applications including computer vision, natural language analysis, and speech recognition among others. Historically, the development of ANNs (e.g., network architectures and learning algorithms) has benefited significantly from collaborations with Psych-Neuro communities (Churchland & Sejnowski, 1988; Hebb, 1949; Hinton et al., 1984; Hopfield, 1982; McCulloch & Pitts, 1943; Turing, 1950; Hassabis et al., 2017; Elman, 1990; Hopfield & Tank, 1986; Jordan, 1997; Hassabis et al., 2017). The information processing capabilities of traditional ANN nodes are rather rigid when compared to the plasticity of real neurons. A typical traditional ANN node linearly integrate its input signals and run the integration through a transformation called an activation function, which simply takes in a scalar value and outputs another. Of the most popular Activation Functions are sigmoid (Mikolov et al., 2010), tanh (Kalman & Kwasny, 1992) and ReLU (Nair & Hinton, 2010). ",
+        "bbox": [
+            174,
+            513,
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+            694
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Researchers have shown that it could be beneficial to deploy layer-/node- specific activation functions in a deep ANN (Chen & Chang, 1996; Solazzi & Uncini, 2000; Goh & Mandic, 2003; He et al., 2015; Agostinelli et al., 2014). However, each ANN node is traditionally stuck with a fixed activation function once trained. Therefore, the same input integration will always produce the same output. This fails to replicate the amazing capability of individual biological neurons to conduct complex nonlinear mappings from inputs to outputs (Antic et al., 2010; Hassabis et al., 2017; Marblestone et al., 2016). In this study, we propose one new modification to ANN architectures by adding a new type of node, termed modulators, to modulate the activation sensitivity of the ANN nodes targeted by modulators (see Figures 1-3 for examples). In one possible setting, a modulator and its target ANN nodes share the same inputs. The modulator maps the input into a modulation signal, which is fed into each target node. Each target node multiples its input integration by the modulator signal prior to transformation by its traditional activation function. Examples of neuronal principles that may be captured by our new modification include intrinsic excitability, diverse firing modes, type 1 and type 2 forms of firing rate integration, activity dependent facilitation and depression and, most notably, neuromodulation (Marder et al., 1996; Sherman, 2001; Ward, 2003; Ringrose & Paro, 2004). ",
+        "bbox": [
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+            702,
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Our modulator is relevant to the attention mechanism (Larochelle & Hinton, 2010; Mnih et al., 2014), which dynamically restricts information pathways and has been found to be very useful in practice. Attention mechanisms apply the attention weights, which are calculated in run-time, to the outputs of ANN nodes or LSTM cells. Notably, the gating mechanism in a Simple LSTM cell can also be viewed as a dynamical information modifier. A gate takes the input of the LSTM cell and outputs gating signals for filtering the outputs of its target ANN nodes in the same LSTM cell. A similar gating mechanism was proposed in the Gated Linear Unit (Dauphin et al., 2016) for CNNs. Different from the attention and gating mechanisms, which are applied to the outputs of the target nodes, our modulation mechanism adjusts the sensitivities of the target ANN nodes in run-time by changing the slopes of the corresponding activation functions. Hence, the modulator can also be used as a complement to the attention and gate mechanisms. ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Below we will explain our modulator mechanism in detail. Experimentation shows that the modulation mechanism can help achieve better test stability and higher test performance using easy to implement and significantly simpler models. Finally, we conclude the paper with discussions on the relevance to the properties of actual neurons. ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2 METHODS ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            339,
+            290,
+            356
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "We designed two modulation mechanisms, one for CNNs and the other for LSTMs. In modulating CNNs, our modulator (see Figure 1) is a layer-specific one that is best compared to the biological phenomenon of neuromodulation. Each CNN layer before activation has one modulator, which shares the input $\\vec { x }$ with other CNN nodes in the same layer (Figure 1Left). The modulator (Figure 1Right) of the ${ { l } ^ { t h } }$ CNN layer calculates a scalar modulation signal as $s _ { l } = \\tau _ { l } ( \\vec { w } _ { l } ^ { T } \\vec { x } )$ , where $\\tau _ { l } ( \\cdot )$ is the activation function of the ${ { l } ^ { t h } }$ modulator, and feeds $s _ { l }$ to every other CNN node in the same layer. The $k ^ { t h }$ modulated CNN node in the $l ^ { t h }$ layer linearly integrates its inputs as a traditional ANN nodes $v _ { l , k } = \\vec { w } _ { l , k } ^ { T } \\vec { x }$ and modulates the integration to get $u _ { l , k } = s _ { l } \\cdot v _ { l , k }$ prior to its traditional activation step $\\varphi _ { l , k } ( \\cdot )$ . The final output is $o _ { l , k } = \\varphi _ { l , k } \\big ( \\tau _ { l } \\big ( \\vec { w } _ { l } ^ { T } \\vec { x } \\big ) \\cdot \\vec { w } _ { l , k } ^ { T } \\vec { x } \\big )$ . The above modulation mechanism is slightly modified to expand Densely Connected CNNs (Iandola et al., 2014)(see Figure 2). A modulator is added to each dense block layer to modulate the outputs of its convolution nodes. Given a specific input, the modulator outputs a scalar modulation signal that is multiplied to the scalar outputs of the target convolution nodes in the same layer. ",
+        "bbox": [
+            174,
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In addition to the Cellgate, there are three modifying gates (Forget, Input, and Output) in a traditional LSTM cell. Each gate is a full layer of ANN nodes. Each of ANN node in a gate uses sigmoid to transform the integration of the input into regulation signals. The traditional LSTM cell transforms the input integration to an intermediate output (i.e., $\\tilde { C } _ { t }$ in Figure 3). The Forget gate regulates what is removed from the old cell state (i.e., $t - 1$ in Figure 3), and the Input gate what in $\\tilde { C } _ { t }$ is added to obtain the new cell state (i.e., $_ t )$ . The new cell state is transformed and then regulated by the output gate to become part of the input of the next time point. In modulating LSTM (see Figure 3), for the purpose of easier implementation, we create a new ”modulation gate” (the round dash rectangle in Figure 3) for node-specific sensitivity-adjustment which is most analogous to neuronal facilitation and depression. Different from a conventional LSTM that calculates $\\tilde { C } _ { t } ~ = ~ \\varphi ( W _ { c } [ \\vec { x } _ { t } , \\vec { h } _ { t - 1 } ] )$ , a modulated LSTM calculates $\\tilde { C } _ { t } = \\varphi ( \\tau ( W _ { M } [ \\vec { x } _ { t } , \\vec { h } _ { t - 1 } ] ) \\cdot ( W _ { c } [ \\vec { x } _ { t } , \\vec { h } _ { t - 1 } ] ) )$ . ",
+        "bbox": [
+            174,
+            564,
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In the above designs, both a multi-layer CNN and single-layer LSTM had multiple modulator nodes within each model. A generalization to the above designs is to allow a modulator to take the outputs from other CNN layers or those of the LSTM cell at other time points as the inputs. ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "image",
+        "img_path": "images/c5c160d685633168dd2635293a5acbfdb7626255f33b162ce5d04a56e73223d9.jpg",
+        "image_caption": [
+            "Figure 1: Modulator expansion to CNN. Left: Each CNN layer before activation layer has a modulator, whose input $\\vec { x }$ is the same to that of other CNN nodes in the same layer. Right: The modulator maps the input into a scalar modulation signal, which is fed to every other CNN node in the same layer. Every modulated node multiples the integration of its inputs by the modulation signal prior to traditional activation. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/b984fc11468aabad40e054698845a113db29818d4254c47f352299cfa6a51783.jpg",
+        "image_caption": [
+            "Figure 2: Modulator expansion to a dense block in a DenseNet. Left: A dense block example that contains two dense block layers. Right: A dense block layer transforms its input element-wisely before convolution. Hence, the modulation applied to the previous dense block layer affects the transformation activity of the next dense block layer. Modulation is applied to the output of each node in the target convolution layer. We ignore other steps (e.g, batch normalization and drop-out) in a dense block layer for visualization purpose. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            217,
+            342,
+            802,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/37043457478b59922e080e7107e2727a9d8066360814232945774db4a645b73b.jpg",
+        "image_caption": [
+            "Figure 3: Modulator expansion to a Simple LSTM cell. A Simple LSTM cell wraps the Input Integration and Activation steps in the orange box into one node. Our modification adds a modulator (the green box) that maps $[ \\vec { x _ { t } } , \\vec { h } _ { t - 1 } ]$ , i.e., the concatenation of the input at time $t$ and the LSTM output at time $t - 1$ , into modulation signals that are used to adjust the sensitivity of transforming the integration of $[ \\vec { x } _ { t } , \\vec { h } _ { t - 1 } ]$ . "
+        ],
+        "image_footnote": [],
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+    },
+    {
+        "type": "text",
+        "text": "3 EXPERIMENTAL RESULTS ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.1 MODULATED CNNS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            133,
+            354,
+            148
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In our experiments with CNNs, the activation functions of the traditional CNN nodes was ReLU, with our modulator nodes using a sigmoid. We tested six total settings: a vanilla CNN vs a modulated vanilla CNN, a vanilla DenseNet vs a modulated DenseNet, and a vanilla DenseNet-lite vs a modulated DenseNet-lite. The vanilla CNN has 2 convolution blocks, each of which contains two sequential convolution layers, a pooling layer, and a dropout layer. A fully connected layer of 512 nodes is appended at the very end of the model. The convolution layers in the first block have 32 filters with a size of 3x3 while the convolution layers in the second block have 64 filters with a size of 3x3. We apply a dropout of 0.25 to each block. The vanilla DenseNet used the structure (40 in depth and 12 in growth-rate) reported in the original DenseNet paper (Iandola et al., 2014) and a dropout of 0.5 is used in our experiment. The vanilla DenseNet-lite has a similar structure to the vanilla DenseNet, however, uses a smaller growth-rate of 10 instead of 12 in the original configuration, which results in $28 \\%$ fewer parameters. The modulators are added to the vanilla CNN, the vanilla DenseNet, and the vanilla DenseNet-lite in the way described in Figures 1 and 2 to obtain their modulated versions, respectively. Table 1 summarizes the numbers of the parameters in the above models to indicate their complexities. The modulated networks have slightly more parameters than their vanilla versions do. All the experiments were run for 150 epochs on 4 NVIDIA Titan $\\mathrm { X p }$ GPUs with a mini-batch size of 128. ",
+        "bbox": [
+            174,
+            160,
+            825,
+            395
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "table",
+        "img_path": "images/349813aee792a401a03a71a540c1a74d6f4b8c5effddb974fca2b00735169c9a.jpg",
+        "table_caption": [
+            "Table 1: Compare the numbers of parameters in the CNNs. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>Total parameters</td></tr><tr><td>vanilla CNN</td><td></td></tr><tr><td>modulated CNN</td><td>1.25M 1.25 M</td></tr><tr><td>vanilla DenseNet</td><td>1.00 M</td></tr><tr><td>modulated DenseNet</td><td>1.07 M</td></tr><tr><td>vanilla DenseNet-lite</td><td>0.71M</td></tr><tr><td>modulatedDenseNet-lite</td><td>0.77 M</td></tr></table>",
+        "bbox": [
+            334,
+            439,
+            660,
+            554
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "CIFAR-10 dataset (Krizhevsky & Hinton, 2009) was used in this experiment. CIFAR-10 consists of colored images at a resolution of $3 2 \\mathrm { x } 3 2 $ pixels. The training and test set are containing 50000 and 10000 images respectively. We held $20 \\%$ of the training data for validation and applied data augmentation of shifting and mirroring on the training data. All the CNN models are trained using the Adam (Kingma & Ba, 2014) optimization method with a learning rate of 1e-3 and shrinks by a factor of 10 at $50 \\%$ and $80 \\%$ of the training progress. ",
+        "bbox": [
+            173,
+            574,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "As shown in Figure 4, the vanilla CNN model begins to overfit after 80 training epochs. Although the modulated CNN model is slightly more complex, it is less prone to overfitting and excels its vanilla counterpart by a large margin (see Table 2). Modulation also significantly helps DenseNets in training, validation, and test. The modulated DenseNet/DenseNet-lite models consistently outperform their vanilla counterparts by a noticeable margin (see Figures 5(a) and 5(b)) during training. The validation and test results of the modulated DenseNet/DenseNet-lite models are also better than those of their vanilla counterparts. It is not surprising that the vanilla DenseNet-lite model underperforms the vanilla DenseNet model. Interestingly, despite having $28 \\%$ fewer parameters than the vanilla DenseNet model, the modulated DenseNet-lite model outperforms the vanilla DenseNet model (see the dash orange curve vs the solid blue curve in Figure 5(b) and Table 2). ",
+        "bbox": [
+            174,
+            665,
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+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/979c87cb2f3f0b3a1b3068b4bfd1be3c0d7bbe08a776b1d76f191d2c7fd63fd1.jpg",
+        "image_caption": [
+            "Figure 4: Modulation increases the robustness of CNNs. The $\\mathbf { X }$ -axis is the validation epoch, and the y-axis is the top-1 accuracy. The vanilla CNN begins to show sign of overfitting after 80 epochs, while the modulated CNN keeps improving. "
+        ],
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+    {
+        "type": "text",
+        "text": "(a) Comparison of the training results of vanilla DenseNet, moduldate DenseNet, vanilla DenseNet-lite, and modulate DenseNet-lite. The $\\mathbf { X }$ -axis is the training epoch, and the y-axis is the top-1 accuracy. ",
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+        "image_caption": [
+            "(b) Comparison of the validation results of vanilla DenseNet, modulate DenseNet, vanilla DenseNet-lite, and modulate DenseNet-lite. The $\\mathbf { X }$ -axis is the validation epoch, and the y-axis is the top-1 accuracy. "
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "Figure 5: Modulation improves the performance of DenseNets. Both training and validation results show that the modulated versions perform better than their vanilla versions. In addition, modulated DenseNet-lite clearly outperforms vanilla DenseNet even though the former has $28 \\%$ less parameters than the latter. ",
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+    {
+        "type": "table",
+        "img_path": "images/5481f9374ea8c5e56517e6a6cf504212fd84632ed1fb34236f49d5cfd19a173e.jpg",
+        "table_caption": [
+            "Table 2: Test results (top-1 classification accuracy) of vanilla and modulated CNNs. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>Training</td><td>Validation</td><td>Test</td></tr><tr><td></td><td></td><td></td><td></td></tr><tr><td>vanilla CNN</td><td>0.649</td><td>0.694</td><td>0.690</td></tr><tr><td>modulated CNN</td><td>0.775</td><td>0.782</td><td>0.782</td></tr><tr><td>vanilla DenseNet</td><td>0.889</td><td>0.888</td><td>0.889</td></tr><tr><td>modulatedDenseNet</td><td>0.905</td><td>0.902</td><td>0.902</td></tr><tr><td>vanilla DenseNet-lite</td><td>0.881</td><td>0.885</td><td>0.885</td></tr><tr><td>modulatedDenseNet-lite</td><td>0.894</td><td>0.893</td><td>0.894</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "3.2 MODULATED LSTM ",
+        "text_level": 1,
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+        "text": "Two datasets were used in the LSTM experiments. The first one is the NAMES dataset (Sean, 2016), in which the goal is to take a name as a string and classify its ethnicity or country of origin. Approximately $10 \\%$ of the data-set was reserved for testing. The second experiment used the SST2 data-set (Socher et al., 2013), which requires a trained model to classify whether a movie review is positive or negative based on the raw text in the review. The SST2 is identical to the SST1 with the exception of the neutral category removed (Socher et al., 2013), leaving only positive and negative reviews. About $20 \\%$ of the data-set was reserved for testing. ",
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+        "type": "text",
+        "text": "Since modulators noticeably increase the parameters in a modulated LSTM, to perform fair comparisons, we create three versions of vanilla LSTMs (see Controls 1, 2, & 3 in Figure 6). Control 1 has an identical total LSTM cell size. Control 2 has the identical number of nodes per layer. Control 3 has an extra Input gate so that it has both an identical total number of nodes and identical nodes per layer. The numbers of parameters in the modulated LSTM and control LSTMs are listed in Table 3 for comparison. ",
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+        "img_path": "images/d442f3647890830ca9aa78beeb8caf14b332eab9759ecf37d412295c66ce6703.jpg",
+        "image_caption": [
+            "Figure 6: The configurations of the modulated LSTM and three control versions of the vanilla LSTMs. "
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+        "text": "Modulated condition has $5 \\mathrm { N }$ total LSTM nodes,N nodes per gate& N linear layer nodes (hidden_dim $= \\mathbf { N } ]$ Control1 has $5 \\mathrm { N }$ totalLSTM nodes, $5 / 4 \\mathrm { N }$ per (standard LSTM) gate& 5/4Nlinear nodes (hidden_dim $= 5 / 4 \\mathrm { N }$ Control 2 has $4 \\mathrm { N }$ totalLSTM nodes,Nper (standardLSTM) gate&Nlinear nodes (hidden_dim $\\mathbf { \\tau } = \\mathbf { N } .$ ） Control 3 has $5 \\mathrm { N }$ total LSTM nodes,N per(with extra Ingate) gate &N linear nodes (hidden_dim $\\mathbf { \\tau } = \\mathbf { N }$ ",
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+        "type": "text",
+        "text": "The hyper-parameters for the first experiment were set as following: the hidden dimension was set to 32, batch size to 32, embedding dimension to 128, initial learning rate to .01, learning rate decay to 1e-4, an SGD optimizer was used, with dropout of 0.2 applied to the last hidden state of the LSTM and 100 epochs were collected. This condition was tested on the name categorization data-set. The number of parameters in this model ranged from $4 . 1 \\ \\mathrm { K }$ to $6 . 4 ~ \\mathrm { K }$ , depending on the condition. We repeated the experimental runs 30 times. Based on the simplicity of the data-set and the relative sparsity of parameters, this condition will be referred to as Simple-LSTM. As for the second experiment: the hidden dimension was set to 150, he batch size was set to 5, the embedding dimension was set to 300, the initial learning rate was set to 1e-3, there was no learning rate decay, an Adam optimizer was used with no dropout and 100 epochs were collected. The number of parameters in this model ranged from $5 7 . 6 \\mathrm { ~ K ~ }$ to $9 0 ~ \\mathrm { K }$ , depending on the control setup. This experiment was repeated 100 times. Based on the complexity of the data-set and the relatively large amount of parameters, this condition will be referred to as Advanced-LSTM. In all experiments, the models were trained for 100 epochs. ",
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+    {
+        "type": "table",
+        "img_path": "images/747f962a7121ce9a3abd06e0e56e21e9e17403e95f687edb3cb42f2731246e8e.jpg",
+        "table_caption": [
+            "Table 3: The number of parameters in a LSTM cell. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Base Model</td><td>Modulated</td><td>Control 1</td><td>Control 2</td><td>Control 3</td></tr><tr><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Simple-LSTM</td><td>5.1K</td><td>6.4K</td><td>4.1 K</td><td>5.1K</td></tr><tr><td>Advanced-LSTM</td><td>72K</td><td>90K</td><td>57.6K</td><td>72K</td></tr></table>",
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+        "type": "table",
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+        "table_caption": [
+            "Table 4: Modulation Performance Tests on LSTM ",
+            "Table 5: LSTM node Activation function visualizations "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model Dataset</td><td>Modulator Activation</td><td>Performance Statistics</td><td>Modulated</td><td>Control 1</td><td>Control 2</td><td>Control 3</td></tr><tr><td rowspan=\"4\">Simple-LSTM NAMES</td><td rowspan=\"4\">Sigmoid</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>mean</td><td>0.77898</td><td>0.77490</td><td>0.77516</td><td>0.77602</td></tr><tr><td>std</td><td>0.00526</td><td>0.00565 0.74778</td><td>0.00531</td><td>0.00650</td></tr><tr><td>Hedge&#x27;s G p-value</td><td>1</td><td>p&lt;.006</td><td>0.72173 p&lt;.007</td><td>0.49924 p&lt;.06</td></tr><tr><td rowspan=\"5\">Advanced-LSTM SST2</td><td rowspan=\"5\">Tanhshrink</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>mean</td><td>0.77482</td><td>0.73629</td><td>0.74327</td><td>0.73628</td></tr><tr><td>std</td><td>0.01150</td><td>0.04855</td><td>0.04687</td><td>0.04701</td></tr><tr><td>Hedge&#x27;s G</td><td>1</td><td>1.09182</td><td>0.92435</td><td>1.12593</td></tr><tr><td>p-value</td><td></td><td>p&lt;.001</td><td>p&lt;.001</td><td>p&lt;.001</td></tr></table>",
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+        "img_path": "images/f47bd4f498d318f62a2008330bc634096126d73a31d334867935dab7d6588ad3.jpg",
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+            "Simple-LSTM (sigmoid t1) "
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+    {
+        "type": "text",
+        "text": "In this node, the Ingate produces diverse clusters of potential outputs fora given input.However,specific input-output relationships seem somewhat poorly defined, illustrated by the low density of the clusters. ",
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+    {
+        "type": "text",
+        "text": "The added source of variability from the adjustable slope appears to finetune the Activation clusters in a homeostatic manner. Four Activation clusters and three Activation Function modes are distinguishable. ",
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+        "image_caption": [
+            "Advanced-LSTM (tanhshrink τ1) "
+        ],
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+    {
+        "type": "text",
+        "text": "In this node, the Activation clusters produced by the Ingate appear to be rather undefined. This approach may be interpretable as explorative, since the two dimensional space is being examined,but this comes at the cost of having poorly-defined boundaries. ",
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+    {
+        "type": "text",
+        "text": "The boundaries of the input-output relationship are well-defined since the Activation clusters are denser.Due to the potential for negative slopes, this node has learned an input-modulator interaction that produces only negative outputs,akin to an inhibitory neuron ",
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+    {
+        "type": "text",
+        "text": "We can observe from the results in Table 4 that, the mean test performance of both modulated LSTMs outperformed all three control groups and achieved the highest validation performance. Statistical significance varied between the two LSTM models. In the Vanilla-LSTM $\\left( \\mathbf { n } = 3 0 \\right)$ ), with $\\tau _ { l } ( \\cdot )$ set to sigmoid, statistical significance ranged between $\\mathbf { p } { < } . 0 6$ (Control 3) and $\\mathrm { P } { < } . 0 0 1$ (Control 2). In the Advanced-LSTM $( \\mathbf { n } = 1 0 0 )$ ), with $\\tau _ { l } ( \\cdot )$ set to tanhshrink, statistical significance was a consistently $\\mathrm { P } { < } . 0 0 1$ in all conditions. In all cases, variance was lowest in the modulated condition. We further zoom in the activation data-flow and visualized the the effect of our modulation in Table 3.2. The control condition and modulated condition was compared side by side. On the left we can observe the impact of the Ingate on the amplitude of the tanh activation function, on the right we can observe our modulation adjust the slope as well. Each input generates a context dependent activation as shown in continuous lines and specific activations are represented by the blue dots which corresponded to a point on a specific line. Our modulation modification provides new aptitudes for the model to learn, generalize and appears to add a stabilizing feature to the dynamic input-output relationship. ",
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+    {
+        "type": "text",
+        "text": "4 CONCLUSION ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We propose a modulation mechanism addition to traditional ANNs so that the shape of the activation function can be context dependent. Experimental results show that the modulated models consistently outperform their original versions. Our experiment also implied adding modulator can reduce overfitting. We demonstrated even with fewer parameters, the modulated model can still perform on par with it vanilla version of a bigger size. This modulation idea can also be expanded to other setting, such as, different modulator activation or different structure inside the modulator. ",
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+    {
+        "type": "text",
+        "text": "5 DISCUSSION ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "It was frequently observed in preliminary testing that arbitrarily increasing model parameters actually hurt network performance, so future studies will be aimed at investigating the relationship between the number of model parameters and the performance of the network. Additionally, it will be important to determine the interaction between specific network implementations and the ideal Activation Function wrapping for slope-determining neurons. Lastly, it may be useful to investigate layer-wide single-node modulation on models with parallel LSTM’s. ",
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+    {
+        "type": "text",
+        "text": "Epigenetics refers to the activation and inactivation of genes (Weinhold, 2006), often as a result of environmental factors. These changes in gene-expression result in modifications to the generation and regulation of cellular proteins, such as ion channels, that regulate how the cell controls the flow of current through the cell membrane (Meadows et al., 2016). The modulation of these proteins will strongly influence the tendency of a neuron to fire and hence affect the neurons function as a single computational node. These proteins, in turn, can influence epigenetic expression in the form of dynamic control (Kawasaki et al., 2004). ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Regarding the effects of these signals, we can compare the output of neurons and nodes from a variety of perspectives. First and foremost, intrinsic excitability refers to the ease with which a neurons electrical potential can increase, and this feature has been found to impact plasticity itself (Desai et al., 1999). From this view, the output of a node in an artificial neural network would correspond to a neurons firing rate, which Intrinsic Excitability is a large contributor to, and our extra gate would be setting the node’s intrinsic excitability. With the analogy of firing rate, another phenomenon can be considered. Neurons may experience various modes of information integration, typically labeled Type 1 and Type 2. Type 1 refers to continuous firing rate integration, while Type 2 refers to discontinuous information (Tateno et al., 2004). This is computationally explained as a function of interneuron communication resulting in neuron-activity nullclines with either heavy overlap or discontinuous saddle points (Miller, 2016). In biology, a neuron may switch between Type 1 and Type 2 depending on the presence of neuromodulator (Stiefel & Gutkin, 2012). Controlling the degree to which the tanh function encodes to a binary space, our modification may be conceived as determining the form of information integration. The final possible firing rate equivalence refers to the ability of real neurons to switch between different firing modes. While the common mode of firing, Tonic firing, generally encodes information in rate frequency, neurons in a Bursting mode (though there are many types of bursts) tend to encode information in a binary mode - either firing bursts or not (Tateno et al., 2004). Here too, our modification encompasses a biological phenomenon by enabling the switch between binary and continuous information. ",
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+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Another analogy to an ANN nodes output would be the neurotransmitter released. With this view, our modification is best expressed as an analogy to Activity Dependent Facilitation and Depression, phenomena which cause neurons to release either more or less neurotransmitter. Facilitation and depression occur in response to the same input: past activity (Reyes et al., 1998). Our modification enables a network to use previous activity to determine its current sensitivity to input, allowing for both Facilitation and Depression. On the topic of neurotransmitter release, neuromodulation is the most relevant topic to the previously shown experiments. Once again, Marblestone et al. (2016) explains the situation perfectly, expressing that research (Bargmann, 2012; Bargmann & Marder, 2013) has shown ”the same neuron or circuit can exhibit different input-output responses depending on a global circuit state, as reflected by the concentrations of various neuromodulators”. Relating to our modification, the slope of the activation function may be conceptualized as the mechanism of neuromodulation, with the new gate acting analogously to a source of neuromodulator for all nodes in the network. ",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Returning to a Machine Learning approach, the ability to adjust the slope of an Activation Function has an immediate benefit in making the back-propagation gradient dynamic. For example, for Activations near 0, where the tanh Function gradient is largest, the effect of our modification on node output is minimal. However, at this point, our modification has the ability to decrease the gradient, perhaps acting as pseudo-learning-rate. On the other hand, at activations near 1 and -1, where the tanh Function gradient reaches 0, our modification causes the gradient to reappear, allowing for information to be extracted from inputs outside of the standard range. Additionally, by implementing a slope that is conditional on node input, the node has the ability to generate a wide range of functional Activation Functions, including asymmetric functions. Lastly, injecting noise has been found to help deep neural networks with noisy datasets (Zheng et al., 2016), which is noteworthy since noise may act as a stabilizer for neuronal firing rates, (Touboul et al., 2012). With this in mind, Table 3.2 demonstrates increased clustering in two-dimensional node-Activation space, when the Activation Function slope is made to be dynamic. This indicates that noise may be a mediator of our modification, improving network performance through stabilization, induced by increasing the variability of the input-output relationship. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "In summary, we have shown evidence that nodes in LSTMs and CNNs benefit from added complexity to their input-output dynamic. Specifically, having a node that adjusts the slope of the main layer’s nodes’ activation functions mimics the functionality of neuromodulators and is shown to benefit the network. The exact mechanism by which this modification improves network performance remains unknown, yet it is possible to support this approach from both a neuroscientific and machine-learning perspective. We believe this demonstrates the need for further research into discovering novel non-computationally-demanding methods of applying principles of neuroscience to artificial networks. ",
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+    {
+        "type": "text",
+        "text": "REFERENCES ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            674,
+            285,
+            689
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Forest Agostinelli, Matthew Hoffman, Peter Sadowski, and Pierre Baldi. Learning activation functions to improve deep neural networks. arXiv preprint arXiv:1412.6830, 2014. ",
+        "bbox": [
+            174,
+            699,
+            820,
+            727
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Srdjan D Antic, Wen-Liang Zhou, Anna R Moore, Shaina M Short, and Katerina D Ikonomu. The decade of the dendritic nmda spike. Journal of neuroscience research, 88(14):2991–3001, 2010. ",
+        "bbox": [
+            174,
+            737,
+            821,
+            766
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Cornelia I Bargmann. Beyond the connectome: how neuromodulators shape neural circuits. Bioessays, 34(6):458–465, 2012. ",
+        "bbox": [
+            173,
+            776,
+            821,
+            806
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Cornelia I Bargmann and Eve Marder. From the connectome to brain function. Nature methods, 10 (6):483, 2013. ",
+        "bbox": [
+            173,
+            816,
+            825,
+            844
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Chyi-Tsong Chen and Wei-Der Chang. A feedforward neural network with function shape autotuning. Neural networks, 9(4):627–641, 1996. ",
+        "bbox": [
+            173,
+            856,
+            823,
+            885
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Patricia S Churchland and Terrence J Sejnowski. Perspectives on cognitive neuroscience. Science, 242(4879):741–745, 1988. ",
+        "bbox": [
+            173,
+            895,
+            821,
+            922
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Yann N Dauphin, Angela Fan, Michael Auli, and David Grangier. Language modeling with gated convolutional networks. arXiv preprint arXiv:1612.08083, 2016. ",
+        "bbox": [
+            171,
+            103,
+            825,
+            132
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Niraj S Desai, Lana C Rutherford, and Gina G Turrigiano. Plasticity in the intrinsic excitability of cortical pyramidal neurons. Nature neuroscience, 2(6):515, 1999. ",
+        "bbox": [
+            173,
+            140,
+            823,
+            170
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Jeffrey L Elman. Finding structure in time. Cognitive science, 14(2):179–211, 1990. ",
+        "bbox": [
+            173,
+            178,
+            730,
+            194
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Su Lee Goh and Danilo P Mandic. Recurrent neural networks with trainable amplitude of activation functions. Neural Networks, 16(8):1095–1100, 2003. ",
+        "bbox": [
+            173,
+            202,
+            823,
+            231
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Demis Hassabis, Dharshan Kumaran, Christopher Summerfield, and Matthew Botvinick. Neuroscience-inspired artificial intelligence. Neuron, 95(2):245–258, 2017. ",
+        "bbox": [
+            171,
+            239,
+            821,
+            268
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Delving deep into rectifiers: Surpassing human-level performance on imagenet classification. In Proceedings of the IEEE international conference on computer vision, pp. 1026–1034, 2015. ",
+        "bbox": [
+            176,
+            276,
+            823,
+            320
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Donald O Hebb. The organization of behavior: A neurophysiological approach, 1949. ",
+        "bbox": [
+            174,
+            328,
+            736,
+            344
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Geoffrey E Hinton, James L McClelland, David E Rumelhart, et al. Distributed representations. Carnegie-Mellon University Pittsburgh, PA, 1984. ",
+        "bbox": [
+            173,
+            352,
+            821,
+            381
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Sepp Hochreiter and Jurgen Schmidhuber. Long short-term memory. ¨ Neural computation, 9(8): 1735–1780, 1997. ",
+        "bbox": [
+            173,
+            390,
+            823,
+            417
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "John J Hopfield. Neural networks and physical systems with emergent collective computational abilities. Proceedings of the national academy of sciences, 79(8):2554–2558, 1982. ",
+        "bbox": [
+            171,
+            426,
+            823,
+            457
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "John J Hopfield and David W Tank. Computing with neural circuits: A model. Science, 233(4764): 625–633, 1986. ",
+        "bbox": [
+            169,
+            464,
+            823,
+            493
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Forrest Iandola, Matt Moskewicz, Sergey Karayev, Ross Girshick, Trevor Darrell, and Kurt Keutzer. Densenet: Implementing efficient convnet descriptor pyramids. arXiv preprint arXiv:1404.1869, 2014. ",
+        "bbox": [
+            176,
+            501,
+            823,
+            545
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Michael I Jordan. Serial order: A parallel distributed processing approach. In Advances in psychology, volume 121, pp. 471–495. Elsevier, 1997. ",
+        "bbox": [
+            169,
+            553,
+            823,
+            583
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Barry L Kalman and Stan C Kwasny. Why tanh: choosing a sigmoidal function. In Neural Networks, 1992. IJCNN., International Joint Conference on, volume 4, pp. 578–581. IEEE, 1992. ",
+        "bbox": [
+            173,
+            590,
+            823,
+            621
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Yasuhiko Kawasaki, Tatsuro Kohno, Zhi-Ye Zhuang, Gary J Brenner, Haibin Wang, Catrien Van Der Meer, Katia Befort, Clifford J Woolf, and Ru-Rong Ji. Ionotropic and metabotropic receptors, protein kinase a, protein kinase c, and src contribute to c-fiber-induced erk activation and camp response element-binding protein phosphorylation in dorsal horn neurons, leading to central sensitization. Journal of Neuroscience, 24(38):8310–8321, 2004. ",
+        "bbox": [
+            173,
+            627,
+            825,
+            699
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Diederik P Kingma and Jimmy Ba. Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980, 2014. ",
+        "bbox": [
+            174,
+            707,
+            821,
+            736
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Alex Krizhevsky and Geoffrey Hinton. Learning multiple layers of features from tiny images. Technical report, Citeseer, 2009. ",
+        "bbox": [
+            173,
+            744,
+            820,
+            773
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Hugo Larochelle and Geoffrey E Hinton. Learning to combine foveal glimpses with a third-order boltzmann machine. In Advances in neural information processing systems, pp. 1243–1251, 2010. ",
+        "bbox": [
+            173,
+            781,
+            821,
+            813
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Yann LeCun, Leon Bottou, Yoshua Bengio, and Patrick Haffner. Gradient-based learning applied to ´ document recognition. Proceedings of the IEEE, 86(11):2278–2324, 1998. ",
+        "bbox": [
+            174,
+            819,
+            823,
+            849
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Adam H Marblestone, Greg Wayne, and Konrad P Kording. Toward an integration of deep learning and neuroscience. Frontiers in computational neuroscience, 10:94, 2016. ",
+        "bbox": [
+            174,
+            857,
+            823,
+            887
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Mitchell P Marcus, Mary Ann Marcinkiewicz, and Beatrice Santorini. Building a large annotated corpus of english: The penn treebank. Computational linguistics, 19(2):313–330, 1993. ",
+        "bbox": [
+            174,
+            895,
+            821,
+            924
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Eve Marder, LF Abbott, Gina G Turrigiano, Zheng Liu, and Jorge Golowasch. Memory from the dynamics of intrinsic membrane currents. Proceedings of the national academy of sciences, 93 (24):13481–13486, 1996. ",
+        "bbox": [
+            174,
+            103,
+            823,
+            146
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Warren S McCulloch and Walter Pitts. A logical calculus of the ideas immanent in nervous activity. The bulletin of mathematical biophysics, 5(4):115–133, 1943. ",
+        "bbox": [
+            171,
+            155,
+            823,
+            184
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Jarrod P Meadows, Mikael C Guzman-Karlsson, Scott Phillips, Jordan A Brown, Sarah K Strange, J David Sweatt, and John J Hablitz. Dynamic dna methylation regulates neuronal intrinsic membrane excitability. Sci. Signal., 9(442):ra83–ra83, 2016. ",
+        "bbox": [
+            174,
+            193,
+            821,
+            236
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Stephen Merity, Nitish Shirish Keskar, and Richard Socher. Regularizing and Optimizing LSTM Language Models. arXiv preprint arXiv:1708.02182, 2017. ",
+        "bbox": [
+            173,
+            243,
+            823,
+            273
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Stephen Merity, Nitish Shirish Keskar, and Richard Socher. An Analysis of Neural Language Modeling at Multiple Scales. arXiv preprint arXiv:1803.08240, 2018. ",
+        "bbox": [
+            173,
+            281,
+            821,
+            311
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Toma´s Mikolov, Martin Karafi ˇ at, Luk ´ a´s Burget, Jan ˇ Cernock ˇ y, and Sanjeev Khudanpur. Recurrent \\` neural network based language model. In Eleventh Annual Conference of the International Speech Communication Association, 2010. ",
+        "bbox": [
+            173,
+            319,
+            825,
+            364
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Paul Miller. Dynamical systems, attractors, and neural circuits. F1000Research, 5, 2016. ",
+        "bbox": [
+            169,
+            372,
+            758,
+            388
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Volodymyr Mnih, Nicolas Heess, Alex Graves, et al. Recurrent models of visual attention. In Advances in neural information processing systems, pp. 2204–2212, 2014. ",
+        "bbox": [
+            173,
+            396,
+            825,
+            426
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Vinod Nair and Geoffrey E Hinton. Rectified linear units improve restricted boltzmann machines. In Proceedings of the 27th international conference on machine learning (ICML-10), pp. 807–814, 2010. ",
+        "bbox": [
+            176,
+            434,
+            823,
+            477
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Alex Reyes, Rafael Lujan, Andrej Rozov, Nail Burnashev, Peter Somogyi, and Bert Sakmann. Target-cell-specific facilitation and depression in neocortical circuits. Nature neuroscience, 1 (4):279, 1998. ",
+        "bbox": [
+            174,
+            486,
+            823,
+            529
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Leonie Ringrose and Renato Paro. Epigenetic regulation of cellular memory by the polycomb and trithorax group proteins. Annu. Rev. Genet., 38:413–443, 2004. ",
+        "bbox": [
+            171,
+            537,
+            823,
+            566
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Robertson Sean. Names dataset. https://github.com/spro/practical-pytorch/ tree/master/data/names, 2016. ",
+        "bbox": [
+            169,
+            575,
+            823,
+            604
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "S Murray Sherman. Tonic and burst firing: dual modes of thalamocortical relay. Trends in neurosciences, 24(2):122–126, 2001. ",
+        "bbox": [
+            173,
+            613,
+            821,
+            642
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Richard Socher, Alex Perelygin, Jean Wu, Jason Chuang, Christopher D Manning, Andrew $\\mathrm { N g }$ , and Christopher Potts. Recursive deep models for semantic compositionality over a sentiment treebank. In Proceedings of the 2013 conference on empirical methods in natural language processing, pp. 1631–1642, 2013. ",
+        "bbox": [
+            173,
+            651,
+            825,
+            708
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Mirko Solazzi and Aurelio Uncini. Artificial neural networks with adaptive multidimensional spline activation functions. In Neural Networks, 2000. IJCNN 2000, Proceedings of the IEEE-INNSENNS International Joint Conference on, volume 3, pp. 471–476. IEEE, 2000. ",
+        "bbox": [
+            174,
+            715,
+            823,
+            760
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Klaus M Stiefel and Boris S Gutkin. Cholinergic neuromodulation controls prc type in cortical pyramidal neurons. In Phase response curves in neuroscience, pp. 279–305. Springer, 2012. ",
+        "bbox": [
+            169,
+            767,
+            825,
+            797
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "T Tateno, A Harsch, and HPC Robinson. Threshold firing frequency–current relationships of neurons in rat somatosensory cortex: type 1 and type 2 dynamics. Journal of neurophysiology, 92(4): 2283–2294, 2004. ",
+        "bbox": [
+            176,
+            805,
+            821,
+            848
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Jonathan Touboul, Geoffroy Hermann, and Olivier Faugeras. Noise-induced behaviors in neural mean field dynamics. SIAM Journal on Applied Dynamical Systems, 11(1):49–81, 2012. ",
+        "bbox": [
+            173,
+            857,
+            821,
+            886
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "A. M. Turing. I.computing machinery and intelligence. Mind, LIX(236):433460, 1950. doi: 10. 1093/mind/lix.236.433. ",
+        "bbox": [
+            173,
+            895,
+            821,
+            922
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Lawrence M Ward. Synchronous neural oscillations and cognitive processes. Trends in cognitive sciences, 7(12):553–559, 2003. ",
+        "bbox": [
+            171,
+            103,
+            823,
+            132
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Bob Weinhold. Epigenetics: the science of change. Environmental health perspectives, 114(3): A160, 2006. ",
+        "bbox": [
+            173,
+            141,
+            821,
+            170
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Stephan Zheng, Yang Song, Thomas Leung, and Ian Goodfellow. Improving the robustness of deep neural networks via stability training. In Proceedings of the ieee conference on computer vision and pattern recognition, pp. 4480–4488, 2016. ",
+        "bbox": [
+            176,
+            179,
+            823,
+            222
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "6 APPENDIX ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            102,
+            294,
+            118
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "6.1 SUPPLEMENTARY DATA METHODOLOGY ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            132,
+            496,
+            147
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Additionally we tested our modulator gate, with $\\tau _ { l } ( \\cdot )$ set to sigmoid, on a much more computationally demanding three-layered LSTM network with weight drop method named awd-lstm-lm (Merity et al., 2017; 2018). This model was equipped to handle the Penn-Treebank dataset (Marcus et al., 1993) and was trained to minimize word perplexity. The network was trained for 500 epochs, however, the sample size was limited due to extremely long training times. ",
+        "bbox": [
+            173,
+            159,
+            825,
+            229
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "table",
+        "img_path": "images/0307d0abc7cee02636f01554f2c98527364aa28c142d711ddf423caf5ff60124.jpg",
+        "table_caption": [
+            "Table 6: Network parameters per cell "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>Modulated</td><td>Control</td></tr><tr><td></td><td></td><td></td></tr><tr><td>awd-lstm-lm</td><td>6.61 M</td><td>5.29 M</td></tr></table>",
+        "bbox": [
+            364,
+            266,
+            635,
+            313
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "6.2 SUPPLEMENTARY DATA RESULTS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            340,
+            446,
+            356
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "On the Penn-Treebank dataset with the awd-lstm-lm implementation, sample size was restricted to 2 per condition, due to long training times and limited resources. However on the data collected, our model outperformed template perplexity, achieving an average of 58.4730 compared to the template average 58.7115. Due to the lack of a control for model parameters, interpretation of these results rests on the assumption that the author fine-tuned network parameters such that the template parameters maximized performance. ",
+        "bbox": [
+            173,
+            367,
+            826,
+            450
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "7 SUPPLEMENTARY DATA FIGURES & TABLES ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            470,
+            575,
+            488
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "7.1 AWD-LSTM-LM ON PENN-TREEBANK ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            501,
+            470,
+            516
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "table",
+        "img_path": "images/389144c3fe3a6e1bf0b61943655f8ce43175d59df5caed8ea535114737cda00f.jpg",
+        "table_caption": [
+            "Table 7: Comparison of mean test Perplexities lower $=$ better "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>Epochs</td><td>Modulated</td><td>Control</td><td>Statistical Analysis</td></tr><tr><td></td><td></td><td></td><td></td><td>T: 1.842</td></tr><tr><td rowspan=\"3\">awd-lstm-lm on Penn-Treebank</td><td>500</td><td>58.4730</td><td>58.7115</td><td>DOF: 1.9</td></tr><tr><td></td><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td><td>Hedges&#x27;s G:1.853</td></tr></table>",
+        "bbox": [
+            236,
+            560,
+            759,
+            635
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "image",
+        "img_path": "images/a3b3373fc615d43ca4c37975c1996f570d182eb7e80e00687a999c483d972ed1.jpg",
+        "image_caption": [
+            "Figure 7: Validation Perplexity progress (lowe $r = b _ { \\mathrm { { \\ell } } }$ etter) "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            267,
+            660,
+            720,
+            888
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "7.2 SUPPLEMENTAL LSTM DATA ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            103,
+            418,
+            117
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "Table 8: LSTM test performance histograms illustrating improved test-retest reliability ",
+        "bbox": [
+            212,
+            132,
+            782,
+            148
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "table",
+        "img_path": "images/7718a508cb86c539e1c108343e12d8e51376cde2befc3cba614656e33a840ab6.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>Simple- LSTM(Names categorization)</td><td rowspan=1 colspan=1> Advanced- LSTM(SST2)</td></tr><tr><td rowspan=1 colspan=1>Modulated</td><td rowspan=1 colspan=1>Prenbegg0.76 0.77 0.78 0.79Accuracy</td><td rowspan=3 colspan=1>14irenbeg120.60 0.650.700.750.80Accuracy14Pirenbeng1210 0.600.650.700.750.8Accuracy14 Prranbeg30.600.650.700.750.8Accuracy</td></tr><tr><td rowspan=1 colspan=1>Control 1</td><td rowspan=1 colspan=1>Pirenbee0.76 0.77 0.78 0.79Accuracy</td></tr><tr><td rowspan=1 colspan=1>Control 2</td><td rowspan=1 colspan=1>Pireneeng. 0.77 0.78 0.79Accuracy</td></tr><tr><td rowspan=1 colspan=1>Control 3</td><td rowspan=1 colspan=1>Prenbeng0.76 0.77 0.78 0.79Accuracy</td><td rowspan=1 colspan=1>14rrenbeng1210 0.600.650.700.750.80Accuracy</td></tr></table>",
+        "bbox": [
+            303,
+            164,
+            669,
+            549
+        ],
+        "page_idx": 13
+    }
+]